Showing posts with label Math. Show all posts
Showing posts with label Math. Show all posts

### How Many and How to Calculate Pints, Quarts, Gallons to and from Pounds.

#### Alternate Titles or Questions

•  How to Convert Pints to Quarts to Gallons to and from Pounds
• Volume to Weight Conversions or Weight to Volume Conversions – 8:4:1:8.
• How many pounds in X pints, quarts, or gallons?
• How much does X gallons, quarts, or pints weigh?
A list of most-searched-for questions and answers is included. Also a specific section relating to home water heaters size, volume, and weight.

 Volume to Weight Conversions. Weight to Volume Conversions.Simple math to convert or calculate pints, quarts, gallons, and pounds.

Be forewarned, this page is US-centric. As an example, in the UK a pint is 1.25 pounds. There are also issues of temperature and density, both of which are addressed further down the page. The purpose of this page is for practical, everyday business-of-living uses only. For that, it will serve you well.

## First – The Quick Answers to Volume Amounts and Ratios

### Volume Definitions

• 2 pints equals 1 quart.
• 4 quarts equals 1 gallon.
• 8 pints equals 1 gallon.

### Or to Put It Another Way...

• 1 quart equals 2 pints.
• 1 gallon equals 8 pints.
• 1 gallon equals 4 quarts

## Converting Volume to Weight

Converting volume to weight has everything to do with the density of the liquid. Fortunately, this question usually has to do with:
• How much does the gasoline in your gas tank or a gas can weigh?
• How much does a specific container of water or other mostly-water grocery items weigh?
• Questions relating to home water heater size, calculated water volume and the resulting weight.
The rule of thumb, and the expression to remember, is: "A pint's a pound the world around." The resulting estimates and extrapolations from this rule will serve you well for most everyday purposes.

### Basic Formulas

• A pint weighs a pound.
• There are two pints in a quart, so a quart weighs 2 pounds.
• There are four quarts in a gallon, so a gallon weighs 8 pounds.
• And the eight pints in a gallon, also weighing 8 pounds.
This pretty much answers the question. Here are some other typical examples...

#### Some Household Examples

• A 1-quart bottle of Gatorade weighs 2 pounds. Note: there are 2 pints in a quart and 4 quarts in a gallon. As a side note: there are 16 fluid ounces in a pint, 32 fluid ounces in a quart; 1 and 2 pounds respectively.
• A 2-liter bottle of Pepsi would convert to a weight of a little over 4 pounds. Note: A liter is slightly more than a quart.

#### Some gallon examples

• A 1-gallon container would convert to a weight of 8 pounds.
• A 5-gallon container weighs 40 pounds.
• A 10-gallon container weighs 80 pounds.
• A full, 25-gallon SUV gas tank means you are hauling around 200 pounds of fuel.
• A typical city water tower can hold anywhere from 300,00 to 600,000 gallons of water, which converts to a weight of 2,400,000 to 4,800,000 pounds of water sitting on those "stilts".

## The Density of the Liquid Significantly Affects the Rules Concerning Volume Conversion Calculations to Weight

A major component of converting fluid volume to a weight measurement is the density of the fluid. For gasoline, water, and most grocery items; the rule of a-pint's-a-pound will serve you just fine. However, as an example, the rule probably wouldn't work too well with any significant volume of engine oil. As an extreme example, the liquid metal/element mercury would totally throw the pint's-a-pound rule out the window. So of course would any molten metal or alloy.

In the interests of "full disclosure", fluid density is also affected by temperature. This is why many people fill their gas tank first thing in the morning. There is more gas per gallon at 50 degrees Fahrenheit than at 90 degrees Fahrenheit. It should be noted the percentage difference is in the low, single-digits.

## List of Frequent Volume-to-Weight Conversion Q&A

#### The Most-Searched-for Questions and Answers for How Many Pounds

• How much does 1.5 quarts weigh? Answer is 3 pounds.
• How much does 2 quarts weigh? Answer is 4 pounds.
• How much does 3 quarts weigh? Answer is 6 pounds.
• How much does 5 quarts weigh? Answer is 10 pounds.
• How much does 6 quarts weigh? Answer is 12 pounds.
• How much does 10 quarts weigh? Answer is 20 pounds.
• How much does 16 quarts weigh? Answer is 32 pounds.
• How much does 5 gallons weigh? Answer is 40 pounds.
• How much does 10 gallons weigh? Answer is 80 pounds.
• How much does 15 gallons weigh? Answer is 120 pounds.
• How much does 20 gallons weigh? Answer is 160 pounds.
• How much does 50 gallons weigh? Answer is 400 pounds.
• How much does 55 gallons weigh? Answer is 440 pounds.
• How many pints is a pound? Answer is 1.0 pint.
• How many quarts is a pound? Answer is 0.5 quarts.
• How many gallons is a pound? Answer is 0.125 gallons.

 The formulas for the volume of a sphere, the volume of a cube, the volume of a cylinder, the volume of a rectangular prism.

### More Water and Gasoline Volume-to-Weight Examples

Depending on what unit of measurement you use, volume will equal cubic English or cubic Metric; examples being cubic inches or cubic centimeters.

Side note: the tilde (~) is the mathematical symbol for approximate.

#### English

• 29 cubic inches equals ~1 pint, which equals ~1 pound.
• 58 cubic inches equals ~2 pints, which equals ~1 quart, which equals ~1/4 of a gallon, which equals ~2 pounds.
• 231 cubic inches equals ~4 quarts, which equals 1 gallon, which equals 8 pounds.

#### Metric

Most of the world uses Metric. There is a reason for that. As an example, 1000 cubic centimeters equals one liter, 1000 grams equals one kilogram, etc.; all nice, neat, and tidy. The United States and others are trying to get with the program; Metric is already included with English measurement on most U.S. consumer items. It's only a matter of time.

## How Much Does the Water Weigh in a Full Water Heater– Water Tank Size Volume Formula and Answers –

 Serendipitous energy.gov page on everything about water heaters, including how to buy one.

### How to Calculate the Weight of the Water in a Home Water Heater

How much does the total amount of water in a water heater weigh, volume to weight conversion.

From the above NASA chart we see the volume formula for a cylinder is V = (πd2h)/4.

Water tank heaters come in all sizes. For the purposes of this example, we will say the water tank heater has a measured height of approximately 54 inches; what with this, that, and the other, the water part is probably around 48". The diameter measured as 18"; what with insulation, etc., 16 probably works.

So,
d = 16
h = 48

Thus,
V = (3.14 * 16 * 16 * 48) divided by 4.

Since all numbers are inches, the answer will be in cubic inches. We reduce the formula as follows:
V = (3.14 * 256 * 48) divided by 4.
V = (3.14 * 12288)/4
V = 38514/4
V = 9646 cubic inches

231 cubic inches is equal to a gallon, so we divide 9646 by 231.
9646/231 = 41.76 gallons.

What with the inner measurements being estimates, looks like it is a 40 gallon water heater.
A gallon weighs 8 pounds.
So multiplying 40 times 8 gives 320.
A 40-gallon water heater contains 320 pounds of cold water.

Knowing the volume and weight of a 40-gallon water tank heater makes it easy to extrapolate the volume and weight of other water heaters.
• 10 gallon water heater is 2310 cubic inches and the water weighs 80 pound.
• 20 gallon water heater is 4620 cubic inches and the water weighs 160 pounds.
• 30 gallon water heater is 6930 cubic inches and the water weighs 240 pounds.
• 40 gallon water heater is 9240 cubic inches and the water weighs 320 pounds.
• 50 gallon water heater is 11550 cubic inches and the water weighs 400 pounds.
• 80 gallon water heater is 18480 cubic inches and the water weighs 640 pounds.
• 100 gallon water heater is 23100 cubic inches and the water weighs 800 pounds.
Do keep in mind the temperature versus density considerations and the expansion of water when heated, i.e., a fully hot water heater tank weighs slightly less than a cold or warm water tank heater that's been freshly refilled after water usage. The difference between hot and cold water density versus volume is significant enough that most water heaters have temperature/pressure relief valves and a drainage tube or pipe to compensate for this.

### Converting Cubic Inches to Cubic Feet...

...and the corresponding volume and weight ratios. Surprising how much just one cubic foot of water weighs.

#### One cubic foot of water weighs ~60 pounds (59.844 pounds at room temperature).

A cubic foot is 12 inches times 12 inches times 12 inches. So 1728 cubic inches equals 1 cubic foot. To convert cubic inches to cubic feet, simply divide the cubic inches by 1728. So using the above examples, we would have
• 2310 cubic inches equals 1.34 cubic feet equaling 10 gallons equaling 80 lb.
• 4620 cubic inches equals 2.68 cubic feet equaling 20 gallons equaling 160 lb.
• 6930 cubic inches equals 4.02 cubic feet equaling 30 gallons equaling 240 lb.
• 9240 cubic inches equals 5.36 cubic feet equaling 40 gallons equaling 320 lb.
• 11550 cubic inches equals 6.70 cubic feet equaling 50 gallons equaling 400 lb.
• 18480 cubic inches equals 10.72 cubic feet equaling 80 gallons equaling 640 lb.
• 23100 cubic inches equals 13.40 cubic feet equaling 100 gallons equaling 800 lb.
*I happened to stumble across this on Wikipedia: "Pound (mass), a unit of mass often abbreviated incorrectly as 'lbs' in plural. Abbreviations of units of measure do not use an 's' on the end for plural."

A side note. For anyone interested in doing their own quick calculations here or for anything and anywhere else and not wanting to bother with calling up a spreadsheet, etc., here's a handy Google Calculator. Opens in a separate tab or window. After arriving and before entering numbers, you will need to click its rectangular number-entry box first to get its attention.

May all your calculations be prosperous ones.

### How to Stop Being Overcharged on Sales Tax

Have you been overcharged on sales tax? Here is a way on how to mentally calculate sales taxes on the spot and stop being cheated, catch errors, and prevent fraud attempts.

## Business or Store Overcharging on Sales Tax?

When it comes to sales taxes, fraud is not that rare of an occurrence. Many times, smaller stores do deliberately overcharge sales tax. In fact, I’ve seen news stories that even the larger, national chain stores have been caught overcharging sales taxes. And employees in all stores have also been known to make price and thus sales tax mistakes as well.

Mentally calculating sales tax to prevent being overcharged is easy. It all has to do with rounding, no degree in rocket surgery required. You are simply doing a quick approximation to prevent yourself from being a victim of sales tax fraud or simply to prevent being mistakenly overcharged.

[Be forewarned, this page is US-centric. Canada and most European countries have sales or a value added tax (VAT) far exceeding 10%. However, if the VAT tax is close to another round number, one can still make this method work.]

• Most sales taxes never exceed 10 percent, but most sales taxes are reasonably close to 10 percent.
• Most thieves are greedy and will thus exceed the 10 percent amount.
• Even my dog can mentally calculate 10% of something.
• Even my dog can mentally add 10% of something to something.

You do not need any of these...

## How to Mentally Calculate Sales Tax – Some Examples

The best way for this tutorial to demonstrate mentally calculating sales taxes is by giving lots of examples. In reality, you already know how to do this. You just don't know you know yet. So let's begin. You walk up to the counter and engage in a purchase which sells for...

\$49.99
1. You round the price to \$50.
2. You calculate the 10% as \$5.
3. You add the \$50 plus \$5 to get \$55.
4. If the counter person wants more than \$55, welcome to the world of sales tax fraud and overcharges.

#### Other Examples...

\$29.99
1. You round it to \$30.
2. 10% is \$3.
3. Total is \$33.
4. If the final price is over \$33, welcome to the world of sales tax fraud and overcharges.
\$5.99
1. Round to \$6.
2. 10% is \$.60.
3. Total is \$6.60.
4. Anything over \$6.60, welcome to the world of sales tax fraud and overcharges.
\$79.98
1. \$80.
2. \$8.
3. \$88.
4. Over \$88, cheated.
It should be noted that honest mistakes do happen. You will find out soon enough if the overcharge was deliberate or accidental.

## What to Do When the Person at the Counter is Overcharging You on the Sales Tax

This depends on your mood, time constraints, the amount of money involved, the store and neighborhood, etc. Below are some typical scenarios and what one can do in each situation; followed by what you can also do after the fact.

#### You Don't Care About the Amount Involved

1. Say nothing.
2. Pay it.
3. Say nothing. Or say the routine "Thanks."
4. [Optional] Locate and take one of the business cards offered on the counter.
5. Leave.
6. Once outside, note the date and time.
7. Never go back.
8. Maybe tell everyone you know.

#### You Do Care About the Amount Involved (Option One)

1. Don't pay it.
2. Say nothing.
3. [Optional] Locate and take one of the business cards offered on the counter.
4. Leave. Be advised, however, the counterperson (probably the owner) will immediately know that you know he was trying to cheat you. And you took one of his cards... And sales tax fraud is a very serious offense...
5. Once outside, note the date and time.
6. Never go back.
7. Maybe tell everyone you know.

#### You Do Care About the Amount Involved (Option Two)

• Politely point out the total is incorrect and explain why you think so.

• If the counterperson reviews and corrects the error...
1. Pay it.
2. Call it a day.
3. Maybe or maybe not give the place another chance in the future.

• If the counterperson denies, disputes, or otherwise argues with your statement...
1. [Optional] Locate and take one of the business cards offered on the counter.
2. Leave.
3. Once outside, note the date and time.
4. Never go back.
5. Tell everyone you know.

## How to Report Stores and Other Businesses Who Overcharge Sales Taxes

Not only are you doing a good deed for society, you might even make some money in the process.
1. Find your state's website dealing with all things sales tax.
2. Find where to report what you experienced. As an example, in California the California State Board of Equalization would be where to go. California does not pay a reward the last time I checked. However, reporting the fraud is still a good idea; wouldn't you like the thief (employee or owner) removed, so you can have an honest, local place to shop? Reports can be made anonymously and will still be investigated.
3. For other states, determine if you might get a reward. Tell them your experience in detail, including date and time. Give them all the information on the business card. If you don't have the store's business card, that is ok; just be sure the store name and address you are reporting is correct. And don't worry; they're not going to just take your word for it. They will probably send the equivalent of a few "mystery shoppers" to the store to confirm. When they have absolutely verified and proven it is not an isolated incident; only then will the hammer fall on the deserving thief.
More than likely the store location is leased. With any luck, the thieving employee or owner will soon be gone; hopefully replaced with a new, honest employee or business.

### How to Really Calculate Miles per Gallon and Cost per Mile Using Formula Template

For folks who want accurate miles-per-gallon and cost-per-mile answers.

For quick, easy answers; simply use the MPG and CPM formula templates and you're done.

 Not pretty.

This page will serve you well if your gas gauge is broken, inaccurate, or is otherwise giving you problems. Or if you just want to know how well your car is doing. Can also be used for possibly figuring out ways to improve your mileage.

Needless to say, one needs to know the miles driven, how much gas was used, and the price of the gas before the templates will be of any use to you. If you do not already have these numbers, Section I below has everything you need to know on how to get started.

" Ω " Handy Google calculator. Opens in a separate tab or window.
• Both " / " and " ÷ " means divide.
• After arriving at the calculator and before entering numbers, you will need to click its numbers box first to get its attention.

### Distance Traveled Precalculation

______________________  -   ______________________  =  ______________________
(When you refill the tank)        (From previous fill-up of tank)

As previously mentioned, if you are just looking for approximate answers, then you can simply use the templates and call it a day. If you are looking for the most accurate results possible, see Section I.

## How to Calculate Miles per Gallon Formula Template

___________________  /  ___________________  =  ___________________
Miles Driven                        Gallons of Gas Used                Miles per Gallon

#### Example

1. You drove 100 miles and used 5 gallons of gas.
3. 100 miles traveled, divided by 5 gallons of gas used, gives you 20 miles per gallon.
4. 100/5 = 20 mpg.

## How to Calculate Gas Cost per Mile Formula Template

___________________  /  ___________________  =  ___________________
Price per Gallon                  Miles per Gallon                          Cost per Mile

#### Example

1. You paid \$5 for a gallon of gas, and you get 10 miles-per-gallon (mpg).
3. \$5 paid, divided by 10 miles traveled per gallon (mpg), gives you \$.50 cost per mile.
4. 5/10 = \$.50 cost-per-mile

#### So what does the miles-per-gallon answer actually tell you? It tells you that...

• This particular vehicle,
• being mechanically maintained at a given level of efficiency,
• using a specific brand and grade of gasoline,
• being filled at a particular time of day,
• from a particular gas station and a particular pump at a particular  fill speed,
• and being driven a certain commute route,
• by a specific driver...
...gets so many miles per gallon.

#### If the numbers used to make the calculation were accurate, this can lead to some interesting experimentation. What if...

• A different gas station or pump was used? Not all stations and pumps are the same.
• A different pump fill speed was used?
• The tank was filled at a different time of day? Temperature affects fluid density, first thing in the morning is best; that is when the gas is coldest and most dense.
• A different brand and/or grade of gasoline was used? See Section II.
• A different commute route was tried?
• Deficiencies were found as to the vehicle's maintenance?
• The vehicle's ignition timing was experimented with (but staying within smog emission specifications)? See Section II.
• The driver notices and alters a particular driving habit?
Probably other ideas might also come to mind over time.

## Section I - Using a Reasonably Scientific Method and Mistakes to Avoid

If you are looking to get the most accurate results possible, this procedure will help you do that. If you are just looking for an approximation, then you can skip it all and fill in the templates with your existing numbers.
1. Pick a week, or other time period, when you will be doing your most typical driving pattern.
2. Have two pens and paper in the car.
3. Use the gas station you normally use. Fill the gas tank at your usual time. Note the pump number you are using. Note the pump speed you normally use. Do not top off. While waiting, write down your odometer reading, include tenths. If you have a trip-odometer, reset it to zero. Remember to not be distracted by all this to the point you forget to put back the gas cap.
4. Commence with your week; the usual work commute, errands, etc. Combining your work commute with errands will increase your gas mileage, but only do so if it is what you intend to usually do. Continue your routine until you have less than a quarter-tank. Don't strive for a gas-gauge reading of empty unless it is what you normally do.
5. Make sure you still have the pens and paper in your car.
7. Attempt to use the same pump number you used before. Set to the same pump speed as before. While waiting: write down your odometer reading; write down your trip-odometer reading; include tenths from both. When the pump-handle clicks: write down how many gallons; and very definitely include tenths. Write down the price you paid per gallon. Save the receipt; if the gas station is at least half-coordinated, some or all of this information will be printed there for you. Does it match what's showing on the pump? Do not top off. If so inclined, reset trip-odometer to zero. And the gas cap thing again...
8. Proceed with your normal routine. You'll do the calculations with the templates at your leisure.

## Section II - List of Notes About Fuel Economy, Improving Gas Mileage and Saving Money

Tune-ups and tire pressure: These are the Big Two as to getting the best mileage. A couple notes...  Over-inflating tires increases gas mileage, but causes an immediate and significant increase in tire wear; so don't do that. Under-inflated tires reduce your mileage; and it doesn't do your sidewalls any good either. As for tune ups, spark plugs are especially important. A fouled or carbon-built-up plug reduces mileage drastically, not to mention it will probably cause you to flunk a smog check. A personal note: Two different mechanics quoted me a price of over \$100 to change a set of 6 spark plugs, plus the inflated cost of the plugs. In both cases, I departed the premises immediately. I ended up changing the plugs myself, it's not that hard to learn to do. Buy yourself a Chilton or Haynes manual for your particular make and model of car, they have all sorts of useful information. Some auto parts stores even have tool-loaner programs if you don't want to buy your own.

Looking ahead and coasting up to stop lights: Is a close third.

Speed: Once you are above 40 mph or so; the faster you go, the lower your mileage.

Weight: If you are carrying excess, unnecessary weight in the trunk, it will:
• Reduce mileage
• Increase engine wear and tear
• Wear out your brakes faster
Ethanol: Do you have ethanol-times-of-year versus non-ethanol-times-of-year? It can be interesting to make mileage comparisons between the two. You probably won't be happy with the ethanol results.

Gasoline Grade: Putting premium in a car that takes regular will do absolutely nothing for your mileage. However, if your car is in the midgrade octane category and what with there being some octane rating overlap, it might be worth experimenting with trying both the lower and higher octanes; especially if you are also experimenting with the ignition timing.

Temperature and humidity: Mileage is better during cooler times of the year than during heatwaves. And the higher the humidity, the better the mileage. Yep, one does get better mileage on rainy days.

Air filter: When is the last time you replaced the air filter? A clogged air filter does reduce mileage.

Fuel density and time of day: As mentioned earlier, always fill your tank first thing in the morning. Fluid density is affected by temperature. The colder it is, the more gas you get per gallon.

Logbook: If so inclined, this is as good a time as any to start one, especially if you want to try any of the aforementioned experiments..

## A Couple of Relevant Federal Websites

I thought I'd include a couple of useful federal websites for your future reference. Both are worth browsing the next time you have some time to kill.

If only urban freeway traffic looked like this...
From www.epa.gov/air-pollution-transportation. Has all sorts of links regarding vehicles and fuel efficiency and saving gas in general.

From www.fueleconomy.gov/trip. This goes directly to their trip calculator page. What makes this calculator unique is you can specify the make and model of car you are using or are curious about. In addition to the total fuel cost calculation, they throw in a map and text directions as well. The rest of the site is also worth browsing.

## Includes Complete Lessons and Examples.

(The templates alone might immediately provide the solution.)

It is guessed you are here to figure out a math answer to a particular electrical or electronics problem.

This is the place to figure out watts, amps, volts, or ohms from any of the other two by using Ohm's law and its derivatives. The math is surprisingly simple. You should have your answer in no time. Don't forget the templates and table of contents.

In most circumstances, the only math required is multiplication and division. Ohm's law and its derivatives uses some basic letters to represent watts, amps, volts, and ohms.
• "P" is the industry standard to designate power by the unit of measurement, watts. "W" is sometimes used.
• "I" is the industry standard to designate current by the unit of measurement, amps.
• "E" and "V" are both used to designate electromotive-force by the unit of measurement, volts. The industry formula standard used to be "E", but now both "E" and "V" are being used interchangeably.
• "R" is the industry standard to designate resistance by the unit of measurement, ohms.
And that's all there is to it. No degree in rocket surgery required. No need to memorize, they are succinctly reprinted as needed.

If your inquiry concerns a particular appliance, device, etc.; check to see if there is any sort of specifications label, metal plate, or even just a sticker. Even if it doesn't provide the outright answer, it will hopefully have enough other information to enable you to calculate the answer from the templates.  If you happen to have the manual (maybe it is still online?), then you may become lucky indeed. As an example, if it tells you it consumes 200 watts and you know your house voltage is 120 volts, then you can easily calculate how many amps it uses and/or what its internal resistance in ohms will be.

" Ω " This handy, multi-purpose symbol (scattered here, there, everywhere for mobile users) opens the Google calculator in a separate tab or window.
• Both " * " and " x " means multiply.
• Both " / " and " ÷ " means divide.
• "( )" means do whatever is inside the parenthesis first.
• After arriving and before entering numbers, you will need to click its rectangular number-entry box first to get its attention.

## Comprehensive List of Ohm's Law Formulas and Examples

Here is a list of formulas and templates. With any luck, you will find one you can use and won't have to bother clicking the related title for the included lesson and examples.

### Calculate how many WATTS from volts, amps, ohms.

P = EI          _______________  *  _______________  =  _______________
Volts                           Amps                           Watts

P = E2/R      _______________  /  _______________  =  _______________
Volts Squared                   Ohms                           Watts

P = I2R        _______________  *  _______________  =  _______________
Amps Squared                  Ohms                           Watts

### Calculate how many AMPS from watts, volts, ohms.

I = P/E        _______________  _______________  =  _______________
Watts                         Volts                            Amps

I = E/R        _______________  /  _______________  =  _______________
Volts                         Ohms                            Amps

I = √(P/R)   Sq Rt  (  _______________  /  _______________  )   =   _______________
Watts                          Ohms                                   Amps

### Calculate how many VOLTS from amps, watts, ohms.

E = P/I        _______________  /  _______________  =  _______________
Watts                         Amps                            Volts

E = IR        _______________  *  _______________  =  _______________
Amps                         Ohms                            Volts

E = √(PR)   Sq Rt  (  _______________  *  _______________  )   =   _______________
Watts                          Ohms                                   Volts

### Calculate how many OHMS from volts, amps, watts.

R = E/I      _______________  /  _______________  =  _______________
Volts                           Amps                           Ohms

R = E2/P    _______________  /  _______________  =  _______________
Volts Squared                   Watts                          Ohms

R = P/I2     _______________  /  _______________  =  _______________
Watts                    Amps Squared                  Ohms

### Lessons

There are four, independent, separate tutorials on this page. Simply select the one in the table of contents specifically addressing that which you you wish to find. Each how-to segment includes examples. Thanks to the laws of physics; whether it be trying to calculate how many amps, watts, ohms, or volts; Ohm's law will always provide three different, possible ways for finding the answer.

Hopefully, between the specifications plate, manual(s), and the above math; you will be able to find the answer to your question. Otherwise...

### What Is a VOM ( Electronics Definition ) And Some General Notes...

VOM is the acronym for Volt Ohm Milliammeter, More specifically, it is known as a multimeter or a multitester. The usual VOM can measure AC and DC voltage, current in milliamps, and resistance in ohms and megohms. For the purposes of this page, it is usually needed to find the resistance. Once the number of ohms are known, more of the templates and formulas can be used when the usual volt/amp/watt amounts aren't available.

When it comes to test instruments, skip the cheap ones. What a test instrument tells you will in turn cause you to make important decisions. As such, a quality test instrument is much more important than the usual RadioShack novelty toy, piece of wiring, batteries, etc. And whatever you do, do not buy a kit to make your own test instrument. Buying and building kits for other things is fine, but leave the VOM manufacturing to the professionals with the quality reputations (this is the voice of personal experience talking).

Do not buy a VOM until you truly know what you are doing. Cheaper meters are extremely inaccurate when it comes to measuring certain ranges of resistance, etc. Even voltage and milliampere measurements can be suspect. Really research the subject first.

.

## How Many WATTS - How to Calculate or Convert Watts to and from Any Two of Either Volts, Amps, or Ohms.

(P=watts, E=volts, I=amps, R=ohms)

Includes amps to watts and volts to watts.

Watts is the composite measurement of electromotive force and current, otherwise known as voltage and amperage. It is how we quantify electrical energy amounts and usage.

Three ways to figure out the electrical energy amount, measured in watts...

### #1. P = EI — Watts Are Equal to Volts Times Amps

Ω (P=watts, E=volts, I=amps, R=ohms)

#### Ω  Some examples...

• Tungsten filament light bulb. 120 volts times .8333 amps equals 100 watts. 120 * .8333 = 100
• Microwave oven. 120 volts times 5.8333 amps equals 700 watts. 120 * 5.8333 = 700
• Microwave oven. 120 volts times 9.1666 amps equals 1100 watts. 120 * 9.1666 = 1100
• Some air conditioners. 240 volts times 4 amps equals 960 watts. 240 * 4 = 960
• Car battery. 12 volts times 3 amps equals 36 watts. 12 * 3 = 36
• Car voltage when engine is running. 14.5 volts times 3 amps equals 43.5 watts. 14.5 * 3 = 43.5
• Car battery. 12 volts times 15 amps equals 180 watts. 12 * 15 = 180
• Car voltage when engine is running. 14.5 volts times 15 amps equals 217.5 watts. 14.5 * 15 = 217.5
• Most laptop batteries. 19 volts times 3.5 amps equals 66.5 watts. 19 * 3.5 = 66.5
Side note: the prefix, "milli", means one one-thousandth.
• There are 1000 milliwatts in a watt.
• There are a 1000 millivolts in a volt.
• There are a 1000 milliamps in an amp.

#### Ω More examples...

• A toy using a 9-volt battery consumes 250 milliamps (.25 amps). Multiplying 9 volts by 250 milliamps calculates out to 2.25 watts. 9 * .25  = 2.25
• A 350-millivolt subcircuit uses 455 milliamps (.455 amps). Multiplying 350 millivolts by 455 milliamps indicates that part of the circuit is using 159 milliwatts (rounded) of energy. 350 * 455 = 159.25
• A 4.5 volt LED array uses 75 milliamps. Multiplying 4.5 volts by .075 shows the LED array consumes  337.5 milliwatts. 4.5 * .075 = 337.5

### #2. P = E²/R — Watts Are Equal to Volts Squared Divided by Ohms

Ω (P=watts, E=volts, I=amps, R=ohms)

#### Ω Some examples...

• 110 volts squared, then divided by 65 ohms equals 186.15 watts. 110²/65 = 12100/65 = 186.15
• 120 volts squared, then divided by 125 ohms equals  115.2 watts. 120²/125 = 14400/125 = 115.2
• 70 volts squared, then divided by 42 ohms equals 116.67 watts.70²/42 = 4900/42 =116.67
• 12 volts squared, then divided by 24 ohms equals 6 watts. 12²/24 = 144/24 = 6
• 12 volts squared, then divided by 100 ohms equals 1.44 watts. 12²/100 = 144/100 = 1.44
• 6 volts squared, then divided by 100 ohms equals 360 milliwatts. 6²/100 = 36/100 = .36
• A motor  requires 40 volts and has an internal resistance of 25 ohms. 40 volts squared, then divided by 25 ohms has a total energy usage of 64 watts. 40²/25 = 1600/25 = 64
• There are 7.5 volts running through a component with 5 ohms resistance. Its wattage would be a total of 11.25 watts. 7.5²/5 = 56.25/5 = 11.25

### #3. P = I²R — Watts Are Equal to Amps Squared Times Ohms

Ω (P=watts, E=volts, I=amps, R=ohms) stopping point

#### Ω Some examples...

• 1 amps squared, multiplied by 30 ohms equals 30 watts. 1² * 30 = 1 * 30 = 30
• 5 amps squared, multiplied by 30 ohms equals  750 watts. 5² * 30 = 25 * 30 = 750
• 14 amps squared, multiplied by 2 ohms equals 392 watts.14² * 2 = 196 * 2 =392
• 100 milliamps squared, multiplied by 30 ohms equals 30 milliwatts. .100² * 30 = .01 * 30 = .03
• 334 milliamps squared, multiplied by 15 ohms equals 1.6725 watts. .334² * 15 = .1115 * 15 = 1.6725
• 750 milliamps squared, multiplied by 5 ohms equals 2.8125 watts. .750² * 5 = .5625 * 5 = 2.8125

.

## How Many AMPS - How to Calculate or Convert Amps to and from Any Two of Either Watts, Volts, or Ohms.

(I=amps, E=volts, P=watts, R=ohms)

Includes volts to amps and watts to amps..

It's current and amperage that makes those power meters spin and flips those fuse box switches and circuit breakers on occasion. The 1500-watt space heater is a good example. Microwave ovens can be a close second. An unexpected short circuit in an appliance or house wiring is what causes buildings to burn down if the circuit breaker doesn't do its job.

Three ways to figure out current in amps...

### #1. I = P/E — Amps Are Equal to Watts Divided by Volts

Ω (I=amps, E=volts, P=watts, R=ohms)

#### Ω  Some examples...

• The aforementioned space heater. 1500 watts divided by 120 volts equals 12.5 amps current. 1500/120 = 12.5
• The aforementioned microwave oven. 1100 watts divided by 120 volts equals 9.17 amps current. 1100/120 = 9.17
Turning both of those on at once will flip a 15-amp circuit breaker right there. A 20-amp circuit breaker wouldn't be too thrilled with it either.

#### Ω More examples...

• 2 watts divided by 6 volts equals .33333 amps current. 2/6 = .34
• 5 watts divided by 12 volts equals .416666 amps current. 5/12 = .417
Side note: the prefix, "milli", means one one-thousandth.
• There are a 1000 millivolts in a volt.
• There are a 1000 milliamps in an amp.
• There are 1000 milliwatts in a watt.

#### Ω More examples...

• A 140-watt computer circuit board uses 360 volts from a step up transformer. This is not a circuit board you want to mess with. Dividing 140 watts by 360 volts shows a current of  389 milliamps running through it. 140/360  = .389 amps (or 389 milliamps)
• A 300-milliwatt circuit board is connected to a 3-volt power supply. Dividing 300 milliwatts by 3 volts  indicates the circuit board requires a current of 100 milliamps (.1 amps). .3/3 = .1
• A 20-watt device uses standard 120-volt house current. Dividing 20 watts by 120 volts reveals the device is using .1666 amps or 167 milliamps. 20/120 = .167

### #2. I = E/R — Amps Are Equal to Volts Divided by Ohms

Ω (I=amps, E=volts, P=watts, R=ohms)

#### Ω Some examples...

• 240 volts divided by 500 ohms calculates to a current of 480 milliamps. 240/500 = .480
• 110 volts  divided by 2000 ohms calculates to a current of 55 milliamps. 110/2000 = .055
• 12 volts  divided by 250 ohms calculates to a current of 48 milliamps. 12/250 = .048
• A tiny, hobby motor needs 3 volts to operate and has an internal resistance of 40 ohms. 3 volts divided by 40 ohms indicates a usage of 75 milliamps. 3/40 = .075
• There are 9 volts running through a controller with an internal resistance of 135 ohms. 9 divided by 135 equals a current usage of 67 milliamps. 9/135 = .066666

### #3. I = √(P/R) — Amps Are Equal to the Square Root of the Quotient of  Watts Divided by Ohms

Ω (I=amps, E=volts, P=watts, R=ohms)

Contrary to the general introduction, this third and last resort does involve the use of square roots; so break out the calculator, spreadsheet, or search engine if you haven't done so already.

Basically, all one does is divide watts by ohms; then just find the square root of the quotient to determine the amperage.

"" is the symbol for square root.

#### ΩSome examples...

• 100 watts divided by 4 ohms gives us a quotient of 25. The square root of 25 is 5 amps.  √(100/4) = √25 = 5
• 900 watts divided by 5 ohms gives us a quotient of 180. The square root of 180 is 13.42  amps (rounded).  √(900/5) = √180 =13.4164
• 40 watts divided by 40 ohms gives us a quotient of 1. The square root of 1 is 1 amp.  √(40/40) = √1 =1
• 5 watts divided by 100 ohms gives us a quotient of .05. The square root of .05 results in an answer of 224 milliamps (rounded).  √(5/100) = √(.05) =.2236  Square roots of numbers less than 1.0 are odd that way.

.

## How Many VOLTS - How to Calculate or Convert Volts to and from Any Two of Either Watts, Amps, or Ohms.

(E=volts, P=watts, I=amps, R=ohms)

Includes amps to volts and watts to volts.

Unlike with most watts and amps questions, voltage and voltage-drop questions usually have to do with circuit boards and their sub components. However, here are also some basics...
• Typical US house voltage is 120 volts; though for certain appliances, voltage is boosted to 240 volts.
• The car battery standard is 12 volts.
• The laptop standard is most often 19 volts.
• Standard carbon or alkaline batteries (whether sizes D, C, aa, aaa, etc.) are all 1.5 volts each. Putting them in series is simply additive. As an example, if you see a 6-volt flashlight being advertised, you know it will require four batteries.

Three ways to figure out volts...

### #1. E = P/I — Volts Are Equal to Watts Divided by Amps

Ω (E=volts, P=watts, I=amps, R=ohms)

#### Ω  Some examples...

• 500 watts divided by 5 amps equals 100 volts. 500/5 = 100
• 12 watts divided by .1 amps equals 120 volts. 12/.1 = 120
• 150 watts divided by 2 amps equals 75 volts. 150/2 = 75
• A 6-watt car instrument cluster has half an amp running through it. Is the car engine running or not? Dividing the 6 watts by .5 amps gives us 12 volts. The engine is off (when the engine is running the system voltage ranges from 14 to 14.5 volts). 6/.5 = 12
• A 600-watt starter for a small engine requires 50 amps. Dividing 600 watts by 50 amps indicates that a 12-volt battery can indeed do the job. 600/50 = 12
Side note: the prefix, "milli", means one one-thousandth.
• There are a 1000 millivolts in a volt.
• There are a 1000 milliamps in an amp.
• There are 1000 milliwatts in a watt.

#### Ω More examples...

• A 400-milliwatt (.4 watts) circuit board uses 80 milliamps (.080 amps). Dividing 400 milliwatts by 80  milliamps indicates it is connected to a 5-volt input. 400/80 = 5
• A 180-milliwatt component uses 45 milliamps. Dividing 180 milliwatts by 45 milliamps equals 4 volts. 180/45 = 4

### #2. E = IR — Volts Are Equal to Amps Multiplied by Ohms

Ω (E=volts, P=watts, I=amps, R=ohms)

#### Ω Some examples...

• 10 amps multiplied by 12 ohms equals 120 volts. 10 * 12 = 120
• 35 amps multiplied by 42 ohms equals 1470 volts. 35 * 42 = 1470
• .5 amps multiplied by 6 ohms equals 3 volts. .500 * 6 = 3
• An air conditioner  requires 50 amps. The motor, pump, and other circuitry has a total resistance of 4.8 ohms (surprisingly low actually). That A/C will require 240 volts to operate. 50 * 4.8 = 240
• There are 600 milliamps running through a circuit with a measured resistance of 5 ohms. So that would be 600 milliamps times 5 ohms, giving you 3 volts. .600 * 5 = 3

### #3. E = √(PR) — Volts Are Equal to the Square Root of the Product of Watts Times Ohms

Ω (E=volts, P=watts, I=amps, R=ohms)

Contrary to the general introduction, this third and last resort does involve the use of square roots; so break out the calculator, spreadsheet, or search engine if you haven't done so already.

Basically, all one does is multiply watts times ohms; then just find the square root of the product to determine the voltage.

"" is the symbol for square root.

#### Ω Some examples...

• 14 watts multiplied by 10.285 (rounded) ohms equals a product of 144. The square root of 144 is 12 volts. √(144 * 10.285) = √144 = 12
• 300 watts multiplied by 20 ohms equals a product of 6000. The square root of 6000 is 77.46 volts (rounded).  √(300 * 20) = √6000 = 77.46
• A 900-watt microwave oven magnetron has an internal resistance of 15 ohms. 900 watts times 15 ohms gives a product of 13,500. The square root of 13,500 is 116 volts (rounded).  √(900 * 15) = √13500 = 116.2. What with house voltages ranging from 110 to 120 volts, that will work just fine.
Side note: the prefix, "kilo", means one thousand.
• There are a 1000 volts in a kilovolt (kv).
• There are a 1000 amps in a kiloamp (KA).
• There are 1000 watts in a kilowatt. (kw).

#### Ω An example...

• 1,000 watts (1kw) multiplied by 10 ohms equals a product of 10,000. The square root of 10,000 is 100 volts.  √(1000 * 10) = √10000 = 100

.

## How Many OHMS - How to Calculate or Convert Ohms to and from Any Two of Either Watts, Volts, or Amps.

(R=ohms, E=volts, I=amps, P=watts)

Unlike with most watts and amps questions, resistance and ohms questions usually have to do with circuit boards and their sub components. However, the internal resistance of an appliance or device greatly affects how much power it uses. The classic example of this is the incandescent, tungsten filament light bulb. A single, 100-watt bulb requires almost a full amp of current at 120 volts. That can add up fairly quickly over time. Power meters love it, everyone else hates it.

Three ways to figure out resistance in ohms...

### #1. R = E/I — Ohms Are Equal to Volts Divided by Amps

Ω (R=ohms, E=volts, I=amps, P=watts)

#### Ω  Some examples...

• The aforementioned light bulb. 120 volts divided by .8333 amps equals 144 ohms resistance. 120/.8333 = 144
• 240 volts divided by 3 amps equals 80 ohms resistance. 240/3 = 80
• 12 volts divided by 1.50 amps equals 8 ohms resistance. 12/1.5 = 8
• 19 volts divided by 2.3 amps equals 8.26 ohms resistance. 19/2.3 = 8.26
Side note: the prefix, "milli", means one one-thousandth.
• There are a 1000 millivolts in a volt.
• There are a 1000 milliamps in an amp.
• There are 1000 milliwatts in a watt.

#### Ω More examples...

• A 9-volt circuit board uses 140 milliamps (.140 amps). Dividing 9 volts by 140 milliamps indicates the board has an internal resistance of 64.29 ohms (rounded). 9/.14 = 64.29
• A 500-millivolt component uses 120 milliamps. Dividing 500 millivolts by 120 milliamps indicates the component has a resistance of 4.17 (rounded) ohms. 500/120 = 4.17
• A 4.5 volt LED array uses 15 milliamps. Dividing 4.5 by .015 equates to a resistance of 300 ohms. 4.5/.015 = 300

### #2. R = E²/P — Ohms Are Equal to Volts Squared Divided by Watts

Ω (R=ohms, E=volts, I=amps, P=watts)

#### Ω Some examples...

• 120 volts squared, then divided by 100 watts equals a resistance of 144 ohms. 120²/100 = 14400/100 = 144
• 50 volts squared, then divided by 35 watts equals a resistance of 71.43 ohms.50²/35 = 2500/35 = 71.43
• 6 volts squared, then divided by 4 watts indicates a resistance of  9 ohms. 6²/4 = 36/4 = 9
• A motor  requires 36 volts and uses 40 watts of power. 36 volts squared, then divided by 40 watts has a total resistance of 32.4 ohms. 36²/40 = 1296/40 = 32.4
• There are 1.5 volts running through a component using 2 watts. Its resistance would be 1.125 ohms.1.5²/2 = 2.25/2 = 1.125

### #3. R = P/I² — Ohms Are Equal to Watts Divided by the Square of Amps

Ω (R=ohms, E=volts, I=amps, P=watts)

#### Ω Some examples...

• 150 watts divided by 7 amps squared. The 7 amps squared is 49, so we have 150 watts divided by 49; giving us an answer of 3.06 ohms. 150/7² = 150/49 = 3.06
• 40 watts divided by by 20 amps squared. The 20 amps squared is 400, so we have 40 watts divided by 400, giving us an answer of .1 ohms or 100 milliohms. 40/20² = 40/400 = .1 We are pretty much looking at a 2-volt short circuit on a board that needs fixing, probably a shorted out capacitor.
• A 500-watt refrigerator divided by 11 amps squared. 11 amps squared is 121, so we have 500 watts divided by 121, giving us an answer of 4.13 ohms (rounded).
• A 5-watt circuit sub-board consumes 300 milliamps. So the equation is 5/.3² to give us the resistance in ohms. .3² is .09,  so we have 5/.09 = 55.56 ohms (rounded) in calculated resistance.

## A Final Thought...

 Do be careful. The laws of physics are unforgiving.

### Base 2, 4, 8, 16 Number System Lessons for Binary, Quaternary, Octal, and Hexadecimal

 (HAL says hi.)

## Introduction and Start of Tutorial

These four base numbering system lessons use the exact, same teaching methodology. As such, when you have learned one, you will have learned them all. There is also some repetitiveness, so as to reduce needed reverse scrolling. Comparisons of different base number systems can also prove useful.

If you understand the everyday, base 10 decimal number system we all use; then you already understand the base 2, base 4, base 8, and base 16 numbering systems. You just don’t know that you know yet.

As you know, we use the decimal (base 10) numbering system in our day-to-day lives. Base 10 has ten numbers (0-9) and orders of magnitude that are times ten. The lowest-order number represents itself times one. The next-order number represents itself times ten. The next order number represents itself times 10 x 10 or itself times 100. The next order number represents itself times 10 x 10 x 10 or itself times 1000. And so on.

An example would be the number 7824. This number means there are:
• Four 1’s,
• two 10’s,
• eight 100’s,
• and seven 1000's.
Which represents 4 + 20 + 800 + 7000; for a total of 7824.

Tutorial continues below at the base numbering system lesson of your choice...

(A base-5-quinary tutorial is incidentally available on a separate, standalone page.)

.

## Base 2 – How to Do and Convert Base 2 to Base 10 – Binary Number System Conversions – Includes Examples

0's and 1's
 How to Do Binary, Base 2 Number System Conversions. Includes Examples.

Binary code is the basis of all digital technology; strings of 1’s and 0’s. The different combinations of 1’s and 0’s are how the technology tells itself what to do.

Here is everything you need to know on how to convert from binary code aka base 2 to decimal. And for converting from decimal aka base 10 to binary.

As previously stated: if you understand the decimal (base 10) number system you use every day, then you already understand the binary (base 2) numbering system.

And for folks who entered the search phrase: what is yes in binary? The answer is:
• 1 is yes or indicates true in binary.
• 0 is no or indicates false in binary.

### How to Do the Binary Base 2 Numbering System

Per the introduction, base 10 has ten numbers (0-9) and orders of magnitude that are times ten. The orders of magnitude are l, 10, 100 (10x10) , 1000 (10x10x10), etc.

An example would be the number 497. This number means that there are:
• Seven 1’s,
• nine 10’s,
• and four 100’s.
Which represents 7 +90 +400; for a total of 497.

The binary, base 2 numerical system (0's and 1's) uses the same structure, the only difference being the order of magnitude. Base 2 has two numbers (0-1) and orders of magnitude that are times two. The lowest-order number represents itself times one. The next order number represents itself times two. The next order number represents itself times 2x2 or itself times 4. The next order number represents itself times 2x2x2 or itself times 8. The next order number represents itself as 2x2x2x2 or itself times 16, And so on.

#### Orders of Magnitude in Base 2

1 · 2 · 4 · 8 · 16 · 32 · 64 · 128 · 256 · 512· 1024 · 2448 · 4096 · 8192

#### Positional

8192 · 4096 · 2048 · 1024 · 512 · 256 · 128 · 64 · 32 · 16 · 8 · 4 · 2 · 1

A basic, first example of a binary number would be the base 2 number 11111. This would mean there is:
• one 1,
• one 2,
• one 4,
• one 8,
• and one 16.
Which represents 1 + 2 + 4 + 8 + 16; for a total of 31 in Base 10 decimal.

Another base 2 example would be the binary number 101. This number means that there are:
• one 1’s,
• no 2’s,
• and one 4’s.
Which represents 1 + 0 + 4; for a total of 5 in decimal.

Another base 2 example would be the binary number 10110. This number means that there are:
• no 1’s,
• one 2’s,
• one 4’s,
• no 8’s,
• and one 16.
Which represents 0 + 2 + 4 + 0 + 16; for a total of 22 in decimal.

#### Orders of Magnitude in Base 2

1 · 2 · 4 · 8 · 16 · 32 · 64 · 128 · 256 · 512· 1024 · 2448 · 4096 · 8192

#### Positional

8192 · 4096 · 2048 · 1024 · 512 · 256 · 128 · 64 · 32 · 16 · 8 · 4 · 2 · 1

### More Binary (Base 2) to Decimal (Base 10) Conversion Examples

Column headings in the following table are simply a convenience relist of the relevant positional orders of magnitude as applies to each column. There is no significance attached as to where one column ends and the next one begins.

 ---------------------------------- ---------------------------------- ---------------------------------- 8 · 4 · 2 · 1 16 · 8 · 4 · 2 · 1 64 · 32 · 16 · 8 · 4 · 2 · 1 0=0 1101=13 11010=26 1=1 1110=14 11011=27 10=2 1111=15 11100=28 11=3 10000=16 11101=29 100=4 10001=17 11110=30 101=5 10010=18 11111=31 110=6 10011=19 100000=32 111=7 10100=20 100001=33 1000=8 10101=21 100010=34 1001=9 10110=22 100011=35 1010=10 10111=23 100100=36 1011=11 11000=24 100101=37 1100=12 11001=25 100110=38

.

## Base 4 – How to Do and Convert Base 4 to Base 10 – Quaternary Number System Conversions – Includes Examples

0 1 2 3
 How to Do Quaternary, Base 4 Number System Conversions. Includes Examples.

Base 4, also known as the quaternary number system, is predominantly used in DNA genotyping and some electronics applications, etc.

This lesson gives you everything you need to know for converting from quaternary aka base 4 to decimal and for converting from decimal aka base 10 to quaternary. If you understand the decimal number system,or the binary (base 2) numbering system for that matter, then you already understand the quaternary (base 4) number system.

Per the introduction, base 10 has ten numbers (0-9) and orders of magnitude that are times ten. The orders of magnitude are l, 10, 100 (10x10) , 1000 (10x10x10), etc.

An example would be the number 7112. This number means that there are:
• two 1’s,
• one 10’s,
• one 100’s
• and seven 1000’s.
Which represents 2 + 100 + 100 + 7000; for a total of 7112.

### How to Do the Quaternary Base 4 Numbering System

Base 4 uses the same base 10 structure, the only difference being the orders of magnitude. Base 4 has four numbers (0-3) and orders of magnitude that are times four . The lowest-order number represents itself times one. The next-order number represents itself times four. The next order number represents itself times 4x4 or itself times 16. The next order number represents itself times 4x4x4 or itself times 64. The next order number represents itself times 4x4x4x4 or itself times 256. And so on.

#### Orders of Magnitude in Base 4

1 · 4 · 16 · 64 · 256 · 1024· 4096 · 16384

#### Positional

16384 · 4096 · 1024 · 256 · 64 · 16 · 4 · 1

A basic, first example of a quaternary number would be the base 4 number 11111. This would mean there is:
• one 1,
• one 4,
• one 16,
• one 64,
• and one 256.
Which represents 1 + 4 + 16 + 64 + 256; for a total of 341 in Base 10 decimal.

Another base 4 example would be the quaternary number 321. This number means that there are:
• one 1’s,
• two 4’s,
• and three 16’s.
Which represents 1 + 8 + 48; for a total of 57 in decimal.

Another base 4 example would be the quaternary number 3023. This number means that there are:
• three 1’s,
• two 4’s,
• no 16’s,
• and three 64’s.
Which represents 3 + 8 + 0 + 192; for a total of 203 in decimal.

#### Orders of Magnitude in Base 4

1 · 4 · 16 · 64 · 256 · 1024· 4096 · 16384

#### Positional

16384 · 4096 · 1024 · 256 · 64 · 16 · 4 · 1

### More Quaternary (Base 4) to Decimal (Base 10) Conversion Examples

Column headings in the following table are simply a convenience relist of the relevant positional orders of magnitude as applies to each column.

 -------------------------------- -------------------------------- -------------------------------- 4 · 1 16 · 4 · 1 64 · 16 · 4 · 1 0=0 21=9 200=32 1=1 22=10 222=42 2=2 23=11 223=43 3=3 30=12 333=63 10=4 33=15 1000=64 11=5 100=16 1100=80 12=6 102=18 2000=128 13=7 120=24 2030=140 20=8 122=26 3122=218

.

## Base 8 – How to Do and Convert Base 8 to Base 10 – Octal Number System Conversions – Includes Examples

0 1 2 3 4 5 6 7
 How to Do Octal, Base 8 Number System Conversions. Includes Examples.

Base 8, also known as the octal number system, is mostly used in electronics and some DNA applications, etc.

Here is everything you need to know on how to convert from octal aka base 8 to decimal. And for converting from decimal aka base 10 to octal.

As previously stated: if you understand the decimal (base 10) number system you use every day, then you already understand the octal (base 8) numbering system.

Per the introduction, base 10 has ten numbers (0-9) and orders of magnitude that are times ten. The orders of magnitude are l, 10, 100 (10x10) , 1000 (10x10x10), etc.

An example would be the number 2375. This number means that there are:
• five 1’s,
• seven 10’s,
• three 100’s
• and two 1000’s.
Which represents 5 + 70 + 300 + 2000; for a total of 2375.

### How to Do the Octal Base 8 Numbering System

Base 8 uses the same base 10 structure, the only difference being the orders of magnitude. Base 8 has eight numbers (0-7) and orders of magnitude that are times eight. The lowest-order number represents itself times one. The next-order number represents itself times eight. The next order number represents itself times 8x8 or itself times 64. The next order number represents itself times 8x8x8 or itself times 512. And so on.

#### Orders of Magnitude in Base 8

1 · 8 · 64 · 512 · 4096 · 32768 · 262144

#### Positional

262144 · 32768 · 4096 · 512 · 64 · 8 · 1

A basic, first example of an octal number would be the base 8 number 11111. This would mean there is:
• one 1,
• one 8,
• one 64,
• one 512,
• and one 4096.
Which represents 1 + 8 + 64 + 512 + 4096; for a total of 4681 in Base 10 decimal.

Another base 8 example would be the octal number 321. This number means that there are:
• one 1’s,
• two 8’s,
• and three 64’s.
Which represents 1 + 16 + 192; for a total of 209 in decimal.

Another base 8 example would be the octal number 4075. This number means that there are:
• five 1’s,
• seven 8’s,
• no 64’s,
• and four 512’s.
Which represents 5 + 56 + 0 + 2048; for a total of 2109 in decimal.

#### Orders of Magnitude in Base 8

1 · 8 · 64 · 512 · 4096 · 32768 · 262144

#### Positional

262144 · 32768 · 4096 · 512 · 64 · 8 · 1

### More Octal (Base 8) to Decimal (Base 10) Conversion Examples

Column headings in the following table are simply a convenience relist of the relevant positional orders of magnitude as applies to each column.

 -------------------------------- -------------------------------- -------------------------------- 8 · 1 8 · 1 512 · 64 · 8 · 1 0=0 15=13 100=64 1=1 16=14 165=117 2=2 17=15 200=128 7=7 20=16 534=348 10=8 25=21 1000=512 11=9 34=28 1100=576 12=10 50=40 2000=1024 13=11 55=45 2006=1030 14=12 77=63 2011=1033

.

## Base 16 – How to Do and Convert Base 16 to Base 10 – Hexadecimal Number System Conversions – Includes Examples

Hex: 0-9, A a, B b, C c, D d, E e, F f
 How to Do Hexadecimal, Base 16 Number System Conversions. Includes Examples.

Hexadecimal (base 16) is the primary base numbering system used by computer programmers. Hex code is used in everything from core dumps to color codes and everything in-between.

Per the introduction, base 10 has ten numbers (0-9) and orders of magnitude that are times ten. The orders of magnitude are l, 10, 100 (10x10) , 1000 (10x10x10), etc.

An example would be the number 5681. This number means there are:
• one 1’s,
• eight 10’s,
• six 100’s,
• and five 1000’s.
Which represents 1 + 80 + 600 + 5000; for a total of 5681.

Base 16 uses the same base 10 structure, the only difference being the orders of magnitude.

### How to Do the Hexadecimal Base 16 Numbering System

 Beware Miscalculations
The orders of magnitude are times sixteen. The lowest-order number represents itself times one. The next-order number represents itself times sixteen. The next order number represents itself times 16x16 or itself times 256. The next order number represents itself times 16x16x16 or itself times 4096. And so on.

1 · 16 · 256 · 4096 · 65536 · 1048576

#### Positional:

1048576 · 65536 · 4096 · 256 · 16 · 1

Base 16 aka hex has sixteen numbers (0-F). The first ten numbers are the usual 0 thru 9. The next six numbers are A=10, B=11, C=12, D=13, E=14, F=15.

Altogether we have:
0=0, 1=1, 2=2, 3=3, 4=4, 5=5, 6=6, 7=7, 8=8, 9=9,
A=10, B=11, C=12, D=13, E=14, F=15.

A basic, first example of a hexadecimal number would be the base 16 number 11111. This would mean there is:
• one 1,
• one 16,
• one 256,
• one 4096,
• and one 65536.
Which represents 1 + 16 + 256 + 4096 + 65536; for a total of 69905 in Base 10 decimal.

Another base 16 example would be the hex number 5C7F. This number means there are:
• fifteen 1’s,
• seven 16’s,
• twelve 256’s,
• and five 4096’s.
Which represents 15 +112 +3072 + 20480; for a total of 23679 in decimal.

Another base 16 example would be the hex number D24A. This number means there are:
• ten 1’s,
• four 16’s,
• two 256’s,
• and thirteen 4096’s.
Which represents 10 +64 +512 + 53248; for a total of 53834 in decimal.

1 · 16 · 256 · 4096 · 65536 · 1048576

#### Positional

1048576 · 65536 · 4096 · 256 · 16 · 1

### More Hexadecimal (Base 16) to Decimal (Base 10) Conversion Examples

Column headings in the following table are simply a convenience relist of the relevant positional orders of magnitude as applies to each column. There is no significance attached as to where one column ends and the next one begins.
A=10, B=11, C=12, D=13, E=14, F=15
 ------------------------------------- ------------------------------------- ------------------------------------- 16 · 1 256 · 16 · 1 65536 · 4096 · 256 · 16 · 1 0=0 16=22 101=257 1=1 17=23 111=273 2=2 1A=26 200=512 9=9 1C=28 3E4=996 A=10 1F=31 3E8=1000 B=11 20=32 BAD=2989 F=15 21=33 FFF=4095 10=16 27=39 1000=4096 11=17 2A=42 1004=4100 12=18 77=119 2BAD=11181 13=19 BD=189 DEAD=57005 14=20 FF=255 10000=65536 15=21 100=256 10100=65792

### Simply a Sequential List of Hexadecimal Numbers

Table created using the Microsoft Excel formula: “=DEC2HEX(cell address here)”.
1 2 3 4 5 6 7 8 9 A B C D E F 10 11 12 13 14 15 16 17 18 19 1A 1B 1C 1D 1E 1F 20 21 22 23 24 25 26 27 28 29 2A 2B 2C 2D 2E 2F 30 31 32 33 34 35 36 37 38 39 3A 3B 3C 3D 3E 3F 40 41 42 43 44 45 46 47 48 49 4A 4B 4C 4D 4E 4F 50 51 52 53 54 55 56 57 58 59 5A 5B 5C 5D 5E 5F 60 61 62 63 64 65 66 67 68 69 6A 6B 6C 6D 6E 6F 70 71 72 73 74 75 76 77 78 79 7A 7B 7C 7D 7E 7F 80 81 82 83 84 85 86 87 88 89 8A 8B 8C 8D 8E 8F 90 91 92 93 94 95 96 97 98 99 9A 9B 9C 9D 9E 9F A0 A1 A2 A3 A4 A5 A6 A7 A8 A9 AA AB AC AD AE AF B0 B1 B2 B3 B4 B5 B6 B7 B8 B9 BA BB BC BD BE BF C0 C1 C2 C3 C4 C5 C6 C7 C8 C9 CA CB CC CD CE CF D0 D1 D2 D3 D4 D5 D6 D7 D8 D9 DA DB DC DD DE DF E0 E1 E2 E3 E4 E5 E6 E7 E8 E9 EA EB EC ED EE EF F0 F1 F2 F3 F4 F5 F6 F7 F8 F9 FA FB FC FD FE FF 100 101 102 103 104 105 106 107 108 109 10A 10B 10C 10D 10E 10F 110 111 112 113 114 115 116 117 118 119 11A 11B 11C 11D 11E 11F 120 121 122 123 124 125 126 127 128 129 12A 12B 12C 12D 12E 12F 130 131 132 133 134 135 136 137 138 139 13A 13B 13C 13D 13E 13F 140 141 142 143 144 145 146 147 148 149 14A 14B 14C 14D 14E 14F 150 151 152 153 154 155 156 157 158 159 15A 15B 15C 15D 15E 15F 160 161 162 163 164 165 166 167 168 169 16A 16B 16C 16D 16E 16F 170 171 172 173 174 175 176 177 178 179 17A 17B 17C 17D 17E 17F 180 181 182 183 184 185 186 187 188 189 18A 18B 18C 18D 18E 18F 190 191 192 193 194 195 196 197 198 199 19A 19B 19C 19D 19E 19F 1A0 1A1 1A2 1A3 1A4 1A5 1A6 1A7 1A8 1A9 1AA 1AB 1AC 1AD 1AE 1AF 1B0 1B1 1B2 1B3 1B4 1B5 1B6 1B7 1B8 1B9 1BA 1BB 1BC 1BD 1BE 1BF 1C0 1C1 1C2 1C3 1C4 1C5 1C6 1C7 1C8 1C9 1CA 1CB 1CC 1CD 1CE 1CF 1D0 1D1 1D2 1D3 1D4 1D5 1D6 1D7 1D8 1D9 1DA 1DB 1DC 1DD 1DE 1DF 1E0 1E1 1E2 1E3 1E4 1E5 1E6 1E7 1E8 1E9 1EA 1EB 1EC 1ED 1EE 1EF 1F0 1F1 1F2 1F3 1F4 1F5 1F6 1F7 1F8 1F9 1FA 1FB 1FC 1FD 1FE 1FF 200 201 202 203 204 205 206 207 208 209 20A 20B 20C 20D 20E 20F 210 211 212 213 214 215 216 217 218 219 21A 21B 21C 21D 21E 21F 220 221 222 223 224 225 226 227 228 229 22A 22B 22C 22D 22E 22F 230 231 232 233 234 235 236 237 238 239 23A 23B 23C 23D 23E 23F 240 241 242 243 244 245 246 247 248 249 24A 24B 24C 24D 24E 24F 250 251 252 253 254 255 256 257 258 259 25A 25B 25C 25D 25E 25F 260 261 262 263 264 265 266 267 268 269 26A 26B 26C 26D 26E 26F 270 271 272 273 274 275 276 277 278 279 27A 27B 27C 27D 27E 27F 280 281 282 283 284 285 286 287 288 289 28A 28B 28C 28D 28E 28F 290 291 292 293 294 295 296 297 298 299 29A 29B 29C 29D 29E 29F 2A0 2A1 2A2 2A3 2A4 2A5 2A6 2A7 2A8 2A9 2AA 2AB 2AC 2AD 2AE 2AF 2B0 2B1 2B2 2B3 2B4 2B5 2B6 2B7 2B8 2B9 2BA 2BB 2BC 2BD 2BE 2BF 2C0 2C1 2C2 2C3 2C4 2C5 2C6 2C7 2C8 2C9 2CA 2CB 2CC 2CD 2CE 2CF 2D0 2D1 2D2 2D3 2D4 2D5 2D6 2D7 2D8 2D9 2DA 2DB 2DC 2DD 2DE 2DF 2E0 2E1 2E2 2E3 2E4 2E5 2E6 2E7 2E8 2E9 2EA 2EB 2EC 2ED 2EE 2EF 2F0 2F1 2F2 2F3 2F4 2F5 2F6 2F7 2F8 2F9 2FA 2FB 2FC 2FD 2FE 2FF 300 301 302 303 304 305 306 307 308 309 30A 30B 30C 30D 30E 30F 310 311 312 313 314 315 316 317 318 319 31A 31B 31C 31D 31E 31F 320 321 322 323 324 325 326 327 328 329 32A 32B 32C 32D 32E 32F 330 331 332 333 334 335 336 337 338 339 33A 33B 33C 33D 33E 33F 340 341 342 343 344 345 346 347 348 349 34A 34B 34C 34D 34E 34F 350 351 352 353 354 355 356 357 358 359 35A 35B 35C 35D 35E 35F 360 361 362 363 364 365 366 367 368 369 36A 36B 36C 36D 36E 36F 370 371 372 373 374 375 376 377 378 379 37A 37B 37C 37D 37E 37F 380 381 382 383 384 385 386 387 388 389 38A 38B 38C 38D 38E 38F 390 391 392 393 394 395 396 397 398 399 39A 39B 39C 39D 39E 39F 3A0 3A1 3A2 3A3 3A4 3A5 3A6 3A7 3A8 3A9 3AA 3AB 3AC 3AD 3AE 3AF 3B0 3B1 3B2 3B3 3B4 3B5 3B6 3B7 3B8 3B9 3BA 3BB 3BC 3BD 3BE 3BF 3C0 3C1 3C2 3C3 3C4 3C5 3C6 3C7 3C8 3C9 3CA 3CB 3CC 3CD 3CE 3CF 3D0 3D1 3D2 3D3 3D4 3D5 3D6 3D7 3D8 3D9 3DA 3DB 3DC 3DD 3DE 3DF 3E0 3E1 3E2 3E3 3E4 3E5 3E6 3E7 3E8 3E9 3EA 3EB 3EC 3ED 3EE 3EF 3F0 3F1 3F2 3F3 3F4 3F5 3F6 3F7 3F8 3F9 3FA 3FB 3FC 3FD 3FE 3FF 400 401 402 403 404 405 406 407 408 409 40A 40B 40C 40D 40E 40F 410 411 412 413 414 415 416 417 418 419 41A 41B 41C 41D 41E 41F 420 421 422 423 424 425 426 427 428 429 42A 42B 42C 42D 42E 42F 430 431 432 433 434 435 436 437 438 439 43A 43B 43C 43D 43E 43F 440 441 442 443 444 445 446 447 448 449 44A 44B 44C 44D 44E 44F 450 451 452 453 454 455 456 457 458 459 45A 45B 45C 45D 45E 45F 460 461 462 463 464 465 466 467 468 469 46A 46B 46C 46D 46E 46F 470 471 472 473 474 475 476 477 478 479 47A 47B 47C 47D 47E 47F 480 481 482 483 484 485 486 487 488 489 48A 48B 48C 48D 48E 48F 490 491 492 493 494 495 496 497 498 499 49A 49B 49C 49D 49E 49F 4A0 4A1 4A2 4A3 4A4 4A5 4A6 4A7 4A8 4A9 4AA 4AB 4AC 4AD 4AE 4AF 4B0 4B1 4B2 4B3 4B4 4B5 4B6 4B7 4B8 4B9 4BA 4BB 4BC 4BD 4BE 4BF 4C0 4C1 4C2 4C3 4C4 4C5 4C6 4C7 4C8 4C9 4CA 4CB 4CC 4CD 4CE 4CF 4D0 4D1 4D2 4D3 4D4 4D5 4D6 4D7 4D8 4D9 4DA 4DB 4DC 4DD 4DE 4DF 4E0 4E1 4E2 4E3 4E4 4E5 4E6 4E7 4E8 4E9 4EA 4EB 4EC 4ED 4EE 4EF 4F0 4F1 4F2 4F3 4F4 4F5 4F6 4F7 4F8 4F9 4FA 4FB 4FC 4FD 4FE 4FF 500 501 502 503 504 505 506 507 508 509 50A 50B 50C 50D 50E 50F 510 511 512 513 514 515 516 517 518 519 51A