Electronics Math & Ohm's Law - How to Calculate Watts, Amps, Volts, Ohms - Math Formulas, Examples, Answers

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How to Calculate: Power in Watts, EMF in Volts, Current in Amps, Resistance in Ohms.

A handy math guide for those electrical and electronic math questions.

• How to Quickly and Easily Find Electronics Answers
• Using Ohm's Law and Its Derivatives
• Electronics and Electrical Math Solutions
• Includes Complete Lessons and Examples

The following formula 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, definitions are 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 be 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.

Comprehensive List of Ohm's Law Formulas and Examples

Templates and Table of Contents

Here is a list of formulas and templates. With any luck, you will find one you can use and won't have to bother selecting the related title for the included lessons and examples. This is a large file, if you do make a selection it may take a few seconds to display the appropriate section.

Calculate how many WATTS from volts, amps, ohms (Expanded Lesson/Examples).

Formula Templates:
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 (Expanded Lesson/Examples).

Formula Templates:
I = P/E
Watts  /  Volts  =  Amps

I = E/R
Volts  /  Ohms  =  Amps

I = √(P/R)
Square Root of  ( Watts  /  Ohms )  =  Amps

Calculate how many VOLTS from amps, watts, ohms (Expanded Lesson/Examples).

Formula Templates:
E = P/I
Watts  /  Amps  =  Volts

E = IR
Amps  *  Ohms  =  Volts

E = √(PR)
Square Root of  ( Watts  *  Ohms )  =  Volts

Calculate how many OHMS from volts, amps, watts (Expanded Lesson/Examples).

Formula Templates:
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 with examples on this page. Simply select the expanded how-to Lessons/Examples sub-link in the above template table of contents specifically addressing that which you you wish to find. Thanks to the laws of physics; whether it be trying to calculate how many amps, watts, ohms, or volts; Ohm's law and it's derivatives will always provide three different, possible ways for finding the answer.

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 result in your making critical decisions. As such, a quality test instrument is much more important than the usual former 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 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 can be 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. Only by from reputable sources.

Here is an article from Wired Magazine that I really liked, it gets into the more esoteric and physics aspects: How Do You Define Electric Field, Voltage, and Current? The article even covers what to do if you happen to find yourself near a live, downed power line.

The Ohm's Law math lessons and examples follow or select the lessons/examples links from the above formula templates.

A rough map of world power usage.

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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

 (P=watts, E=volts, I=amps, R=ohms)

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 1000 millivolts in a volt.
• There are 1000 milliamps in an amp.

 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 sub circuit 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

 (P=watts, E=volts, I=amps, R=ohms)

 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

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

 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

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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

 (I=amps, E=volts, P=watts, R=ohms)

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.

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 1000 millivolts in a volt.
• There are 1000 milliamps in an amp.
• There are 1000 milliwatts in a watt.

 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

 (I=amps, E=volts, P=watts, R=ohms)

 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

 (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.

 Some 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.

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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 subcomponents. 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

 (E=volts, P=watts, I=amps, R=ohms)

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 1000 millivolts in a volt.
• There are 1000 milliamps in an amp.
• There are 1000 milliwatts in a watt.

 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

 (E=volts, P=watts, I=amps, R=ohms)

 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

 (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.

 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 1000 volts in a kilovolt (kv).
• There are 1000 amps in a kiloamp (ka).
• There are 1000 watts in a kilowatt. (kw).

 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

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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 subcomponents. 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

 (R=ohms, E=volts, I=amps, P=watts)

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 1000 millivolts in a volt.
• There are 1000 milliamps in an amp.
• There are 1000 milliwatts in a watt.

 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

 (R=ohms, E=volts, I=amps, P=watts)

 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

 (R=ohms, E=volts, I=amps, P=watts)

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.

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A Final Thought...

Do be careful. The laws of physics are unforgiving.

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