Ohms Electronics Mathematics Formulas
Alternate Titles
 How to Figure Out Ohms
 How many ohms in volts, amps, and/or watts.
 Ohms  How to Calculate and Convert Power aka Watts / Volts / Amps to Ohms aka Resistance
If you are looking for the resistor color code info, it is about halfway down the page on the righthand side.
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This is one of four pages having to do with Ohm's Law and its derivatives.
 How to calculate Power aka Watts
 How to calculate Current aka Amps
 How to calculate Electromotive Force aka Volts
 How to calculate Resistance aka Ohms (You Are Here)
Ohms Equals... The Quick, Easy Answer.
Dividing volts by amps will give you resistance in ohms. For examples and other formulas that will give you the answer, or more information in general; continue reading.
Converting Volts and Amps to Ohms
 R = E/I Ohm's Law for resistance.
Converting Volts and Watts to Ohms
 R = E^{2}/P Ohm's Law derivative for resistance.
Converting Watts and Amps to Ohms
 R = P/I^{2 }Ohm's Law derivative for resistance.
How to convert amps / volts / watts to ohms.
Ohms Is the Unit of Measurement for Resistance
The amount of electrical resistance in a circuit, or internally in a device, can be determined by knowing any two of either power, electromotiveforce, or current.
In other words, the number of ohms can be determined by knowing any two of either watts, volts, or amps.
Each set of two has its own formula. There are three formulas.
The algebraic term for "symbol" is "variable".
"R" is the industry standard to designate resistance by the unit of measurement, ohms.
"P" is the industry standard to designate power by the unit of measurement, watts. "W" is sometimes used.
"E" and "V" are both used to designate electromotiveforce by the unit of measurement, volts. The industry standard used to be "E", but now both "E" and "V" are being used interchangeably.
"I" is the industry standard to designate current by the unit of measurement, amps.
How to Convert Volts and Amps to Ohms
#1 Calculating Ohms Using Volts and Amps
All one does is divide volts by amps to get ohms. The next four statements all say the same thing and have the same meaning. Pick whichever one that works for you.
 Resistance equals Electromotiveforce divided Current
 Resistance equals Voltage divided by Amperage
 Resistance equals Volts divided by Amps
 Ohms equals Volts divided by Amps
The two formulas say the exact same thing and have the exact same meaning. Pick whichever one that works for you and make it yours.
 R=E/I
 R=V/I
Some everyday examples:
A 12volt car battery divided by .5 amps equals 24 ohms (maybe a car instrument cluster).
A 240volt house current divided by 3 amps equals 80 ohms (maybe a washer or dryer).
A 12volt car battery divided by 50 amps equals .24 ohms (maybe a starter for a small engine).
Some circuit / formula examples (there are a 1000 millivolts in a volt, there are a 1000 milliamps in 1 amp, there are 1000 milliwatts in a watt):
3 volts divided by 100 milliamps (.1 amps) equals 30 ohms.
300 volts divided by .2 amps (200 milliamps) equals 1500 ohms of resistance.
Some math / algebra examples:
50 ohms = 200 volts / 4 amps
20 ohms = 120 volts / 6 amps
100 ohms = 120 volts / 1.2 amps
How to Convert Watts and Volts to Ohms
*** Resistor Value Color Code ***
Color code for first three bands
 Black = 0
 Brown = 1
 Red = 2
 Orange = 3
 Yellow = 4
 Green = 5
 Blue = 6
 Violet = 7
 Gray = 8
 White = 9
The fourth band indicates tolerance or manufacturing variance. A 5% variance is better quality than a 10% variance.
 Gold = 5%
 Silver = 10%
Resistor Value Color Code Examples
From left to right, the resistor has redgreenorange bands. That would translate to the resistor having a resistance value of 25000 ohms.
Blueyellowred means the resistor has a value of 6400 ohms.
Graybrownbrown equals 810 ohms.
More Examples
Band Colors
 Ohms


blackredblack
 2

graygreenblack
 85

redbluebrown
 260

grayorangered
 8300

redgrayorange
 28000

grayredyellow
 820000

bluegraygreen
 6.8 megohms

violetredblue
 72 megohms

greengrayviolet
 580 megohms

grayredgray
 8200 megohms

redgreenwhite
 25000 megohms

#2 Calculating Ohms Using Watts and Volts
[To square a number means to multiply a number times itself. Example: 3^{2}=9.]
To determine the resistance in ohms, one squares the voltage, and then divides by watts. The next four statements say the same thing with the same meaning.
 Resistance equals Electromotiveforce squared divided by Power
 Resistance equals Voltage squared divided by Watts
 Resistance equals Volts squared divided by Power
 Ohms equals Volts squared divided by Watts
The next four formulas all say the same thing and have the same meaning. Pick whichever one that works for you and make it yours.
 R=E^{2}/P
 R=V^{2}/P
 R = (E x E) / P
 R = (V x V) / P
Some examples:
Example #1:
The 120volt device uses 200 watts. What is its internal electrical resistance? The formula is R=E^{2}/P. 120 volts squared equals 14,400. So you now have 14400/200 which would equal an answer of 72 ohms.
Example #2:
The device uses 2 watts of power and requires a 6volt power source. If a VOM (see note below) was hooked up to it, what should it read?
R=E^{2}/P. So the ohms will equal 36 divided by the 2 watts. The meter should read an 18 ohm resistance.
Some circuit / formula examples: (there are 1000 millivolts in a volt, there are a 1000 milliamps in 1 amp, there are 1000 milliwatts in a watt):
There are 60 volts running through a circuit board which uses 90 watts of power. What is the circuit board's internal resistance? 60 volts squared is 3600. So we have 3600/90 watts. The answer is a resistance of 40 ohms.
There are 3 volts running through a circuit that uses 1.8 watts. The 3 squared is 9. The 9 divided by 1.8 equals 5. So the answer is 5 ohms.
Some math / algebra examples:
If 48 volts and 500 watts, then R=48^{2}/500=2304/500=4.608 ohms
If 1.5 volts and 10 watts, then R=1.5^{2}/10=2.25/10=.225 ohms
A general note about VOM's: A VOM is a multirange, voltohm multitester meter. It is a test instrument to measure voltage, current, and resistance. Do not buy one until you really know what you are doing. Cheaper meters can be inaccurate when it comes to measuring certain ranges of resistance. Really research the subject first.
How to Convert Watts and Amps to Ohms
Just a Tesla Coil demonstration at Fermilab.
#3 Calculating Ohms Using Watts and Amps
[To square a number means to multiply a number times itself. Example: 5^{2}=25.]
To calculate resistance (in ohms), one squares the current (amps), and then divides it into the number of watts. The next four statements each say the same thing and have the same meaning.
 Resistance equals Currentsquared, divided into Power
 Ohms equals ampssquared, divided into watts
 Resistance equals Power divided by Currentsquared
 Ohms equals watts divided by ampssquared
Here are two representations of the same formula:
 R=P/I^{2}
 R = P / (I x I)
An example:
You have 10 amps flowing through a device or circuit that is using 2500 watts of power. What is the internal resistance?
R=P/I^{2}
R = 2500 watts divided by 10^{2 }
R = 2500 divided by (10 x 10)
R = 2500 divided by 100
R = 25 ohms
The Three Formulas for Ohms
Summary
R=E/I (Ohms equals volts divided by amps. Of the three formulas, this is the one that is used 90% of the time.)
R=E^{2}/P
R=P/I^{2}
If you have any suggestions on how this reference article can be improved, please let us know. There is a Comments Section further down the page.
The How to convert amps / volts / watts to ohms page.
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