Ohm's Law: How to Calculate Voltage, Current and Resistance

The Relationship Behind Every Circuit

Published by Georg Ohm in 1827, Ohm's Law is the single most useful equation in electronics. It ties together the three quantities that describe any simple circuit, and once you know two of them, the third is fixed.

The clearest way to picture it is water in a pipe:

Voltage (V) is the pressure pushing the water along.
Current (I) is the rate of flow — how much water passes a point each second.
Resistance (R) is how narrow the pipe is, restricting that flow.

Raise the pressure and more water flows. Narrow the pipe and less does. That is the whole law, and the equation just makes it precise.

The Formula and Its Three Forms

The law is usually written:

V = I × R

Rearranged, it answers whichever question you are actually asking:

Voltage: V = I × R
Current: I = V ÷ R
Resistance: R = V ÷ I

Many people remember this as a triangle with V on top and I and R side by side underneath: cover the value you want, and the arrangement of the other two shows you whether to multiply or divide.

The Units

Voltage is measured in volts (V), after Alessandro Volta.
Current is measured in amperes or amps (A), after André-Marie Ampère.
Resistance is measured in ohms (Ω), after Ohm himself.

Current is abbreviated I rather than C because of the original French term intensité de courant — intensity of current. It trips up every beginner exactly once.

Three Worked Examples

Finding voltage: a current of 0.5 A flows through a 24 Ω resistor. V = 0.5 × 24 = 12 V.

Finding current: 12 V is applied across a 100 Ω resistor. I = 12 ÷ 100 = 0.12 A, or 120 mA.

Finding resistance: a 3,000 W kettle on a UK 230 V supply draws 13.04 A. R = 230 ÷ 13.04 = 17.6 Ω.

The Prefix Mistake That Ruins Answers

This is the error that produces impossible results, and it catches experienced people as well as beginners. Ohm's Law only works in base units: volts, amps, and ohms. Component values are almost never printed that way.

1 mA (milliamp) = 0.001 A
1 µA (microamp) = 0.000001 A
1 kΩ (kilohm) = 1,000 Ω
1 MΩ (megohm) = 1,000,000 Ω

Take 12 V across a 2.2 kΩ resistor. Entered correctly as 2,200 Ω, the current is 12 ÷ 2,200 = 5.45 mA. Enter 2.2 instead and you get 5.45 A — a thousand times too high, and a figure that would melt the resistor rather than run it. If an answer looks absurd, check your prefixes before you check anything else.

Adding Power: The Ohm's Law Wheel

Ohm's Law pairs with the power formula, P = V × I, where power is measured in watts. Substituting one into the other gives two more forms that save you a step:

P = V × I — when you know voltage and current
P = I² × R — when you know current and resistance
P = V² ÷ R — when you know voltage and resistance

Check it against the kettle: 230² ÷ 17.6 = 3,005 W, which is the 3 kW we started with. This family of rearrangements is often drawn as the Ohm's Law wheel, giving twelve formulas from these two simple laws.

A Practical Example: Choosing an LED Resistor

This is the calculation hobbyists reach for most often. An LED needs a series resistor, because connecting one straight across a supply destroys it.

Driving a red LED — forward voltage 2.1 V, desired current 20 mA — from a 9 V battery.

Find the voltage across the resistor: 9 − 2.1 = 6.9 V. The LED takes its share, and the resistor drops the rest.
Apply Ohm's Law: R = 6.9 ÷ 0.02 = 345 Ω.
Pick the next standard value up: 360 Ω. Rounding up is the safe direction, because it lowers the current slightly.
Check the power rating: at 360 Ω the current is 19.17 mA, so P = I²R = 0.132 W. A standard 0.25 W resistor handles that comfortably.

That final step is the one people skip. A resistor with the right resistance but too low a power rating will overheat, discolour, and eventually fail.

Resistors in Series and Parallel

Before applying the law you often need a single combined resistance:

In series (end to end), resistances simply add: 100 Ω + 220 Ω = 320 Ω.
In parallel (side by side), use the product over the sum for two resistors: (100 × 220) ÷ (100 + 220) = 68.75 Ω.

Note that parallel resistance is always lower than the smallest resistor in the group — you have given the current an extra route to take.

Where Ohm's Law Stops Working

Ohm's Law describes ohmic components, whose resistance stays constant regardless of the voltage applied. Plenty of common parts are not ohmic:

Diodes and LEDs conduct almost nothing below their forward voltage, then a great deal above it. This is exactly why the example above works out the resistor around the LED rather than treating the LED as a resistance.
Filament bulbs gain resistance as they heat up, so a cold bulb draws a large inrush current at switch-on.
Thermistors change resistance with temperature by design, and transistors behave differently again.

The law also assumes direct current. In AC circuits containing capacitors or inductors, the quantity opposing current is impedance rather than plain resistance, and it varies with frequency.

Conclusion

Voltage equals current times resistance, in base units, for components whose resistance holds steady. Rearrange it for whichever value you are missing, pair it with P = V × I when you need power, and check your prefixes before you trust any answer. Enter any two values into an Ohm's Law Calculator to get the third instantly — and remember to size the power rating, not just the resistance.

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