Ohm's law, and how to use it
Ohm's law says the current through a resistor is the voltage across it divided by its resistance: I = V / R. With the power law, P = V × I, any two of voltage, current, resistance and power fix the other two. This calculator takes whichever two you know, works out the rest, shows the formula it used and tells you how much power the resistor must handle.
How to use the Ohm's law calculator
- Type any two values into the four fields: voltage, current, resistance or power. The two you typed last are the knowns, marked given.
- Read the other two in their fields and the tiles, each with the formula it came from. Type into any field to make that one a known instead.
- Write values the way they appear on parts: 4.7k,
4k7,470R, 2.2M for resistance; 20m for 20 mA, 1u for 1 µA, 1.5k for 1.5 kW. Lower-case m is milli, capital M is mega. - Check the rating: the panel suggests a standard resistor power rating with a 2× margin. The drawing's triangles mark the two values you gave.
- Open the Calculation tab for the steps written out, or the Results table for all twelve formulas.
The law and the triangle
V = I × R I = V / R R = V / I
Volts across, amps through, ohms of resistance. The triangle (V on top, I and R below) is the usual way to remember the three forms: cover the quantity you want and what is left is the formula. Cover V and you see I beside R, so V = I × R; cover I and you see V over R.
Your values V = I × R: 12 V = 12 mA × 1 kΩ. You gave voltage and resistance; the rest followed.
Ohm's law holds for resistors, wires and heating elements over their normal range: they are ohmic. It does not hold for diodes, LEDs or transistors, whose current is not in proportion to the voltage; for those you use their own curves, and Ohm's law for the resistor in series with them.
Power: the second triangle
P = V × I = V² / R = I² × R
Power is voltage times current, in watts. Putting Ohm's law into it gives the two other forms, which are the ones you usually need: with a known voltage, P = V² / R; with a known current, P = I² × R. All of it becomes heat in the resistor, so choose a resistor rated for at least about twice that power. Small through-hole resistors are ¼ W; ½ W, 1 W, 2 W and 5 W parts exist for more.
All twelve formulas
Whichever two you know, there is a direct formula for each of the other two; this is the "Ohm's law wheel" as a table.
| Known | V | I | R | P |
|---|---|---|---|---|
| V and I | — | — | R = V / I | P = V × I |
| V and R | — | I = V / R | — | P = V² / R |
| V and P | — | I = P / V | R = V² / P | — |
| I and R | V = I × R | — | — | P = I² × R |
| I and P | V = P / I | — | R = P / I² | — |
| R and P | V = √(P × R) | I = √(P / R) | — | — |
Your values, step by step
- Known: V = 12 V and R = 1 kΩ.
- Current: I = V / R = 12 mA.
- Power: P = V² / R = 144 mW.
- Rating: 144 mW of heat, so use at least a 1/2 W resistor.
Worked example: 12 V across 1 kΩ
I = V / R = 12 V / 1 kΩ = 12 mA. P = V × I = 12 V × 12 mA = 144 mW (or V² / R = 144 / 1000 = 144 mW). A ¼ W resistor is fine: it would be rated for almost twice that. Change the resistor to 100 Ω and the current becomes 120 mA with 1.44 W of heat, which needs a 3 W part.
The same law sizes an LED's resistor: with a 5 V supply, a 2 V LED and 20 mA wanted, the resistor sees 3 V, so R = 3 V / 20 mA = 150 Ω, and it dissipates 3 V × 20 mA = 60 mW.
Questions
Which two values should I enter?
Whichever you actually know. A supply and a resistor give the current and the power; a supply and a wanted current give the resistor; a speaker's impedance and an amplifier's power give the voltage and current.
Why does the calculated field change when I type in it?
Typing into a field makes it one of the two known values, and the field you typed longest ago becomes calculated instead. That is how you switch between, say, "what current?" and "what resistor?".
Does Ohm's law work for AC?
For a pure resistor, yes, using RMS values. Capacitors and inductors have reactance that depends on frequency; then the general form uses impedance Z in place of R.
What about several resistors?
Combine them first: the series and parallel calculators give the total, and a voltage divider is Ohm's law applied to two resistors in series.