What do V, I, R and P mean?
Voltage (V, volts) is the push. Current (I, amps) is how much flows. Resistance (R, ohms Ω) is how hard the part makes it to flow. Power (P, watts) is how much energy turns into heat or light every second.
V = I × R
P = V × I
These two rules are all there is. Put one into the other and you get every formula in the table below, so any two values give the other two.
- Type the two values you know. Pick the unit beside each one: mA, kΩ and so on.
- Read the other two. They appear in their boxes, tinted, and in the list beside them.
- Check the power. If a resistor makes more heat than its rating, it gets hot and can burn.
Which formula do I use?
Find the row for what you want, then the formula that uses the two values you have.
| To find | Use one of | ||
|---|---|---|---|
| Voltage (V) | V = I × R | V = P ÷ I | V = √(P × R) |
| Current (I) | I = V ÷ R | I = P ÷ V | I = √(P ÷ R) |
| Resistance (R) | R = V ÷ I | R = V² ÷ P | R = P ÷ I² |
| Power (P) | P = V × I | P = I² × R | P = V² ÷ R |
Can I see a few worked out?
Worked out by the same code as the calculator above.
V 3 V, I 20 mA
For 3 V left over for the resistor at 20 mA: R = 150 Ω, P = 60 mW.
R = V ÷ I · P = V × IV 9 V, I 9 mA
For a 1 kΩ resistor across a 9 V battery: R = 1 kΩ, P = 81 mW.
I = V ÷ R · P = V² ÷ RV 5 V, I 50 mA
For the most a ¼ W 100 Ω resistor can take: R = 100 Ω, P = 250 mW.
V = √(P × R) · I = √(P ÷ R)V 230 V, I 4.348 A
For a 1,000 W heater on 230 V mains: R = 52.9 Ω, P = 1 kW.
I = P ÷ V · R = V² ÷ PWhat do people often get wrong?
Mixing mA and A
5 V ÷ 20 is 0.25, but 5 V ÷ 20 mA is 250 Ω. Convert to amps first, or use the unit boxes.
Forgetting the power rating
The right resistance with too small a rating still overheats. Keep the heat under half the rating.
Using the whole supply voltage
Use the voltage across the part itself. With an LED in series, the resistor only gets what the LED leaves over.
Treating every part like a resistor
LEDs, filament bulbs (their resistance rises as they heat up), motors and batteries do not follow V = I × R with one fixed R. Use the law on the resistors around them.
Short answers to common questions
What is Ohm's law?
Ohm's law says the voltage across a resistor equals the current through it times its resistance: V = I × R. Double the voltage and the current doubles; double the resistance and the current halves.
How do I work out current from voltage and resistance?
Divide the voltage by the resistance: I = V ÷ R. For example 9 V across 1,000 Ω gives 9 ÷ 1000 = 0.009 A, which is 9 mA.
How do I work out the power in a resistor?
Multiply the voltage across it by the current through it: P = V × I. If you only know two other values, use P = I² × R or P = V² ÷ R. The calculator picks the right one for you.
Why must I convert mA to A?
The formulas work in volts, amps, ohms and watts. 20 mA is 0.02 A and 4.7 kΩ is 4,700 Ω. The unit boxes in the calculator do this for you.
What power rating should my resistor have?
At least twice the power it turns into heat. A resistor that makes 0.1 W of heat is fine as a normal ¼ W (0.25 W) part; one that makes 0.2 W needs ½ W.
Does Ohm's law work for LEDs?
Not on its own. An LED keeps a nearly fixed voltage across itself (its forward voltage), so its current is not V ÷ R of the LED. Use Ohm's law on the resistor in series with it, with the voltage left over; the LED resistor calculator does exactly that.
Does it work for AC mains?
For a plain resistive load like a heater or an old filament bulb, yes, using the RMS voltage (230 V or 120 V). Motors, capacitors and coils behave differently and need more than Ohm's law. Never measure or work on mains wiring without training.