Circuits
Ohm's Law Calculator
Enter the two values you know, choose what to solve for, and the formula used is shown with the answer.
Reference data and planning arithmetic. Does not apply ambient or bundling derating, motor rules, or local amendments. Not a substitute for the NEC edition your jurisdiction has adopted, an inspection, or a licensed electrician.
The four relationships
V = I × R I = V ÷ R R = V ÷ I P = V × I
Ohm's law proper is the first three — voltage equals current times resistance. The fourth is Joule's law and combines with it to give P = I²R and P = V²/R, both useful when you know the resistance and one other quantity.
| Known | Solving for | Formula | Result |
|---|---|---|---|
| 120 V across 12 Ω | Current | I = V ÷ R | 10.00 A |
| 10 A through 12 Ω | Voltage | V = I × R | 120 V |
| 120 V drawing 10 A | Resistance | R = V ÷ I | 12 Ω |
| 120 V drawing 10 A | Power | P = V × I | 1200 W |
| 20 A through 0.2 Ω of wire | Heat in the wire | P = I²R | 80 W |
| 40 A through the same wire | Heat in the wire | P = I²R | 320 W — four times |
Where P = I²R explains real behaviour
Power loss in a conductor is I²R, and the square is the interesting part: doubling the current quadruples the heat.
That single relationship explains a lot of practical electrical work. It is why a loose connection burns — contact resistance rises, and the heat at that point rises with it until something fails. It is why transmission runs at high voltage: for the same power, higher voltage means lower current, and lower current means far lower loss. It is why an undersized extension cord on a heater gets warm along its whole length rather than just at the ends.
Where Ohm's law stops being enough
Ohm's law describes resistive DC behaviour. Real AC circuits need more:
- Inductive and capacitive loads have reactance as well as resistance, and the combination is impedance. Motors and transformers are inductive.
- Power factor means V × I gives volt-amps rather than watts.
- Non-linear loads — electronics, LED drivers, variable-frequency drives — do not have a constant resistance at all, and draw current in pulses rather than smoothly.
For sizing conductors, calculating voltage drop and understanding heat in a resistive circuit, Ohm's law is exactly the right tool. For anything with a motor or a power supply in it, it is a first approximation.
Common questions
What is Ohm's law?
Voltage equals current times resistance: V = I x R. Rearranged, I = V/R and R = V/I. Power is a separate relationship, P = V x I.
How do I find amps from volts and ohms?
Divide volts by ohms. A 120 V supply across a 12 ohm load draws 10 A, which is 1,200 W.
Why does doubling current quadruple the heat?
Power loss in a conductor is I²R — proportional to the square of the current. Double the current and the I² term goes up four times. It is why loose connections burn and why undersized wire overheats.