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Ohm's law and the power equation combine to relate power, voltage, and resistance. Since P = V² ÷ R, rearranging gives resistance R = V² ÷ P — the square of the voltage divided by the power.
This is useful for sizing resistive loads such as heating elements or dummy loads: if you know the operating voltage and the target power dissipation, you can calculate the resistance you need in ohms.
R(Ω) = V(V)² ÷ P(W)Derived from P = V² ÷ R (Ohm's law with the power equation).
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| Power↕ | At 12 V↕ | At 120 V↕ |
|---|---|---|
| 10 W | 14.4 Ω | 1,440 Ω |
| 25 W | 5.76 Ω | 576 Ω |
| 60 W | 2.4 Ω | 240 Ω |
| 100 W | 1.44 Ω | 144 Ω |
| 500 W | 0.288 Ω | 28.8 Ω |
| 1,000 W | 0.144 Ω | 14.4 Ω |
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How do you convert watts to ohms?
Square the voltage and divide by the power. Ohms = Volts² ÷ Watts. For example, at 120 V a 60 W load has a resistance of 120² ÷ 60 = 240 Ω.
Why do you need voltage to find ohms?
Power alone does not define resistance — the same power can be produced by many voltage and resistance combinations. Voltage fixes the relationship so resistance can be calculated.
Can I use current instead of voltage?
Yes. If you know the current instead, use R = P ÷ I² (power divided by the square of the current) to find resistance in ohms.