Power and energy
Resistive power: V²/R
- where
- power (W)
- voltage (V)
- resistance (Ω)
Explain this equation
Works out power in a resistance from the voltage across it. Useful for heater elements and resistors on a fixed supply.
P is the power in watts. V is the voltage across the resistance (RMS on AC) and R is its resistance.
Ohm’s law gives I = V/R. Put that into P = VI and you get V × V/R = V²/R. At a fixed voltage, power goes up as resistance goes down.
Sense check: 12 V across 6 Ω gives 24 W. A 230 V element of 26.45 Ω gives about 2 kW. Halve the supply voltage and the power drops to a quarter.
Watch out: square the voltage first, then divide. Also be clear what is fixed: on a fixed current, larger R gives more power, not less.
Square the voltage across the resistor, then divide by resistance. This follows by replacing current in P = VI with V/R.
At fixed voltage a smaller resistance dissipates more power. At fixed current the comparison is different, so always identify what is held constant.
Enter your values to see the result.
Common mistake
Squaring the answer after dividing V by R.
Limits
Pure resistance; voltage is DC or RMS as appropriate.
Sources
The tools calculate the displayed equation. They do not automatically choose cable sizes, approve installations, supply current regulatory tables, certify equipment or replace inspection and testing.