Power and energy
Resistive heating: I²R
- where
- power (W)
- current (A)
- resistance (Ω)
Explain this equation
Works out the heat produced when current flows through a resistance. Used for cable and connection losses, and heating elements.
P is the heat power in watts. I is the current and R is the resistance it flows through, at operating temperature. Use RMS current on AC.
Each ampere drops I × R volts across the resistance, and power is volts times amps, so P = I × IR = I²R. Because current appears twice, heating rises with its square.
Sense check: 10 A through 2 Ω gives 200 W. Double the current and the heat goes up four times, which is why overloads and loose terminals get hot so quickly.
Watch out: this gives power, not temperature. How hot something gets depends on how well it shifts the heat.
Current is squared before multiplying by resistance. If the same resistance carries twice the current, its heating power becomes four times as great.
For AC resistive heating use RMS current. This relationship explains why overcurrent and poor connections matter, but it does not predict temperature without thermal information.
Enter your values to see the result.
Common mistake
Multiplying current by two instead of squaring it.
Limits
Resistance at the operating temperature; use RMS for AC.
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.