Calculate total power in a circuit from current and up to three series resistances (P = I² × R), or solve for the current or one resistance.

Steady DC or RMS AC current through the series path.

Leave blank if unused (counts as 0 Ω).

Leave blank if unused (counts as 0 Ω).

Optional settings

Understanding Total Power

This calculator models up to three passive resistances carrying the same current, such as a series path. Use steady DC current or RMS AC current for ideal resistors, not peak AC current. Enter 0 for unused resistances. It does not calculate reactive/apparent power or determine safe component ratings, wire size or circuit protection.

Total Power Formula

Pₜ = I²R₁ + I²R₂ + I²R₃

If you first combine the resistances, the equation becomes even simpler:

Rₜ = R₁ + R₂ + R₃
Pₜ = I²Rₜ
Symbol Meaning Typical Unit
Pt Total power dissipated by all resistances combined W
I Circuit current through each resistance A
R1, R2, R3 Individual resistance values Ω
Rt Total resistance Ω
V Total voltage across the circuit V

How to Calculate Total Power

  1. Add the resistance values to get the total resistance.
  2. Square the current value.
  3. Multiply the squared current by the total resistance.
  4. The result is the total power in watts.

Examples

If the current is 10 A and the three resistances are 50 Ω, 30 Ω, and 20 Ω:

Pₜ = 10²(50 + 30 + 20) = 10000 W

If the current is 4 A and only two resistances are used, 5 Ω and 7 Ω, the unused resistance contributes 0:

Pₜ = 4²(5 + 7 + 0) = 192 W

Quick Reference

Each comparison holds the other quantity constant: resistance is fixed when changing current, and current is fixed when changing resistance. A fixed-voltage source can change current when resistance changes.

Change Effect on Total Power
Current doubles Total power becomes 4 times larger
Current is cut in half Total power becomes 1/4 as large
All resistances double Total power doubles
Another series resistance is added Total power increases with the total resistance

If You Know Voltage Instead of Current

For positive total resistance, steady DC voltage or RMS voltage across ideal resistors can be used to find current first or compute power directly:

I = (V) / (Rₜ)
Pₜ = (V²) / (Rₜ)

Common Input Errors

  • Using this same-current formula for a parallel circuit without first finding branch power correctly.
  • Mixing units such as mA, A, kA, Ω, and kΩ without converting them consistently.
  • Forgetting that current is squared, which makes power rise very quickly as current increases.
  • Adding resistance values incorrectly before calculating total power.