Enter the voltage (V) (for AC, use RMS voltage) and the resistance (Ω) into the calculator to determine the true (real) power for a purely resistive load (power factor = 1).

True Power Calculator

Enter any 2 values to calculate the missing variable (assumes a purely resistive load; for AC use RMS values).

True Power Formula

True power is the actual rate at which electrical energy is converted into heat, motion, light, or other useful output in a load. For a purely resistive circuit, true power can be calculated directly from the applied voltage and the load resistance.

P_t = \frac{E^2}{R}
Variable Meaning Common Unit
Pt True power delivered to the load watts (W)
E Voltage across the load volts (V)
R Electrical resistance of the load ohms (Ω)

If you need to solve for a different variable, the same relationship can be rearranged as follows:

E = \sqrt{P_t \cdot R}
R = \frac{E^2}{P_t}

How to Calculate True Power

  1. Determine the voltage across the load.
  2. Determine the resistance of the load.
  3. Square the voltage value.
  4. Divide that result by the resistance.
  5. The final value is the true power in watts.

This calculator is useful when any two of the three values are known and you want to solve for the third. If you are calculating by hand, make sure all values are converted into compatible base units before using the equation.

Examples

Example 1

If the voltage across a load is 43 V and the resistance is 85 Ω, then the true power is:

P_t = \frac{43^2}{85} = 21.76

The load is dissipating 21.76 W of true power.

Example 2

If the voltage is 58 V and the resistance is 60 Ω, then:

P_t = \frac{58^2}{60} = 56.07

The true power is 56.07 W.

When to Use This Calculator

  • Estimating the power dissipated by a resistor
  • Checking heating-element or load wattage
  • Analyzing simple DC circuits
  • Evaluating resistive AC loads using RMS voltage
  • Solving for missing voltage or resistance when power is known

AC Circuit Note

This voltage-and-resistance method is most accurate for purely resistive loads. In AC circuits that include inductance, capacitance, or phase shift, real power is commonly related to voltage, current, and power factor.

P = V \cdot I \cdot \cos(\phi)

For that reason, use RMS voltage for AC inputs, and use caution when applying the resistance-based formula to non-resistive loads.

Common Mistakes

  • Entering current instead of voltage
  • Using peak AC voltage instead of RMS voltage
  • Mixing volts, kilovolts, ohms, and kiloohms without converting units when calculating manually
  • Applying the formula to loads with significant reactance or poor power factor
  • Forgetting that very small resistance values can produce very large power results

Unit Tips

The calculator supports multiple unit scales for convenience. If you solve manually, convert values to standard units first so the output power is consistent. In practice, that usually means volts for voltage, ohms for resistance, and watts for power.