# What is the power factor?

Works out the power factor from real power and volts and amps (single or three-phase) or kVA, with the phase angle, reactive power, and the capacitor kVAR needed to correct it to a target.

- Page: https://www.acalculator.org/physics/power-factor-calculator
- JSON spec: https://www.acalculator.org/physics/power-factor-calculator.json
- Version: c91dce11aa51

## Default answer

Example with the default inputs (Supply Single-phase, I know kW, volts and amps, Real power 9.6 kW, Voltage 240 V, Current 50 A, Target power factor 0.95): The power factor is 0.8 (phase angle 36.87°), with 12 kVA and 7.2 kVAR.

## Inputs

| Key | Label | Description |
| --- | --- | --- |
| ph | Supply | Single-phase, or balanced three-phase with the line-to-line voltage. It matters only with volts and amps. |
| from | I know | The real power with volts and amps, or the real power with the apparent power in kVA. |
| p | Real power | The real power the load uses, as a wattmeter or nameplate gives it. |
| v | Voltage | The RMS voltage; for three-phase, the line-to-line voltage. |
| i | Current | The RMS current in each line. |
| kva | Apparent power (kVA) | The apparent power in kilovolt-amperes. |
| pf2 | Target power factor | The power factor to correct to with capacitors, from 0.01 to 1. Leave empty to skip. |

## Outputs

| Key | Label | Description |
| --- | --- | --- |
| pf | Power factor | Real power ÷ apparent power, from 0 to 1. |
| angle | Phase angle (°) | The angle φ between voltage and current, where cos φ is the power factor. |
| kva | Apparent power (kVA) | Volts × amps (× √3 for three-phase) ÷ 1,000. |
| kvar | Reactive power (kVAR) | √(kVA² − kW²). |
| correction | Capacitor kVAR to reach the target | kW × (tan φ now − tan φ at the target): the reactive power capacitors must supply. |
| kvaAfter | kVA after correction | kW ÷ target power factor. |

## Method

S = V × I ÷ 1,000 kVA (single-phase), √3 × V × I ÷ 1,000 (three-phase), or as typed. pf = P ÷ S; φ = arccos pf; Q = P × √(1 − pf²) ÷ pf. Correction to a target pf₂: Qc = Q − P × √(1 − pf₂²) ÷ pf₂; kVA after = P ÷ pf₂.

## Assumptions

- RMS values on a sinusoidal supply; three-phase means a balanced load with line-to-line volts and line amps.
- The correction assumes a lagging (inductive) load such as a motor, corrected with capacitors. A target at or below the present power factor shows no correction.
- Steps are exact on the typed values except √3 and the angle.

## Worked examples

1. from = pvi, ph = single, p = 9,600, v = 240, i = 50, pf2 = 0.95 gives pf = 0.8, angle = 36.869898, kva = 12, kvar = 7.2, correction = 4.044633, kvaAfter = 10.105263. Source: OpenStax, University Physics Volume 2, §15.4 Power in an AC Circuit (P_ave = I_rms V_rms cos φ; cos φ is the power factor), https://openstax.org/books/university-physics-volume-2/pages/15-4-power-in-an-ac-circuit (retrieved 2026-10-05); Wikipedia, "Power factor" (pf = P ÷ S; S² = P² + Q²; correction by capacitors that supply reactive power), https://en.wikipedia.org/wiki/Power_factor (retrieved 2026-10-05).
2. from = ps, ph = single, p = 67,500, kva = 75 gives pf = 0.9, kvar = 32.691742. Source: Wikipedia, "Power factor" (pf = P ÷ S; S² = P² + Q²; correction by capacitors that supply reactive power), https://en.wikipedia.org/wiki/Power_factor (retrieved 2026-10-05).
3. from = pvi, ph = three, p = 60,000, v = 480, i = 90 gives pf = 0.801875, kva = 74.824595. Source: Wikipedia, "Three-phase electric power" (balanced load: S = √3 × line voltage × line current), https://en.wikipedia.org/wiki/Three-phase_electric_power (retrieved 2026-10-05).

## FAQ

### How do I calculate power factor?

Divide the real power in kW by the apparent power in kVA. Apparent power is volts × amps ÷ 1,000 for single-phase, and √3 × volts × amps ÷ 1,000 for three-phase. A load using 9.6 kW at 240 V and 50 A has 12 kVA, so its power factor is 9.6 ÷ 12 = 0.8.

### What is a good power factor?

Closer to 1 is better: the supply then carries no more current than the work needs. Heaters and filament bulbs are near 1. Motors are lower, and lower still at part load. Some utilities charge extra when it falls below a level set in their tariff.

### How do I size a capacitor for power factor correction?

The capacitor must supply the drop in reactive power: kVAR = kW × (tan φ1 − tan φ2), where cos φ1 is the present power factor and cos φ2 the target. For 9.6 kW from 0.8 to 0.95: 9.6 × (0.75 − 0.3287) = 4.04 kVAR.

### What is the phase angle?

In an AC circuit with coils or capacitors, the current peaks a little before or after the voltage. The phase angle φ measures that shift, and the power factor is its cosine. A power factor of 0.8 is a phase angle of 36.87°.

### What is the difference between leading and lagging power factor?

Lagging means the current peaks after the voltage, as in motors and other coils. Leading means it peaks before, as with too many capacitors. The number alone does not tell you which; the correction on this page assumes a lagging load.

### Why does a low power factor matter?

For the same real power, a low power factor means more current. More current heats cables and transformers, causes larger voltage drops, and uses up capacity, which is why utilities may charge for it.

## Sources

- OpenStax, University Physics Volume 2, §15.4 Power in an AC Circuit: average power = I_rms V_rms cos φ, and cos φ is the power factor. https://openstax.org/books/university-physics-volume-2/pages/15-4-power-in-an-ac-circuit (retrieved 2026-10-05)
- Wikipedia, "Power factor": pf = P ÷ S, the power triangle S² = P² + Q², and correction with capacitors. https://en.wikipedia.org/wiki/Power_factor (retrieved 2026-10-05)
- Wikipedia, "Three-phase electric power": for a balanced load, S = √3 × line voltage × line current. https://en.wikipedia.org/wiki/Three-phase_electric_power (retrieved 2026-10-05)