Power Factor Calculator

Enter any compatible set of values to solve power factor (PF), phase angle (φ), and P/Q/S. Includes single-phase and three-phase support and Show Work steps.

How to Use

  1. Select System (Single-phase or Three-phase).
  2. Enter values for P (real), S (apparent), and/or Q (reactive), or use Voltage + Current.
  3. Choose Leading/Lagging to indicate capacitive vs inductive behavior (affects the sign of Q / φ).
  4. Open Show Work to see formulas and step-by-step calculations in base units.
AC Power Readout
PF, angle, and P/Q/S update instantly when enough inputs exist.
PF
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φ
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P
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S
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Q
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State: —
Inputs & Settings
Provide any compatible set. The tool solves what it can without guessing.
Three-phase assumes S = √3 × VLL × I.
Affects sign of Q and angle direction in Show Work.
Real (useful) power consumed by the load.
Magnitude of complex power: S = P / PF.
Power “sloshing” in fields. Sign is based on leading/lagging.
PF is a magnitude: 0 to 1 (or 0% to 100%).
PF = cos(φ). Angle is magnitude; leading/lagging sets direction.
For 3φ, enter line-to-line voltage (VLL).
If V and I are provided, the tool can compute S (VA).
Show Work (step-by-step)
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Work is shown in base units (W, VAR, VA, degrees) for clarity and consistency.

Power Factor Formulas

Quick answer: PF = P / S and PF = cos(φ).

Where P = real power, Q = reactive power, S = apparent power.

  • Power factor: PF = P ÷ S
  • Phase angle: φ = arccos(PF)
  • Power triangle: S² = P² + Q²
  • Reactive: Q = √(S² − P²)
  • Single-phase apparent: S = V × I
  • Three-phase apparent: S = √3 × VLL × I
Leading/lagging indicates whether current leads or lags voltage (used for sign/labeling).

FAQ

What does a low power factor mean?

Low PF means more current is required for the same real power (kW), which can increase losses and voltage drop.

What’s the difference between kW, kVA, and kVAR?

kW is real power (does work), kVA is apparent power (V×I magnitude), and kVAR is reactive power (field energy exchange).

Leading vs lagging — which is which?

Many inductive loads (motors) are typically lagging. Capacitive behavior is typically leading. This tool uses the selection to label/sign Q and φ consistently.

Can PF be greater than 1?

No. PF magnitude is between 0 and 1. If you see > 1, it usually means inputs are inconsistent or units were mixed.

Tool Info

Last updated:

Updates may include additional edge-case handling, unit support, and UI polish.