# Power Factor Calculator (PF = W/VA)

Calculate power factor (cos phi) from real and apparent power. Find real, reactive, and apparent power in the power triangle. For AC circuits and motor loads.

## What this calculates

Power factor tells you how effectively an AC circuit converts supplied power into useful work. A power factor of 1.0 means all the power does useful work. A factor of 0.7 means 30% of the current is wasted sloshing back and forth. Electric utilities charge commercial customers for poor power factor, so it directly affects your bill.

## Inputs

- **Known Values** — options: Apparent Power (VA) + Real Power (W), Real Power (W) + Power Factor, Apparent Power (VA) + Power Factor, Voltage + Current + Power Factor
- **Apparent Power** (VA) — min 0
- **Real Power** (W) — min 0
- **Power Factor** — min 0, max 1
- **Voltage (RMS)** (V) — min 0
- **Current (RMS)** (A) — min 0

## Outputs

- **Power Factor (cos φ)** — Ratio of real to apparent power
- **Phase Angle (φ)** (°) — Phase angle between voltage and current
- **Real Power (P)** (W) — Actual useful power consumed
- **Reactive Power (Q)** (VAR) — Power oscillating between source and load
- **Apparent Power (S)** (VA) — Total power supplied by the source

## Details

## Understanding the Power Triangle

Every AC circuit has three types of power:

- **Real Power (P)** in Watts: the actual work done (heating, spinning motors, lighting)
- **Reactive Power (Q)** in VAR: energy stored and released by inductors and capacitors each cycle
- **Apparent Power (S)** in VA: the total power the source must deliver

They form a right triangle: **S squared = P squared + Q squared**

### Power Factor Formula

**PF = cos(phi) = P / S = Real Power / Apparent Power**

| Power Factor | Phase Angle | Efficiency |
|-------------|-------------|------------|
| 1.00 | 0 degrees | Perfect (resistive) |
| 0.95 | 18 degrees | Excellent |
| 0.85 | 32 degrees | Good (typical motor) |
| 0.70 | 46 degrees | Poor |
| 0.50 | 60 degrees | Very poor |

### Common Power Factors

- **Incandescent bulbs:** 1.0 (purely resistive)
- **LED drivers:** 0.90 - 0.99
- **Electric motors (loaded):** 0.80 - 0.90
- **Electric motors (unloaded):** 0.10 - 0.30
- **Welding machines:** 0.50 - 0.70

### Why It Matters

A motor with PF = 0.7 drawing 1,000W of real power needs 1,429 VA of apparent power. That means the wiring, transformer, and breaker must handle 43% more current than necessary. Utilities add power factor surcharges for commercial accounts below 0.90, and improving power factor with capacitor banks can save significant money.

## Frequently Asked Questions

**Q: What causes poor power factor?**

A: Inductive loads are the main culprit. Electric motors, transformers, and fluorescent ballasts all create magnetic fields that store and release energy each AC cycle, generating reactive power. The current waveform shifts out of phase with the voltage, and the ratio of useful work to total current drops. Capacitors can be added to cancel the inductive effect and improve the power factor.

**Q: Does power factor affect my home electricity bill?**

A: For residential customers, usually not. Home electric meters typically measure only real power (watts), so you pay for what you actually use. Commercial and industrial customers, however, are often charged for apparent power (VA) or penalized for power factors below 0.90-0.95. Large factories invest in power factor correction capacitor banks to avoid these surcharges.

**Q: What is power factor correction?**

A: Power factor correction means adding capacitors (or sometimes synchronous motors) to an AC circuit to offset the reactive power from inductive loads. Capacitors supply leading reactive power that cancels the lagging reactive power from motors. This reduces the total current drawn from the supply, lowering losses and utility charges. A typical target is PF 0.95 or higher.

**Q: Can power factor be greater than 1?**

A: No. Power factor ranges from 0 to 1. A value of 1 means voltage and current are perfectly in phase (purely resistive load). A value of 0 means the phase angle is 90 degrees (purely reactive, no useful work). Most real loads fall between 0.7 and 1.0. If someone reports a PF above 1, it is usually a measurement error.

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Source: https://vastcalc.com/calculators/physics/power-factor
Category: Physics
Last updated: 2026-04-08