# Three-Phase Power Calculator

URL: https://speedycalculator.com/calculators/physics/three-phase/
Last updated: 2026-10-30

> The three-phase power calculator finds the real, apparent and reactive power of a balanced three-phase load from line voltage, line current and power factor, plus the phase voltage and current for star (wye) or delta connections.

## Inputs

- Connection
- Line voltage V_L (V, kV, mV)
- Line current I_L (A, mA, µA, kA)
- Power factor

## Results

- Real power P
- Apparent power S
- Reactive power Q
- Phase voltage
- Phase current
- Phase angle

## Formula

```
P = √3·V_L·I_L·PF,  S = √3·V_L·I_L,  Q = √(S² − P²) · Star: V_ph = V_L/√3, I_ph = I_L · Delta: V_ph = V_L, I_ph = I_L/√3
```

## Explanation

Three-phase power delivers smooth, efficient power for motors and industry. In a star connection each phase sees the line voltage divided by √3; in a delta, each phase carries the line current divided by √3.

### How to use the Three-Phase Power Calculator

- **Connection**
- **Line voltage V_L**
- **Line current I_L**
- **Power factor**

Results update as you type, every field has its own unit menu, and everything is calculated in your browser.

### How it works

Choose the connection, enter the line voltage, line current and power factor.

### Inputs explained

FieldWhat to enterConnectionChoose one: Star (wye), DeltaLine voltage V_LUnits: V, kV, mVLine current I_LUnits: A, mA, µA, kAPower factorA number

### What each result means

- **Real power P** = sqrt(3)×[Line voltage V_L]×[Line current I_L]×[Power factor]÷1000
- **Apparent power S** = sqrt(3)×[Line voltage V_L]×[Line current I_L]÷1000
- **Reactive power Q** = [Apparent power S]×sqrt(1 - [Power factor]^2)
- **Phase angle** = deg(acos([Power factor]))

### Example values

How the main result changes when **Line voltage V_L** changes and everything else stays at the example values above:

Line voltage V_L (V)Real power P (kW)2005.8893008.833540011.777950014.722460017.666980023.5559

## Worked example

Inputs — Connection: Star (wye); Line voltage V_L: 400 V; Line current I_L: 20 A; Power factor: 0.85.

Results — **Real power P = 11.77795 kW**; Apparent power S = 13.85641 kVA; Reactive power Q = 7.29932 kVAR; Phase voltage = 230.94011 V; Phase current = 20 A; Phase angle = 31.7883 °.

## Key terms

- **Line voltage**: Voltage between two phase conductors.

## FAQ

**Why √3?**
Line voltages are 120° apart, so V_L = √3·V_ph in star.

**Is total power the same in star and delta?**
Yes, for the same line voltage and current.

**What is a balanced load?**
Equal impedance on all three phases.

**Why is three-phase used for motors?**
It creates a rotating field and smooth torque.


## Sources

- [OpenStax – University Physics Volume 2](https://openstax.org/details/books/university-physics-volume-2)
- [The Engineering ToolBox](https://www.engineeringtoolbox.com/)