# Three-Phase Power Calculator

> Convert between three-phase current and power: kW, kVA and kVAR from line voltage, current and power factor, or the current a given kW load draws.

Category: Energy & environment · Applies to: Worldwide · Last updated: 2026-10-29
Interactive calculator: https://calculators.geekmidst.com/calculators/three-phase-power-calculator

In a balanced three-phase system, real power is √3 × line voltage × line current × power factor. Use it either way: amps to kW, or kW to amps.

Also called: 3-phase power calculator, kW to amps calculator (three-phase), Three-phase current calculator.

## Inputs
- Find (options: Power from current, Current from power; default from_current)
- Line-to-line voltage (unit V; default 400)
- Line current (unit A; default 10)
- Real power (unit kW; default 11)
- Power factor (default 0.85)

## Results
- Result
- Real power
- Line current
- Apparent power
- Reactive power

## Formula

```
P = √3 × V_L × I_L × PF;  S = √3 × V_L × I_L;  Q = S × sin(arccos PF);  I_L = P ÷ (√3 × V_L × PF)
```

Where:
- V_L: line-to-line voltage
- I_L: line current
- PF: power factor
- S: apparent power
- Q: reactive power

## Worked example
1. S = √3 × 400 × 10 = 6,928 VA = 6.928 kVA.
2. P = 6.928 × 0.85 = 5.889 kW.
3. Q = 6.928 × √(1 − 0.85²) = 6.928 × 0.5268 = 3.65 kVAR.

**Result:** A balanced 400 V three-phase load drawing 10 A at 0.85 power factor uses 5.889 kW.

## What the result means

Use current-from-power to size cables and protective devices, then apply the derating and starting-current rules in your local wiring regulations.

## Assumptions and limits
- The load is balanced across the three phases.
- Voltage is line-to-line (e.g. 400 V, not the 230 V phase-to-neutral value).
- Unbalanced loads need per-phase calculation.
- Motor starting currents are several times running current and are not included.

## Questions

### Where does √3 come from?

In a three-phase system the line-to-line voltage is √3 times the phase voltage, so total power 3 × V_phase × I equals √3 × V_line × I.

### What if I only know phase-to-neutral voltage?

Multiply it by √3 (about 1.732) to get line-to-line voltage; 230 V phase voltage gives about 400 V line voltage.

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Source: GM¹X CalcVerse — https://calculators.geekmidst.com/calculators/three-phase-power-calculator