Online Tool Store
Three-Phase Power Calculator
Calculate three-phase line current and apparent power from line voltage, real power, and power factor, with the formula shown.
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Three-phase power calculator
Enter line voltage, real power, and power factor.
Line current
Apparent power
Formula
I = P / (√3 × V × cos φ)
How the Three-Phase Power Calculator works
- Enter the line-to-line voltage, which is the figure normally quoted for a three-phase supply.
- Add the real power in kW and the load's power factor.
- Read current and apparent power together, since cable and protection are sized on current, not kW.
The method
In a balanced three-phase system, real power depends on line voltage, line current, power factor, and the √3 factor that relates line and phase quantities.
P = √3 x V_line x I_line x cos φ, so I = P / (√3 x V x cos φ)
15,000 / (1.732 x 400 x 0.85) ≈ 25.5 A, and apparent power is 15 / 0.85 = 17.6 kVA.
FAQ
Where does the √3 come from?
From the 120-degree phase relationship between the windings: line voltage is √3 times phase voltage in a star connection, and the same factor appears in the power equation.
Why does power factor matter for cable sizing?
Because cables and protective devices carry current, not kilowatts. A poor power factor means more current for the same useful power, so the installation must be sized larger.
Is this valid for an unbalanced load?
No. These equations assume a balanced three-phase load. Unbalanced systems must be calculated per phase, including neutral current.
How we compare
| Feature | Online Tool Store | A graphing calculator | A stats package |
|---|---|---|---|
| Current and kVA together | ✓ | Formula needed | ✓ |
| Power factor included | ✓ | Manual | Yes |
| Explains the √3 factor | ✓ | ✗ | ✗ |
| Handles unbalanced loads | ✗ | ✗ | ✓ |
Three-Phase Power Calculator assumes a balanced load and says so — unbalanced installations need a per-phase calculation, including the neutral.