How to use this calculator
- Enter or choose find.
- Enter or choose line-to-line voltage.
- Enter or choose power factor.
- The result updates as you type. Use Copy result or Share to keep it.
Method
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)
- V_L
- line-to-line voltage
- I_L
- line current
- PF
- power factor
- S
- apparent power
- Q
- reactive power
Worked example
- S = √3 × 400 × 10 = 6,928 VA = 6.928 kVA.
- P = 6.928 × 0.85 = 5.889 kW.
- Q = 6.928 × √(1 − 0.85²) = 6.928 × 0.5268 = 3.65 kVAR.
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.