3-Phase Power Calculator
Calculate three-phase power from line voltage, line current and power factor — apparent kVA, real kW and reactive kVAR.
How it works
apparent kVA = √3 × V(line) × I(line) ÷ 1000 · real kW = kVA × PF · reactive kVAR = kVA × sin(arccos PF)
In a balanced three-phase system the √3 factor (about 1.732) links the line-to-line voltage and line current to total power across all three phases. Apparent power (kVA) is what the conductors and transformer must carry; real power (kW) is the useful work, scaled down by the power factor; and the reactive part (kVAR) is the magnetizing current that circulates without doing work. Improving power factor toward 1.0 moves kVA closer to kW and frees up capacity.
Worked example
A motor on 480 V three-phase drawing 30 A at 0.9 PF: apparent = 1.732 × 480 × 30 ÷ 1000 = 24.94 kVA. Real power = 24.94 × 0.9 = 22.44 kW, and reactive power = 24.94 × sin(25.8°) = 10.87 kVAR.
Frequently asked questions
Why the √3 factor?
The three phases are 120° apart, so their voltages and currents add vectorially rather than arithmetically. Working the geometry through for a balanced load leaves the familiar √3 (≈1.732) between line and total quantities.
Line-to-line or line-to-neutral voltage?
This formula uses line-to-line voltage (e.g. 480 V, 208 V). If you only have the line-to-neutral value, multiply it by √3 first, or use the equivalent 3 × Vphase × Iphase form.
What is a good power factor?
Utilities like to see 0.95 or better. Motors at light load and older equipment can sag to 0.7–0.8, wasting capacity and sometimes drawing a penalty; capacitor banks or synchronous correction bring it back up.
Related calculators
Educational estimates only — electrical work must follow the National Electrical Code (NEC) and local amendments, and be done or inspected by a licensed electrician.