What the calculator does
Give it the voltage, the type of supply and any one of real power, current, apparent power or a motor's rated shaft output, and it returns the others: the line current in amperes, the real power in kW, the apparent power in kVA, the reactive power in kVAr and the phase angle. It is the arithmetic behind sizing a cable, a breaker, a contactor, a transformer or a generator for a known load.
For a motor, enter the nameplate output in hp and the efficiency: the electrical input is larger than the shaft output by the losses, and the current is drawn from the input. One mechanical horsepower is taken as 745.7 W.
Formula
Single-phase: P = V × I × cos φ S = V × I
Three-phase (balanced): P = √3 × VLL × I × cos φ S = √3 × VLL × I
Q = √(S² − P²) φ = arccos(PF)
Motor input P = output (hp) × 745.7 W ÷ η
where P is real power in watts, S apparent power in volt-amperes, Q reactive power in volt-amperes reactive, I line current, VLL the line-to-line voltage of a three-phase supply, cos φ the power factor and η the motor efficiency. The current in a balanced three-phase circuit is the same in each line; the calculator reports that line current.
Worked example
A 15 kW three-phase load at 400 V with a power factor of 0.85.
- I = 15 000 ÷ (√3 × 400 × 0.85) = 15 000 ÷ 588.9 = 25.47 A per line.
- S = 15 ÷ 0.85 = 17.65 kVA, which is what the transformer or generator must supply.
- Q = √(17.65² − 15²) = 9.30 kVAr; phase angle φ = arccos 0.85 = 31.8°.
The same 15 kW at unity power factor would draw only 21.65 A. That difference is the reason low power factor costs money in cables, switchgear and tariff penalties; the power factor correction calculator works out the capacitor bank that closes the gap.
For a 10 hp motor at 400 V, 0.85 power factor and 90 % efficiency: input = 10 × 745.7 ÷ 0.9 = 8.29 kW, so I = 8 286 ÷ 588.9 = 14.07 A and S = 9.75 kVA.
Typical full-load power factors
| Load | Power factor | Note |
|---|---|---|
| Resistive heaters, incandescent lighting | 1.0 | no reactive component |
| LED and fluorescent lighting with electronic drivers | 0.9–0.95 | lower for cheap drivers without correction |
| Induction motors, full load | 0.80–0.90 | larger motors are higher; fall to 0.5–0.6 at light load |
| Welders, older transformer type | 0.5–0.7 | intermittent, high inrush |
| Switch-mode power supplies, computers | 0.6–0.7 (no PFC) / 0.95+ (active PFC) | check the datasheet |
| Air conditioners, refrigeration | 0.80–0.90 | inverter types are higher |
Assumptions and limitations
- Balanced three-phase. The three lines are assumed to carry equal current. Unbalanced loads carry current in the neutral and the lines differ; calculate each phase separately.
- Sinusoidal waveforms. Loads with electronic power supplies or drives draw distorted current, so the true power factor (displacement × distortion) is lower than the displacement factor alone and the current is higher than this calculator reports for the same kW.
- Running current only. Motors draw five to eight times full-load current when started direct-on-line; breaker and generator selection must allow for it (see the generator sizing calculator).
- Horsepower is mechanical (745.7 W). Some nameplates use metric horsepower (735.5 W); the difference is 1.4 %.
- Not a cable or breaker selector. The current here is the starting point; cable sizing then depends on installation method, grouping, ambient temperature and voltage drop.
Frequently asked questions
Which voltage do I enter for a three-phase supply?
The line-to-line voltage, 400 V for the usual 230/400 V supply in Pakistan and most of the world. If you enter 230 V for a three-phase load you will get a current √3 times too high.
What is the difference between kW and kVA?
kW is the real power that does work and appears on the energy meter. kVA is the apparent power, the product of voltage and current that the wiring and the supply must carry. They are equal only at unity power factor; otherwise kVA = kW ÷ power factor. Generators and transformers are rated in kVA because they are limited by current, not by useful work.
Does a three-phase motor draw less current than a single-phase one of the same power?
Per line, yes. The same 5 kW at 0.85 power factor draws about 25.6 A single-phase at 230 V but only 8.5 A per line at 400 V three-phase, which is why anything above a few kilowatts is three-phase where a supply is available.
Why do I need efficiency for a motor but not for other loads?
A motor nameplate gives the mechanical output at the shaft. The electricity it draws is that output plus its losses, so the input power is output ÷ efficiency. Other loads are rated by their electrical input already.
References
- IEC 60038:2009, IEC standard voltages — 230/400 V as the standard low-voltage three-phase four-wire system
- IEEE Std 1459-2010, Definitions for the Measurement of Electric Power Quantities — real, apparent and reactive power under sinusoidal and non-sinusoidal conditions
- IEC 60034-1:2022, Rotating electrical machines — Rating and performance — motor rating conventions: output power, efficiency and power factor on the nameplate