Three-Phase Power Calculator

Understanding the three-phase power calculator — concept and principle

This calculator finds the real power (kW) and apparent power (kVA) of a balanced three-phase load from the line-to-line voltage, line current and power factor, and shows the corresponding phase (line-to-neutral) voltage. It is used to size motors, generators, cables and breakers in industrial and commercial installations and to check what a three-phase supply can deliver.

Line voltage 400 V is √3 times the 230.9 V phase voltage — that is where the √3 comes from.

How it is calculated

Real power: P = √3 · V_L · I_L · cos φ, divided by 1000 for kW.
Apparent power: S = √3 · V_L · I_L, divided by 1000 for kVA.
Phase voltage (star): V_ph = V_L / √3.
Reactive power: Q = √3 · V_L · I_L · sin φ = √(S² − P²), in kvar.

The principle

A three-phase system has three sinusoidal voltages 120° apart. In a balanced load each phase carries the same power, V_ph · I_ph · cos φ, so the total is three times that. In a star (wye) connection the phase voltage is V_L/√3 and the phase current equals the line current; in a delta connection the phase voltage equals V_L and the phase current is I_L/√3. Either way, 3 · V_ph · I_ph = √3 · V_L · I_L. The √3 comes from the geometry of three phasors 120° apart: the distance between the tips of two unit phasors is √3. A balanced three-phase load also draws constant total power instead of a pulsating one, which is why large motors run smoothly on it.

Worked example

Inputs: V_L = 400 V, I_L = 32 A, PF = 0.9.
Apparent power: √3 × 400 × 32 = 22,170 VA = 22.170 kVA.
Real power: 22,170 × 0.9 = 19,953 W = 19.953 kW.
Phase voltage: 400 ÷ √3 = 230.94 V, the familiar 230 V of a 400 V system.
Reactive power: sin φ = √(1 − 0.81) = 0.43589, so Q = 22.170 × 0.43589 = 9.663788077 kvar.

Each point is the calculator re-run with only “Line-to-line voltage (V)” changed; the gold point is the default example. Change the inputs above and this chart follows your numbers.

Line-to-line voltage (V)	Real power (kW)
100	4.988306326
200	9.976612652
300	14.96491898
400	19.9532253
500	24.94153163
600	29.92983795
800	39.90645061

How to read the result

Compare the kVA with the rating of the transformer, generator or UPS and the current with the breaker and cable rating. Common low-voltage systems are 400/230 V (Europe and many other countries, including 380/220 V in Korea) and 208/120 V or 480/277 V in North America. A low power factor raises current for the same kW.

Common mistakes

Using the phase voltage with the √3 formula, which understates power by a factor of √3. Either use √3 · V_L · I_L or 3 · V_ph · I_ph.
Applying the formula to a heavily unbalanced load; then each phase must be calculated separately and added.
Forgetting motor efficiency: a motor's nameplate kW is mechanical output, so its electrical input is larger.

Keep in mind: The result assumes a balanced, sinusoidal system. Real installations must be designed to local electrical codes, with cable derating and protection checked by a qualified professional.

Frequently asked questions

How do I find the current for a given kW?

Rearrange the formula: I = P ÷ (√3 · V_L · PF). For 20 kW at 400 V and PF 0.9, I ≈ 32.1 A.

Is a 400 V three-phase supply more powerful than 230 V single-phase?

For the same current per conductor, yes, it delivers √3 × 400 ÷ 230 ≈ 3 times as much power.

Does star or delta change the power?

Not for the same line voltage and line current; the formula in line quantities is identical.

Sources: IEC 60038, IEC standard voltages · C. K. Alexander and M. N. O. Sadiku, Fundamentals of Electric Circuits, McGraw-Hill, chapter on three-phase circuits

Checked 8 Nov 2026. Standard textbook formulas in SI units, computed in your browser. For learning and estimates — real designs must follow your local codes and be checked by a qualified engineer.

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