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Three-phase calculator

Use balanced sinusoidal RMS measurements. Phase quantities refer to each load winding; line quantities refer to the supply conductors.

Calculator

Phase voltage
100
Phase current
10
Line-to-line voltage
173.205
Line current
10
Total apparent power (VA)
3,000.00000000
Total real power
2,400
Reactive power magnitude (var)
1,800.00000000
Power factor
0.80000000
Displacement angle magnitude
0.643501

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How this calculator works

In a balanced star load, each winding sees line-to-line voltage divided by the square root of three, and winding current equals line current. In delta, each winding sees line voltage while line current is the square root of three times winding current. Total power sums three equal phase powers. Reactive power is reported as a magnitude because leading or lagging behaviour is not specified. The phase-angle relation assumes sinusoidal waveforms without distortion.

Formula

S = 3 Vphase Iphase = sqrt(3) Vline Iline; P = S cos(phi); |Q| = S sin(phi). Star: Vline = sqrt(3)Vphase, Iline = Iphase. Delta: Vline = Vphase, Iline = sqrt(3)Iphase.

Worked example

A star load with 100 V per phase, 10 A per phase and power factor 0.8 has line voltage 173.2051 V, S = 3000 VA, P = 2400 W and reactive magnitude 1800 var.

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Frequently asked questions

Are phase voltage and line-to-neutral voltage always the same?

They match for a star-connected load with the stated reference. A delta winding is connected line-to-line.

Can I use this for an unbalanced load?

No. Calculate each phase with its own complex voltage and current instead.

Does the tool distinguish leading and lagging power factor?

It reports magnitudes only. The sign of reactive power requires knowing whether the load is capacitive or inductive.

Sources

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