Three Phase Calculator

The three-phase calculator helps you estimate apparent, active, and reactive powers in an AC circuit.

Three-phase real power11.7779 kWat a power factor of 0.85

RMS voltage120.2082 V0.707107 × the peak — a full sine averages zero over a cycle, so the mean quoted is of the rectified waveform

Peak voltage170 V

Peak to peak340 V

Rectified mean108.2254 V

Form factor1.110721RMS ÷ mean — 1.111 for a sine, and what a mean-reading meter must assume

Crest factor1.414214peak ÷ RMS — 1.414 for a sine

Why RMS and not the averageit is the DC-equivalent heating valuepower goes as the square of voltage, so the meaningful average is the root of the mean of the square

Period16.6667 ms

Angular frequency376.9911 rad/s

Ripple frequency after full-wave rectification120 Hztwice the supply — and only once the supply frequency after half-wave, which is why half-wave supplies need far more smoothing

Three-phase apparent power13.8564 kVA√3 × 400 V × 20 A

Reactive power7.2993 kVAR

Phase voltage230.9401 Vline ÷ √3 — the √3 appears because the phases are 120° apart, not because of any factor of three in the power

Power per phase3.926 kW

The formula

V_rms = V_peak ÷ √2 for a sine; three-phase power = √3 × V_L × I_L × pf

Why root mean square

An alternating voltage averages to zero over a cycle, so the average is useless for describing what it does. Power goes as the square of voltage, so the meaningful measure is the square root of the mean of the square — the RMS value, which is the DC voltage that would produce the same heating.

The peak-to-RMS factor depends entirely on the waveform. For a sine it is √2, so a 120 V RMS supply peaks at about 170 V — a fact that matters when choosing capacitor voltage ratings. A square wave has RMS equal to its peak, because it spends all its time there. A triangle wave gives peak/√3.

This is also why cheap multimeters mislead. Many measure the rectified average and multiply by 1.111, the form factor of a sine. On anything that is not a sine — a dimmer output, a switching supply, a motor drive — that assumption fails and the reading is simply wrong. A true-RMS meter squares the actual waveform.

In three-phase systems the √3 comes from the 120° phase relationship between line voltages, not from there being three phases. Line voltage is √3 times phase voltage, and total power is √3 × line voltage × line current × power factor.