Three waves, evenly spaced.

In an ideal balanced three-phase system, the three phase voltages have the same frequency and amplitude. They are separated by 120 electrical degrees: one third of a cycle.

The phases exist at the same time. They do not take turns switching fully on and off.

See the phase relationship.

Follow the positive peaks: L1 → L2 → L3 → L1

Three phases: equal frequency, different timingThree balanced 50 hertz phase-to-neutral sine waves share one time axis from 0 to 20 milliseconds. All have the same approximately 325 volt peak, corresponding to 230 volts RMS. L1 is solid charcoal, L2 dashed orange, and L3 dotted grey. L1 peaks at 0 milliseconds, L2 at 6.67, L3 at 13.33, and L1 again at 20. Each adjacent peak is separated by 120 electrical degrees, or approximately 6.67 milliseconds; one complete cycle is 360 degrees and 20 milliseconds. All three voltages are relative to the same neutral reference.Phase-to-neutral voltage (V)05101520+3250−325Time (ms)L1L2L3L1120°6.67 ms120°6.67 ms120°6.67 msOne cycle = 20 ms (360°)
  1. One common voltage reference. The curves are L1-to-neutral, L2-to-neutral and L3-to-neutral. They are not voltages measured between two phases.
  2. Same frequency, different phase. Each wave repeats every 20 ms. Adjacent positive peaks are a third of a cycle apart: 20 ÷ 3 ≈ 6.67 ms, equivalent to 120°.
  3. Line style identifies each phase. L1 is solid, L2 dashed and L3 dotted. The waves coexist throughout the cycle; none waits for another to finish.
Original plot of an ideal balanced 50 Hz supply. A 230 V RMS phase-to-neutral sine wave has a peak of approximately 325 V; voltage labels are rounded. The example phase sequence is L1 → L2 → L3.

Follow the peaks: each phase reaches the same point in its cycle at a different time. At 50 Hz, a third of a cycle is approximately 6.67 milliseconds.

Which two points are being compared?

Voltage is always measured between points. Phase-to-neutral voltage and phase-to-phase voltage are different quantities.

Here RMS (root mean square) means the effective voltage, expressed by its equivalent heating effect in a resistor. The AC and DC lesson explains why RMS and peak values differ.

For a balanced sinusoidal star supply, the phase-to-phase RMS voltage is √3 times the phase-to-neutral RMS voltage. A nominal 230 V phase-to-neutral example therefore gives approximately 400 V phase-to-phase—not 690 V.

Why it is useful for motors.

Three-phase currents in suitably arranged stator windings create a rotating magnetic field. The motor can use that field to produce torque.

A VFD can generate a controlled three-phase output for a motor. The frequency of that output need not match the incoming mains frequency.

Balance is an ideal, not an assumption.

Real supplies and loads can be unbalanced. Losing a phase or having unequal conditions may affect operation and needs proper engineering investigation.

Understanding three-phase electricity helps explain a fault report. It does not provide instructions for changing connections or testing a live supply.

A closer look

For balanced sinusoidal three-phase operation, real power is √3 × line-to-line RMS voltage × line RMS current × power factor. This assumes the stated balanced conditions; it is not a universal shortcut for distorted or unbalanced measurements.

Check your understanding

Are three phases 120 degrees apart three different frequencies?

Reveal the explanation

No. In the balanced system shown they have the same frequency. The 120-degree separation is a difference in phase position.

Further reading.

Optional reading to explore this lesson in more detail.

  • Fluke: understanding phase relationships

    Read the basics subsection and its first diagram for the 120-degree relationship. This is a manufacturer’s explanation of measurement displays, rather than a guide to wiring a supply.

  • OpenStax: RMS and peak voltage

    Section 20.5 and Example 20.9 explain RMS and peak values for a sine wave. This supports the voltage terminology; it does not cover three-phase connections.