Why Three-phase Voltage is 440 Volts?

As we know, the voltage is the difference in potential between the two-point.

Single-phase

A single-phase power system is one where there is only one alternating voltage source.

Single-phase consists of just two conductors, one is called phase and the other is neutral.

Voltage is measured between a phase and neutral.

Three-phase

While the 3 phase is the voltage between any two out of those three phases.

In 3 phase supply, there are 3 supply lines phase shifted at 120 degrees from each other.

So the net voltage difference between the two phases in accordance with the phase angle of 120 degrees is 440V.

Three-phase power system

As shown in the figure below, the 3 phase supply has three wires (RYB).

The voltage across any one phase and neutral is 220V, and the voltage across the 3 phase is 440V because we check the voltage between any two-phase RY or YB or BR.

Why Three-phase Voltage is 440 Volts

Why 440 volts?

Consider one sine wave that has a maximum amplitude of 220 with respect to its axis. So be it in a positive cycle or in a negative it can go to a max of 220 (+220 or -220).

But when you consider the voltage between one phase to the other then it becomes 440.

Now all the 3 phases have the same max RMS value. That is if considered any of the phases and check their voltage against neutral it will come to 220 or 240 volts or so.

While in the case of three phases the voltage can be used between two phases instead of one phase and neutral. Be it three phases but you can calculate voltage between any two of them at a time.

The maximum voltage that one can get from any two phases is when one is at the top of its positive cycle (i.e +220) and the other at the lowest of its negative cycle (-220).

If we check the voltage between these two points then it is 440 volts ((+220)-(-220)=440).

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12 thoughts on “Why Three-phase Voltage is 440 Volts?”

    • No it is NOT correct.

      You do not take the phase to phase voltage as double the phase to neutral voltage.

      I did the mathematical analysis many years ago when I was at university.

      The voltage of the two phase conductors are not going up and down together with a phase difference of zero degrees.
      Also the voltages are not 180 degrees out of phase with each other, and this is the only way you could obtain a phase to phase voltage which is double the phase to neutral voltage.

      The voltage wave forms in a 3 phase system have 120 degrees phase difference. There are only two ways to calculate the phase to phase voltage, the first is to use trigonometry, sin() function, or use complex numbers to represent each sinusoidal waveforms and do conversions from polar form to argand form and back again.

      220 volts phase voltage is 380 volts phase to phase.

      ALL posters on this website saying anything different are wrong.

      Reply
  1. this article need some modification

    the relation between the voltage of (phase to phase)=sqrt(3) phase to neutral

    we don’t multiply by two

    BR

    Reply
  2. It’s not just multiplied by 2, it’s taking 220 times root 3 then dividing it by the sin of 120(phase to phase angle in 3 phase) so 220×1.732/0.866=440

    Reply
    • This is so wrong: you are mixing up peak voltage and rms voltage in your calculation.
      All the other guys who protest are correct in a 3ph system where neutral to 1ph is 220, the 3ph voltage (from one ph to another) is approx 380V.
      Or 230/400,
      or 254/440
      or 277/440.
      The factor is sq.root of 3. It is pure trigonometry.
      Just don’t mix up peak voltage and rms voltage.

      Reply
  3. AHA is correct
    This article needs to be fixed.
    Examples of 3 Phase converted to single Phase Live/N:
    440V 3 Phase = 440/sqrt(3) = 254V
    415V 3 Phase = 415/sqrt(3) = 240V
    380V 3 Phase = 380/sqrt(3) = 220V
    200V 3 Phase = 200/sqrt(3) = 115V

    If you don’t believe this check the supplies in your own country
    Please fix this website.

    Reply
  4. “the voltage across the 3 phase is 440V because we check the voltage between any two-phase RY or YB or BR”

    Just consider any phase to phase visually and you can see that the voltage cannot be 440VAC.
    120 degree difference in phase relationship negates the possibility.
    For a 440VAC solution, two sines would have to be perfectly in phase.

    Reply
  5. 220V Line to Neutral is 380V Line-Line for 3-phase power. Curtis Gomez is correct. The three phases are120 degrees apart, not 180 degrees apart. Please fix this article.

    Reply

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