Three-phase power calculator
The sqrt(3) in three-phase arithmetic comes from the 120-degree phase relationship, not from anything mysterious.
V
A
%
Real power
12 470.77W
- Apparent power
- 13 856.41 VA
- Reactive power
- 6039.868 var
- Mechanical output at that efficiency
- 11 473.1
- Shaft power
- 15.386 hp
- Line-to-neutral voltage
- 230.94 V
- Phase angle
- 25.842 degrees
Show the working
- Line-to-line voltage = 400
- Line current = 20
- Power factor = 0.9
- Motor efficiency = 92
- root3 = sqrt(3) = 1.732 05
- Apparent power = 1.732 05 * 400 * 20 = 13 856.4
- Real power = 13 856.4 * 0.9 = 12 470.8
- Reactive power = 13 856.4 * sqrt(max(1 - 0.9^2, 0)) = 6039.87
- Mechanical output at that efficiency = 12 470.8 * 92 / 100 = 11 473.1
- Shaft power = 11 473.1 / 745.69987158227022 = 15.3857
- Line-to-neutral voltage = 400 / 1.732 05 = 230.94
- Phase angle = deg(acos(clamp(0.9, -1, 1))) = 25.8419
Values are shown to six significant figures here; the arithmetic itself runs on exact fractions and is only rounded where a number is printed.
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The formula
- S = sqrt(3) V_LL I
- P = S x power factor
- Q = S sin(arccos(pf))
- V_LN = V_LL / sqrt(3)
A 400 V three-phase system has 231 V between each line and neutral, which is the familiar single-phase supply.