Three-Phase Power Calculator

Real, reactive and apparent power from line voltage, line current and power factor — plus the phase voltage, phase current and per-phase impedance for a balanced star or delta load.

Last updated 22 Sep 2026

Three-phase power

V, I, PF → P, Q, S and phase values

Line voltage Vₗₗ (V)Between any two lines: 400 V or 415 V in India and most of the Gulf, 208 V or 480 V in North America.

Line current (A)The current measured in one line with a clamp meter, for a balanced load.

Power factorcos φ. About 0.85 for a loaded induction motor, 1.0 for heating elements.

Load connectionChanges the voltage across and the current through each of the three load branches — never the total power for the same line values.

Three lines feeding a balanced load, drawn in the connection you chose. In star every branch sees the line voltage divided by √3 and carries the full line current; in delta every branch sees the full line voltage and carries the line current divided by √3. The dots show the size of each RMS current; a real 50 Hz or 60 Hz current reverses a hundred or a hundred and twenty times a second, so the direction drawn is only a convention.

18.33kWExample

415 V line-to-line, 30 A per line, power factor 0.85, star-connected

Balanced three-phase quantities

P = √3 V_LL I_L cos φ S = √3 V_LL I_L Q = √(S² − P²); star: V_ph = V_LL/√3, I_ph = I_L; delta: V_ph = V_LL, I_ph = I_L/√3

V_LL: line-to-line voltage, the figure a three-phase supply is named by
I_L: line current — what a clamp meter reads on one incoming line
cos φ: power factor of the balanced load
Z: impedance of one branch = V_ph ÷ I_ph

Worked example

415 V line-to-line, 30 A per line, power factor 0.85, star-connected
S = √3 × 415 × 30 = 21,564 VA
P = S × 0.85 = 18,329 W (18.33 kW); Q = √(S² − P²) = 11,360 var
Star: each branch sees 415 ÷ √3 = 239.6 V and carries 30 A, so Z = 7.987 Ω per phase
Delta with the same line values: 415 V across each branch, 17.32 A through it, Z = 23.96 Ω
The same 18.33 kW drawn single-phase at 239.6 V would need 90.0 A — three times the current in one conductor

Star and delta, same line voltage and current

Computed from this page’s own formulas at the default inputs. The same three impedances reconnected from star to delta draw three times the power — that is how star-delta motor starting works.
Quantity	Star (Y)	Delta (Δ)
Voltage across each branch	V_LL ÷ √3 (239.6 V at 415 V)	V_LL (415 V)
Current through each branch	I_L (30 A)	I_L ÷ √3 (17.32 A)
Impedance of each branch	7.987 Ω	23.96 Ω — three times the star value
Total power	√3 V_LL I_L PF	the same
Neutral	may exist; carries no current when balanced	none

Three-phase power, star and delta

A three-phase supply is three alternating voltages of equal size, 120° apart. Its useful property is that the total power delivered to a balanced load is constant from instant to instant, where single-phase power pulses twice a cycle; that is why motors run more smoothly on it and why every industrial supply is three-phase.

The √3. Each branch of the load takes V_phase × I_phase × cos φ, and there are three of them. Written in the quantities you can actually measure at the incoming cable — the line-to-line voltage and the line current — that becomes P = √3 × V_LL × I_L × cos φ. The √3 is not a fudge factor: it is the ratio between the line and phase quantities, and it appears in the voltage for a star load and in the current for a delta one.

The example. 415 V, 30 A per line, power factor 0.85 is 21,564 VA of apparent power, 18.33 kW of real power and 11.36 kVAR of reactive power. Connected in star, each winding or element sees 239.6 V and carries the full 30 A, so each branch is 7.987 Ω. Connected in delta, the same line values mean 415 V across each branch and only 17.32 A through it, so each branch is 23.96 Ω — three times as much impedance for the same total power. Turn that round and you have the star-delta starter: the same motor windings in star draw a third of the current and produce a third of the torque of the same windings in delta.

Balanced, and what happens when it is not. These formulas assume the three phases carry equal currents. Domestic and small commercial installations are single-phase loads spread over three phases, so they are never exactly balanced, and the neutral carries the difference. Measure each line separately and add the three phase powers when the imbalance matters; the two-wattmeter method is the classic measurement for a three-wire load of any balance.

To go from watts to line amps directly, use the watts to amps calculator; to convert a kVA rating, the kVA to kW calculator; to correct a low power factor, the power factor calculator. Cable for a three-phase run is sized with the wire size calculator and checked with the voltage drop calculator.

Frequently asked questions

What is the formula for three-phase power?

P = √3 × line voltage × line current × power factor. With 415 V, 30 A and 0.85 that is 18.33 kW. Apparent power leaves out the power factor; reactive power is √(S² − P²).

Why √3 and not 3?

Because the three phases are 120° apart, not in step. Three times V_phase × I_phase is the same number as √3 × V_LL × I_L, since V_LL = √3 V_phase in a star system. Using 3 with line values overstates the power by √3.

Does star or delta change the power?

Not for the same line voltage and line current — the totals are identical. It changes what each branch sees: a delta branch takes the full line voltage and a third of the current of the same load in star, so for a given set of impedances, delta draws three times the power.

How do I measure three-phase power?

Clamp one line for the current, measure line-to-line for the voltage, and get the power factor from a meter or the motor’s nameplate. For anything but a balanced load, use a three-phase power meter or the two-wattmeter method.

Can I use this for 208 V or 480 V?

Yes — enter the line-to-line voltage, whatever it is. 208 V gives a phase voltage of 120 V, and 480 V gives 277 V.

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References

Hughes E, Hiley J, Brown K, Smith I M. Electrical and Electronic Technology, 12th ed. Pearson 2016: three-phase star and delta relationships, the power triangle and power-factor improvement.
IEC 60038:2009, IEC standard voltages: 230/400 V is the standard low-voltage three-phase system.
IEC 60364-4-43:2008, Low-voltage electrical installations — Protection against overcurrent, clause 433.1: I_B ≤ I_n ≤ I_Z and I₂ ≤ 1.45 × I_Z.