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Three-Phase Real Power

Also known as 1.732 formula · three phase kW · √3 power formula

P=3 VLIL PFP = \sqrt{3} \, V_{L} I_{L} \, \text{PF}
sig figs

Worked example: 480 V, 100 A, 0.85 PF → 70.67 kW. Press Try an example to run it live, then adjust anything.

Enter your known values, leave one input blank, and solves for the missing one. Tap a variable’s symbol to see what it means, with a typical value. Change any unit and the answer follows.

Constant used: built into this formula, no need to enter
3=1.7320508075688772\sqrt{3} = 1.7320508075688772Square Root of Three · exact

Where Three-Phase Real Power fits

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Your answer feeds
Power Factor from Real and Apparent PowerReactive Power (Power Triangle)Power-Factor Correction kvarMotor Efficiency
In these toolkits

See also

Single-Phase Real Power with Power Factor: Both use real power and line current.Three-Phase Motor Full-Load Current: Both use line-to-line voltage and power factor.Power Factor from Real and Apparent Power: Both use real power and power factor.Power-Factor Correction kvar: Both use real power and power factor.Delta Line and Phase Current: Both use line current.Voltage Drop, Three Phase: Both use line current.
5 more relatedMotor Locked-Rotor Starting Current: Both use line-to-line voltage.Three-Phase Apparent Power: Both use line-to-line voltage.Wye Line and Phase Voltage: Both use line-to-line voltage.Phase Angle from Power Factor: Both use power factor.Transformer Efficiency from Core and Copper Losses: Both use power factor.
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Three-Phase Real Power explained

MPVLILPF

The √3 is the whole story of three-phase power. Each of the three phases carries Vphase × Iphase, but the meter and the nameplate quote line quantities, and the 120° spacing between phases turns the sum of three phase powers into √3 × VL × IL. Multiply by the power factor and you have the real, billable, heat-and-torque-producing watts. A 480 V feeder carrying 100 A at 0.85 PF delivers 1.732 × 480 × 100 × 0.85 ≈ 70.7 kW.

The trap is mixing line and phase values: the √3 belongs in the formula only when VL and IL are both line quantities. Drop the power factor and you get apparent power in VA, not watts: the two differ by 15% on that feeder, which is exactly why a 100 kVA transformer will not carry 100 kW of motor load. Nikola Tesla's polyphase patents of 1888 made this arithmetic the foundation of every industrial plant since.

Three-Phase Real Power formula

P=3 VLIL PFP = \sqrt{3} \, V_{L} I_{L} \, \text{PF}
Where
  • PP= Real power (W)
  • VLV_{L}= Line-to-line voltage (V)
  • ILI_{L}= Line current (A)
  • PF\text{PF}= Power factor
In these toolkits

Three-phase power and power factor

8 formulasReal, reactive and apparent power, power factor, phase angle and correction kvar — the power triangle as an electrician uses it.

Motor calculations

5 formulasFull-load current, synchronous speed, slip, efficiency and input power — reading a motor nameplate and checking what it actually draws.

Revised 16 October 2026
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formula.expert. (2026, October 16). Three-Phase Real Power Formula & Calculator. https://formula.expert/solvers/three-phase-real-power

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