Three-Phase Real Power

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

P = \sqrt{3} \, V_{L} I_{L} \, \text{PF}

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

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\sqrt{3} = 1.7320508075688772

Square Root of Three · exact

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Three-Phase Real Power explained

The √3 is the whole story of three-phase power. Each of the three phases carries V_phase × I_phase, but the meter and the nameplate quote line quantities, and the 120° spacing between phases turns the sum of three phase powers into √3 × V_L × I_L. 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 V_L and I_L 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 = \sqrt{3} \, V_{L} I_{L} \, \text{PF}

Where

$P$ = Real power (W)
$V_{L}$ = Line-to-line voltage (V)
$I_{L}$ = Line current (A)
$\text{PF}$ = Power factor

Missing one of these? Work it out first, then come back

Real power — Single-Phase Real Power with Power Factor, Power Factor from Real and Apparent Power
Line-to-line voltage — Single-Phase Real Power with Power Factor, Three-Phase Apparent Power
Line current — Single-Phase Real Power with Power Factor, Three-Phase Apparent Power
Power factor — Single-Phase Real Power with Power Factor, Power Factor from Real and Apparent Power

Part of these formula sets

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.