What is the three-phase power formula?

P = √3 × V_L × I_L × PF, where V_L is line-to-line voltage in volts, I_L is line current in amps, and PF is the power factor (0 to 1). For example, 400 V, 10 A, PF 0.8 gives P = √3 × 400 × 10 × 0.8 = 5,542.56 W.

How do I calculate apparent power S in three-phase?

S = √3 × V_L × I_L, in volt-amperes (VA). Apparent power is the vector sum of real power P and reactive power Q, so S is always equal to or larger than P.

How do I find the line current from kW in three-phase?

Rearrange the power formula: I = P ÷ (√3 × V_L × PF). For a 5.5 kW motor at 400 V with PF 0.8: I = 5,500 ÷ (√3 × 400 × 0.8) = 9.9232 A.

What is the difference between wye (star) and delta connections?

In wye, V_L = √3 × V_ph and I_L = I_ph, with a neutral point available. In delta, V_L = V_ph and I_L = √3 × I_ph, with no neutral. The line quantities V_L and I_L are what you measure between phases and in each supply wire.

How do I size a power factor correction capacitor bank?

Required reactive power is Qc = P × (tan φ₁ − tan φ₂), where φ₁ and φ₂ are the phase angles before and after correction. For delta-connected capacitors, each capacitor is C = Qc ÷ (3 × 2πf × V_L²); for wye it is three times larger: C = Qc ÷ (2πf × V_L²).

How do I convert kW to horsepower (HP)?

Divide watts by 745.7 (mechanical HP). For example, 5,542.56 W ÷ 745.7 = 7.4327 HP. This tool shows HP alongside kW in every power result.

Why does three-phase use less current than single-phase for the same power?

Three-phase delivers power through three conductors, so I_3ph = P ÷ (√3 × V_L × PF) versus I_1ph = P ÷ (V × PF). A 5.5 kW load at PF 0.8 draws 29.89 A on 230 V single-phase but only 9.92 A on 400 V three-phase — about 3 times less.

How do I calculate reactive power Q?

Q = √(S² − P²), in volt-amperes reactive (var). It represents power oscillating between source and load due to inductance or capacitance; for 400 V, 10 A, PF 0.8, Q = √(6,928.20² − 5,542.56²) = 4,156.92 var.

What is the relationship between 400 V line and 230 V phase voltage?

In a wye system, V_ph = V_L ÷ √3, so 400 V ÷ √3 = 230.94 V. That is why 400 V three-phase outlets can also supply 230 V single-phase between any phase and neutral.

What power factor values are typical for common loads?

Resistive heaters ≈ 1.0, induction motors 0.7–0.9 depending on load, fluorescent lighting 0.5–0.9, and variable-speed drives 0.9+ with correction. Utilities often penalize power factors below 0.85–0.9, which is when capacitor banks pay off.

Does frequency (50 Hz vs 60 Hz) matter for these calculations?

P, S, Q, and line/phase conversions do not depend on frequency. Frequency only affects capacitor sizing for power factor correction, since C = Qc ÷ (3 × 2πf × V_L²) — a 60 Hz bank needs about 17% less capacitance than a 50 Hz bank for the same kVAR.

Can I use this calculator for 208 V, 415 V, or 480 V systems?

Yes — enter any line voltage; presets include 208, 380, 400, 415, and 480 V. The √3 formulas are identical for every three-phase system; only the numbers change.

What is line voltage versus phase voltage?

Line voltage (V_L) is measured between any two phase conductors; phase voltage (V_ph) is measured between one phase and neutral (wye) or across one winding (delta). In wye they differ by √3; in delta they are equal.

Which related tools should I use next?

For general electrical unit conversion use the electrical unit converter , for voltage-specific conversions (divider, dB) use the voltage converter , and for sizing conductors by current and distance use the 12 V wire size calculator . This tool covers three-phase power, current, power factor correction, and line/phase conversion in one place.

Three Phase Power Calculator

Real power P = √3·V_L·I_L·PF, apparent power S, reactive power Q, current solver, wye/delta line↔phase conversion, power-factor correction capacitor sizing, and a single-phase comparison — all in one page, 100% in your browser.

Three-phase power from V, I, PF

Enter line-to-line voltage, line current and power factor. Balanced 3-wire/4-wire system assumed.

Line voltage V_L (V)

Line current I_L (A)

Power factor PF (0–1)

Formulas & methodology

All calculations assume a balanced three-phase system (equal phase loads). Line quantities V_L, I_L are what you measure with a multimeter/clamp meter on the supply conductors.

P = √3 · V_L · I_L · PF (watts)

S = √3 · V_L · I_L (volt-amperes)

Q = √(S² − P²) (volt-amperes reactive)

I = P ÷ (√3 · V_L · PF) (current solver)

Qc = P · (tan φ₁ − tan φ₂); C_Δ = Qc ÷ (3·2πf·V_L²), C_Y = Qc ÷ (2πf·V_L²)

Wye vs delta reference

Relation	Wye (Y)	Delta (Δ)
Voltage	V_L = √3 · V_ph	V_L = V_ph
Current	I_L = I_ph	I_L = √3 · I_ph
Neutral	Yes	No

Worked example

A 400 V, 10 A, PF 0.8 load: P = √3 × 400 × 10 × 0.8 = 5,542.56 W; S = √3 × 400 × 10 = 6,928.20 VA; Q = √(6,928.20² − 5,542.56²) = 4,156.92 var; power angle φ = arccos(0.8) = 36.87°; that is 7.4327 HP.

Scope boundary

This tool covers: three-phase power/current/PF calculations, wye↔delta line/phase conversion, capacitor bank sizing, and 1-phase vs 3-phase comparison.

Not duplicated here: general unit conversion lives in the electrical unit converter; voltage divider, dB and RMS voltage tools live in the voltage converter; conductor sizing by length and ampacity lives in the 12 V wire size calculator.

Frequently asked questions

Free tool by NRTechStudio

Three Phase Power Calculator

Three-phase power from V, I, PF

Line current from power

Power factor correction capacitor

Line ↔ phase conversion (wye / delta)

Single-phase vs three-phase comparison

Formulas & methodology

Wye vs delta reference

Worked example

Scope boundary

Frequently asked questions

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