When to use this calculator

Three-phase power calculations come up whenever a load, source or piece of equipment needs to be checked against its rating. Common uses include:

Sizing feeders, transformers and generators from a load given in kW, kVA or motor horsepower
Finding line current from a nameplate kVA and voltage, or kVA from a measured current
Converting between real, reactive and apparent power when only two of them are known
Checking a facility's power factor and sizing capacitor banks to avoid utility power factor penalties
Finding phase voltage and current for wye- or delta-connected loads

3-Phase Power Calculator

Select the values you know in box 1 and enter them in box 2. The calculator automatically determines which additional values can be calculated. Select a load configuration to also calculate phase voltage and phase current.

1. Select Known Parameters

Select each input that's known.

2. Enter Known Values

Enter the known inputs here to calculate the values to the right. Unit selections also set the units shown for calculated values.

Load Configuration

Power factor direction

3. Power Factor Correction (optional)

Size a shunt capacitor bank to raise a lagging power factor to a target value. Real and reactive power must be known or calculable.

Calculate capacitor kVAR for a target power factor

Target power factor, lagging (0–1)

Example: 480 V, 1,000 kVA and 0.8 lagging power factor corrected to 0.95 lagging.

Equations and calculation basis

Three-phase apparent power: S = √3 × V_LL × I_L / 1,000
S = √(P² + Q²)
Real and reactive power: P = S × PF
|Q| = S × √(1 − PF²)
Line current and voltage: I_L = 1,000 × S / (√3 × V_LL)
V_LL = 1,000 × S / (√3 × I_L)
Power factor from two power values: PF = P / S
PF = √(1 − (Q / S)²)
PF = P / √(P² + Q²)
Apparent power from power factor: S = P / PF
S = |Q| / √(1 − PF²)
Wye phase values: V_phase = V_LL / √3
I_phase = I_L
Delta phase values: V_phase = V_LL
I_phase = I_L / √3
Phase angle: φ = cos⁻¹(PF)
tan φ = Q / P
Power factor correction: Q_C = P × (tan φ₁ − tan φ₂)
φ₁ = existing angle, φ₂ = cos⁻¹(target PF)
Motor horsepower: P_kW = hp × 0.7457 / η
η = motor efficiency (hp is shaft output)

P is real power in kW, Q is reactive power in kVAR, and S is apparent power in kVA. Voltage is in volts and current is in amperes. PF is the magnitude of cos φ, from 0 to 1. This calculator uses nonnegative real power and reports positive Q for lagging loads and negative Q for leading loads.

Power factor is undefined at zero apparent power. These equations assume balanced sinusoidal voltages and currents, they do not account for harmonics or phase imbalance. Select Load Configuration to calculate phase values. Wye or Delta changes phase values, not total power for the same line voltage and current.

When more inputs are provided than necessary, the calculator checks them for consistency. Differences greater than 0.1% are flagged; rounded entries within that tolerance are accepted.

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