Calculate real, apparent, and reactive power for a balanced three-phase electrical system from line voltage, line current, and power factor.
Quick Facts
Formula
P = √3 × V_line × I_line × PF
Apparent power S drops the PF term; reactive power Q = S × sin(φ), where φ = cos⁻¹(PF).
Results
Calculated
Real Power (P)
—
True power doing work
Apparent Power (S)
—
Total power delivered
Reactive Power (Q)
—
Non-working power
Phase Voltage
—
Per-phase voltage for the chosen connection
Ready
Enter line voltage, current, and power factor, then press Calculate.
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How to use this calculator
Enter the line-to-line voltage, the line current, and the power factor of the load, then choose whether the system is wired wye (star) or delta. Click Calculate to get real, apparent, and reactive power plus the per-phase voltage. Click Clear to reset all fields and start a new calculation.
Understanding the inputs
Line-to-line voltage is the RMS voltage measured between any two of the three supply lines (400 V and 480 V are common industrial values). Line current is the RMS current flowing in each line. Power factor is cos(φ), the ratio of real power to apparent power, ranging from just above 0 (highly reactive load) to 1 (purely resistive load). Connection type only affects the phase voltage shown in the results — the power formulas use line values and give the same total power for either wiring.
Interpreting the results
Real power (P, kW) is the power actually converted to work, heat, or light. Apparent power (S, kVA) is the total power the source must supply, including the portion used to build magnetic and electric fields in motors and transformers. Reactive power (Q, kVAR) is that non-working portion. Together they form a right triangle where S² = P² + Q². A power factor near 1 means most apparent power is doing useful work; a low power factor means the system carries a large reactive burden relative to the useful output.
Frequently Asked Questions
What is the formula for three-phase power?
Real power in a balanced three-phase system is P = √3 × V_line × I_line × PF, where V_line is the line-to-line voltage, I_line is the line current, and PF is the power factor (cosine of the angle between voltage and current). Apparent power drops the PF term: S = √3 × V_line × I_line.
What is the difference between wye (star) and delta connections?
In a wye (star) connection, the line voltage is √3 times the phase voltage and the line current equals the phase current. In a delta connection, the line voltage equals the phase voltage and the line current is √3 times the phase current. Total power works out the same either way when calculated from line values.
What is the difference between real, apparent, and reactive power?
Real power (kW) is the power that actually does work, such as running a motor. Apparent power (kVA) is the total power delivered by the source, including power used to build magnetic and electric fields. Reactive power (kVAR) is that non-working portion. The three form a right triangle: apparent² = real² + reactive².
Why does √3 appear in three-phase formulas?
The factor √3 (about 1.732) comes from the 120-degree phase separation between the three voltage waveforms. Relating line quantities to phase quantities through that geometry, and summing the instantaneous power of three sinusoids spaced 120 degrees apart, produces the √3 multiplier in the standard power formula.