Power Systems Fundamentals
Three-Phase Power Calculator
Solve for real, reactive, and apparent power and power factor from any two known values.
About this calculator
Real power (P), reactive power (Q), apparent power (S), and power factor (pf) are related by the power triangle: S² = P² + Q², and pf = P/S. Like Ohm's law, this is two independent equations in four unknowns, so any two known quantities determine the other two. This calculator applies the correct rearrangement automatically and also converts apparent power to line current using the system voltage, for either a three-phase (S = √3 · V_LL · I_L) or single-phase (S = V · I) system.
Use it to size equipment from a nameplate real-power rating, back-calculate current draw from a known load, or check whether a facility's power factor is likely to trigger a utility penalty. The line current shown is a magnitude only — for a full three-phase fault or unbalance study, that requires per-phase analysis this calculator does not perform.
Common pitfall: this calculator assumes a balanced system and treats power factor as a magnitude. Whether the load is inductive (lagging) or capacitive (leading) changes the sign of Q but not the arithmetic shown here — the leading/lagging selector only affects the label on the reactive power result, so double-check it matches your load type before quoting a sign convention in a report.
Assumptions
- Balanced three-phase system assumed in three-phase mode.
- Voltage entered is line-to-line for three-phase, or the single-phase RMS voltage for single-phase.
- Power factor is treated as a magnitude; leading vs. lagging only changes the sign convention, not the values shown.
When to use this calculator
Appropriate for
- Sizing or checking a balanced three-phase load from any two of real, reactive, apparent power, or power factor
- Converting between kW, kVAR, and kVA for a symmetric, sinusoidal-steady-state system
- Quick early-stage load estimates before a detailed study
Not suitable for
- Unbalanced or single-phase loads, where per-phase analysis is required instead
- Systems with significant harmonic distortion, where true RMS power and distortion power factor differ from the displacement values here
- Final equipment specification, protection settings, or code-compliance sizing — this is a preliminary relationship, not a design deliverable
What this calculator does not cover
- Balanced three-phase systems only — unbalanced loading requires per-phase or symmetrical-component analysis.
- Sinusoidal quantities assumed: with nonlinear (harmonic-rich) loads, displacement and true power factor diverge and apparent power includes distortion power this triangle does not capture.
- As with every calculator on this site: results are preliminary and educational, are not verified for any specific installation, and must be reviewed against the applicable code edition and stamped by a licensed Professional Engineer before real-world use.
Frequently asked questions
How is apparent power related to real and reactive power?
They form a right triangle: S² = P² + Q², where S is apparent power (kVA), P is real power (kW), and Q is reactive power (kVAR). Power factor is the ratio pf = P/S.
Why does the calculator need a voltage if I only want P, Q, and S?
It doesn't — voltage is only used to derive the auxiliary line current output. The P/Q/S/pf power-triangle solve works independently of voltage.
Does leading vs. lagging power factor change the calculation?
No — it changes only whether the load is described as capacitive (leading) or inductive (lagging) in the result label. The magnitude arithmetic for P, Q, and S is identical either way.
References
- IEEE Std 100, The Authoritative Dictionary of IEEE Standards Terms — power triangle definitions
- Glover, Sarma, Overbye, Power System Analysis and Design, 6th ed., Ch. 2
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