Apparent Power Calculator
In AC circuits with reactive loads (inductors and capacitors), total power has three components: real power P (watts, does useful work), reactive power Q (VAR, stores and returns energy), and apparent power S (VA, the vector sum of both). The relationship is S = sqrt(P squared + Q squared), forming the power triangle. Power factor is the ratio P/S. This calculator accepts real power and reactive power to compute apparent power and power factor, which are essential for sizing generators, UPS systems, and transformers, and for understanding utility billing.
Power triangle formula
S = sqrt(P^2 + Q^2) (VA)
Power Factor = P / S = cos(theta)
theta = arctan(Q / P) (degrees)
P is real power in watts, Q is reactive power in VAR, S is apparent power in volt-amperes. Example: P = 3,000 W, Q = 4,000 VAR gives S = sqrt(9,000,000 + 16,000,000) = sqrt(25,000,000) = 5,000 VA, pf = 3,000/5,000 = 0.60.
Power factor in practice
- Most inductive loads (motors, fluorescent ballasts, transformers) have lagging power factor below 1.0, drawing more apparent power than real power.
- Capacitive loads (capacitor banks, some variable-frequency drives) have leading power factor; they can counteract inductive reactive power.
- IEEE Standard 519 and utility tariffs often require industrial customers to maintain power factor above 0.85 to avoid demand charges.
- UPS systems and generators are sized in VA (apparent power), so a poor power factor load requires more VA capacity for the same watt output.
Frequently asked questions
What is apparent power?
Apparent power (S) is the total power drawn from the supply in a circuit with both resistive and reactive components. It is measured in volt-amperes (VA). Apparent power equals the product of RMS voltage and RMS current: S = V * I.
How is apparent power related to real and reactive power?
The power triangle relates the three: S^2 = P^2 + Q^2, where P is real power in watts (W) and Q is reactive power in volt-amperes reactive (VAR). Real power does useful work; reactive power oscillates between the source and reactive components.
What is power factor?
Power factor (pf) = P / S = cos(theta), where theta is the phase angle between voltage and current. A power factor of 1.0 means all apparent power is real power (purely resistive circuit). A lower power factor means more current is drawn for the same useful work done.
Why does low power factor matter?
With a low power factor, the electrical supply system must deliver more current (higher S) for the same real power output. This wastes capacity in conductors, transformers, and generators. Utilities often charge commercial customers a penalty for low power factor.
How do you improve power factor?
Power factor correction adds capacitors to counteract inductive reactive power from motors and transformers. The capacitor's leading reactive power cancels the lagging reactive power, reducing Q and therefore S for the same P.
Official sources
- IEEE Standard 519: IEEE 519, Recommended Practice for Harmonic Control.
- NIST: NIST SP 811, Guide for SI Units.
Reviewed by the CalculatorHub team, edited by James Graham, 15 June 2026. See our methodology.