ElectroHub

Power Triangle Calculator

AC power splits into the part that does work and the part that merely shuttles energy back and forth. The power triangle relates them, and the ratio of the useful part to the total is the power factor your electricity bill cares about.

Power Triangle — S² = P² + Q²

Real (P), reactive (Q) and apparent (S) power. Fill exactly two fields and leave the rest blank.

Real power P
Reactive power Q
Apparent power S
Power factor
Phase angle φ
Power triangle
P = 300 WQ = 400 VARφ=53.1°S = 500 VA
  1. 1.Given: P = 300 W, pf = 0.6
  2. 2.FormulaS = P ÷ pfSubstituteS = 300 ÷ 0.6ResultS = 500 VA
  3. 3.FormulaQ = √(S² − P²)SubstituteQ = √(500² − 300²)ResultQ = 400 VAR
  4. 4.Formulapf = P ÷ SSubstitutepf = 300 ÷ 500Resultpf = 0.6 (φ = 53.1301°)
Common trap: Only real power (W) does work and shows up on the energy bill's kWh — reactive power (VAR) just sloshes between source and load. But the wires and transformer must be sized for the full apparent power (VA), which is why utilities penalise a poor power factor.

The formula

S² = P² + Q² ; P = S × cos φ ; pf = P / S

P
real (active) power — does the work (watts)
Q
reactive power — stored and returned each cycle (VAr)
S
apparent power — what the cable and transformer must carry (VA)
pf
power factor, cos φ (0 to 1)

Worked example

A load draws 8 kW at a power factor of 0.8 lagging.

  1. S = P / pf = 8 / 0.8 = 10 kVA
  2. Q = √(S² − P²) = √(100 − 64)
  3. Q = √36

S = 10 kVA and Q = 6 kVAr — the supply carries 10 kVA to deliver 8 kW of useful work.

Where you'll use it

Sizing cables, transformers and generators, which are rated in kVA precisely because they must carry the apparent power. It is also the setup for every power-factor correction question.

The laws behind it

Parts this applies to

Resistor (fixed)Capacitor (aluminium electrolytic)Capacitor (tantalum)LED (light-emitting diode)MOSFETRectifier DiodeSchottky DiodeZener Diode

Related calculators

Power Factor Correction CalculatorQ_c = P × (tan φ₁ − tan φ₂), where φ = arccos(pf)Three-Phase Power CalculatorS = √3 × V_L × I_LRLC Impedance CalculatorZ = √(R² + (X_L − X_C)²)RMS, Average and Form Factor CalculatorSine wave: V_rms = V_peak / √2