Power Factor Calculator
Calculate power factor step by step: PF = P ÷ S = cos φ, and Q = √(S² − P²).
In short
Formula: PF = P ÷ S = cos φ, and Q = √(S² − P²).
Power factor
0.8
- Phase angle
- 36.87°
- Reactive power
- 600 var
- As a percentage
- 80%
What this calculator does
Calculate power factor step by step: PF = P ÷ S = cos φ, and Q = √(S² − P²). Worked example, questions and limitations included.
Use it to turn Real power, Apparent power into a checked result you can compare, copy, or rerun with different assumptions.
The page shows the formula, a numeric worked example, and the assumptions that affect this electrical calculation.
Inputs and what they mean
- Real power
- — number value.
- Apparent power
- — number value.
How to use it
- Enter each value in the unit shown next to the box (use the unit converter first if your numbers are in other units).
- Check the breakdown to see every intermediate step.
- Read the limitations before relying on the result.
Formula
Real power (W) does the work; apparent power (VA) is V × I; reactive power (var) circulates.
PF must be between 0 and 1, so real power cannot exceed apparent power.
Assumes sinusoidal waveforms; distorted currents need true power factor.
PF = P ÷ S = cos φ, and Q = √(S² − P²).
Inputs used: Real power, Apparent power.
Worked example
800 W from 1,000 VA
- PF = 800 ÷ 1,000 = 0.8.
- φ = cos⁻¹ 0.8 = 36.87°.
- Q = √(1,000² − 800²) = 600 var.
Reading the result
The headline figure is the main answer. Any breakdown underneath shows the parts that make it up, so you can check the working and see what changes when you adjust an input.
Limitations and assumptions
- Displacement power factor only; harmonics are not modelled.
- Sign of reactive power (leading/lagging) is not determined.
- Single operating point.
- Results are estimates for planning and learning. Real designs, installations and bids must be checked by a qualified, licensed professional against the codes that apply where you work.
- The result depends on the values you enter for this power factor calculator; it does not supply missing rates, rules, prices, dates, or assumptions for you.
Common questions
Why does low power factor matter?
It means more current for the same useful power, increasing cable losses. Some utilities charge commercial customers for poor power factor.
Can the calculator tell leading from lagging?
No. Real and apparent power alone do not show whether the load is inductive (lagging) or capacitive (leading).
How is power factor corrected?
Usually with capacitors for inductive loads. Sizing correction needs the reactive power shown here plus a target power factor.
How do I use the Power Factor Calculator?
Enter the required values for Real power, Apparent power. The calculator applies the formula on this page and shows the main result with any supporting breakdown so you can check the arithmetic.
What formula does the Power Factor Calculator use?
PF = P ÷ S = cos φ, and Q = √(S² − P²). The visible formula section above lists the calculation path and the edge cases the page handles, so the result can be checked without relying on the form alone.
Can the Power Factor Calculator be used for exact decisions?
Use it as a calculation aid, not as a substitute for checking the underlying rule, contract, policy, or professional advice that applies to your situation. When a result depends on local rules, personal details, prices, or dates, enter those values yourself and confirm them before acting.
Related tools
Calculate electrical power step by step: P = V × I = I² × R = V² ÷ R (DC or resistive AC using RMS values).
Calculate voltage divider step by step: Vout = Vin × R2 ÷ (R1 + R2).
Calculate resistance step by step: R = V ÷ I, or for a conductor R = ρ × L ÷ A (A in m²).