Power Factor Calculator Formula

Understand the math behind the power factor calculator. Each variable explained with a worked example.

Use the Power Factor Calculator

Formulas Used

Power Factor

pf = real_power / apparent_power

Reactive Power (Q)

reactive = sqrt(pow(apparent_power, 2) - pow(real_power, 2))

Phase Angle

phase_angle = (180 / pi) * sqrt(1 - pow(real_power / apparent_power, 2)) / (real_power / apparent_power)

Variables

VariableDescriptionDefault
real_powerReal Power (P)(kW)25
apparent_powerApparent Power (S)(kVA)30

How It Works

Power Factor

Power factor indicates how effectively electrical power is being converted to useful work.

Formulas

PF = P / S = kW / kVA

Q = sqrt(S^2 - P^2)

A power factor of 1.0 means all power is real (useful). Low power factor means more current flows than needed, increasing losses. Industrial facilities typically aim for PF > 0.95 to avoid utility penalties.

Worked Example

A facility drawing 30 kVA with 25 kW real power.

real_power = 25apparent_power = 30
  1. 01PF = 25 / 30 = 0.833
  2. 02Q = sqrt(30^2 - 25^2) = sqrt(900 - 625) = sqrt(275) = 16.58 kVAR
  3. 03Phase angle = arccos(0.833) = 33.6 degrees

Ready to run the numbers?

Open Power Factor Calculator