Power Factor Equations

Power factor measures the phase angle between the instantaneous voltage and the instantaneous current in a circuit. Voltage (E) leads current (I) by 90° in an inductive (L) circuit and voltage (E) lags current (I) by 90° in a capacitive (C) circuit.

A popular mnemonic is ELI the ICE man since E is leading (coming before) I in ELI, and E is lagging (coming after) I in ICE.

power factor ( P_f ) = cos ( q )
Apparent Power ( P ) = I * V
True Power = P
I = Current
q = Phase angle
V = Voltage

Power Formulas

Apparent Power
P = I * V
P = I² * R
P = V² / R

True Power
P = I * V * cos (q)
P = I² * Z * cos (q)
P = V² * cos (q) / Z
P = P_a * P_f

Impedance
Z = V² * cos (q) / P
Z = P / [I² * cos (q)]

Current
I = P / [V * cos (q)]
I = sqrt {P / [Z * cos (q)]}

Voltage
V = P / [I * cos (q)]
V = sqrt [P * Z / cos (q)]

where

P = power in Watts
V = Voltage in Volts
I = current in Amps
R = resistance in Ohms (Ω)
Z = impedance in Ohms (Ω)
q = phase angle between I and V in degrees
P_a = apparent power in Volt·Amps (VA)
P_f = power factor

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