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Power Factor Equations

Power Factor Formulas Equations - RF Cafe

Power Factor (PF) = cos (θ)

Apparent Power (P) = I * V

True Power = P

I = Current

θ = Phase angle

V = Voltage

A calculator is included in the Free Espresso Engineering Workbook.


Power factor measures the phase angle (θ) 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 Formulas
Apparent Power

PA = I * V  [VA]

PA = I2 * R  [VA]

PA = V2 / R  [VA]

True Power (Real)

Pt = I * V * cos (θ)  [W]

PT = I2 * Z * cos (θ)  [W]

PT = V2 * cos (θ) / Z  [W]

Reactive Power (Q)

PR = I * V * sin (θ)  [VAR]

PR = I2 * Z * sin (θ)  [VAR]

PR = V2 * sin (θ) / Z  [VAR]


I = P / [V * cos (θ)]

I = sqrt {P / [Z * cos (θ)]}


V = P / [I * cos (θ)]

V = sqrt [P * Z / cos (θ)]


Z = V2 * cos (θ) / P

Z = P / [I2 * cos (θ)]



P = PT ± jPR

P = power in Watts

V = voltage in Volts

I = current in Amps

R = resistance in Ohms (Ω)

Z = impedance in Ohms (Ω)

θ = phase angle between I and V in degrees

PF = power factor

PA = apparent power in Volt·Amps (VA)

PR = apparent power in Volt·Amps (VA)

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