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Power Factor Equations
 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]

Current

I = P / [V * cos (θ)]

I = sqrt {P / [Z * cos (θ)]}

Voltage

V = P / [I * cos (θ)]

V = sqrt [P * Z / cos (θ)]

Impedance

Z = V2 * cos (θ) / P

Z = P / [I2 * cos (θ)]

 where P = PT ± jPRP = power in WattsV = 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)