Power Formulas Reference

DC power

P = V · I

Watts = Volts × Amps

P = I² · R

Current squared × resistance

P = V² / R

Voltage squared / resistance

Energy

W = P · t (watt-seconds = joules)

kWh

P(kW) × t(hours) — utility billing unit

AC single-phase

Real power P

= V · I · cos φ (watts)

Apparent power S

= V · I (VA)

Reactive power Q

= V · I · sin φ (VAR)

Power factor

PF = cos φ = P / S

Always use RMS

V and I in AC formulas are RMS values

AC three-phase

Real power

= √3 · V_line · I_line · cos φ

Apparent power

= √3 · V_line · I_line

Line vs phase

V_line = √3 · V_phase (wye); I_line = √3 · I_phase (delta)

Mechanical power

Rotational

P = τ · ω (torque × angular velocity in rad/s)

From RPM

P(W) = τ(N·m) · RPM · 2π / 60

Horsepower

1 hp = 746 W (mechanical); 1 hp = 745.7 W (metric)

Linear

P = F · v (force × velocity)

Unit conversions