Shaft Power and Torque Calculator
Calculate mechanical shaft power from torque and rotational speed.
Convert between horsepower, kilowatts, torque (Nm or lb·ft), and RPM.
Find torque from power or speed from torque and power.
Mechanical Shaft Power P = τ × ω = τ × 2π × n / 60 Where: P = power (Watts) τ = torque (Newton-meters, N·m) ω = angular velocity (rad/s) n = rotational speed (RPM — revolutions per minute)
In Imperial Units P (hp) = τ (lb·ft) × n (RPM) / 5252 The constant 5252 = 33,000 ft·lb/min ÷ (2π) → exact. One horsepower = 550 ft·lb/s = 33,000 ft·lb/min = 745.7 Watts.
Derived Formulas τ = P / ω = P × 60 / (2π × n) → torque from power and speed n = P / (τ × 2π / 60) → speed from power and torque P_kW = τ_Nm × n_RPM / 9549 → convenient constant for SI units
Gear / Transmission Effects Output torque = Input torque × gear ratio (ignoring losses) Output speed = Input speed / gear ratio Power is conserved (minus friction losses): P_out = P_in × η
Typical Power Levels Human pedaling (sustained): ~100–250 W (0.13–0.34 hp) Car engine (economy): 50–100 kW (70–135 hp) Car engine (sports): 200–500 kW (270–670 hp) Jet turbine (large): 10–100 MW Typical electric motor range: 0.1 kW to 10 MW