When to use: Use to convert between shaft power and torque units for motors, pumps, fans, compressors, and rotating machinery. The fundamental relationship is Power = Torque × Angular Velocity. In US units: HP = Torque (ft-lb) × RPM / 5252. Useful for motor selection, belt drive sizing, coupling selection, and verifying nameplate data.
This calculator converts between mechanical shaft power (HP and kW), torque in ft-lb, in-lb, and N·m, and shaft speed in RPM and rad/s using the fundamental relationship P = T × ω. Engineers use it to verify motor nameplate data, size couplings and belt drives, calculate gearbox output torque, and check power requirements for pumps, fans, and compressors.
The fundamental mechanical power relationship is P = T × ω, where P is power, T is torque, and ω is angular velocity. In US customary units, this becomes HP = T (ft-lb) × RPM / 5252, where 5252 is the combined conversion factor (2π/60 × 1 HP/550 ft-lb/s). To convert to SI: 1 HP = 0.7457 kW and 1 ft-lb = 1.35582 N·m. Angular velocity in rad/s equals RPM × 2π/60.
For motors and driven equipment, the shaft power chain involves multiple efficiency stages. The motor converts electrical power (kW input) to mechanical shaft power at motor efficiency η_motor (typically 90–95% for NEMA Premium). A gearbox then transmits shaft power with gearbox efficiency η_gb (typically 97–99% per stage). The driven equipment (pump, fan, compressor) converts shaft power to fluid power at equipment efficiency η_eq. Overall efficiency = η_motor × η_gb × η_eq.
NEMA MG-1 defines standard motor frame sizes, synchronous speeds (3600, 1800, 1200, 900, 720, 600 RPM at 60 Hz for 2, 4, 6, 8, 10, 12-pole motors), nameplate power ratings, and minimum efficiency levels. ASHRAE 90.1 Table 10.8 mandates minimum motor efficiency for motors used in HVAC systems. IEC 60034-30-1 defines international efficiency classes IE1 through IE4. AGMA (American Gear Manufacturers Association) standards govern gearbox rating, service factors, and torque capacity.
When selecting a motor, the nameplate HP must exceed the required BHP by the service factor (SF), typically 1.15 for standard motors. Running a motor above its nameplate continuous HP reduces insulation life by roughly 50% for each 10°C rise in winding temperature. Torque is a critical consideration for belt drives — the belt must transmit the full torque without slipping, requiring proper belt selection for width, cross-section, and sheave geometry based on torque and RPM from the drive manufacturer's catalog. For direct-coupled applications, coupling selection is based on transmitted torque plus a service factor for shock loads from pumps and compressors.
Select the input mode: enter power in HP, power in kW, or torque in ft-lb. Enter the shaft speed in RPM — common motor speeds are shown in the quick-reference panel (3600, 1800, 1200, 900 RPM for 60 Hz motors). The calculator outputs all power and torque equivalents simultaneously: HP, kW, Watts, torque in ft-lb, in-lb, and N·m, and angular velocity in rad/s. Use the result to specify coupling torque rating, belt drive capacity, gearbox input rating, or to verify that the motor nameplate values are consistent with the mechanical system requirements.
5252 = 33,000 ft-lb/min per HP ÷ (2π radians/revolution) = 33,000 / (2π × 60 RPM per rad/s). It arises from combining the definition of 1 HP as 33,000 ft-lb/min (James Watt's original estimate of a horse's work output) with the angular velocity conversion from RPM to rad/s. The formula HP = T(ft-lb) × RPM / 5252 is exact by definition.
Induction motors run slightly below synchronous speed — a 4-pole 60 Hz motor has a synchronous speed of 1800 RPM but typically runs at 1740–1760 RPM at full load. This difference (40–60 RPM) is the slip, and slip produces the relative motion between rotor and stator magnetic field that induces rotor current and generates torque. At no load, slip approaches zero. At locked rotor (starting), slip is 100% and starting torque is typically 150–200% of rated torque.
For a speed-reducing gearbox with ratio R (input RPM / output RPM): output torque = input torque × R × η_gb, where η_gb is gearbox efficiency (typically 0.97–0.99 per gear stage). Output power = input power × η_gb. The output shaft of a 10:1 gearbox driven by a 10 HP motor at 1750 RPM input delivers approximately 9.7 HP at 175 RPM output shaft speed, with output torque ≈ 10 × input torque × 0.97.
Water horsepower (WHP) is the hydraulic power actually transferred to the fluid: WHP = GPM × TDH / 3960. Brake horsepower (BHP) is the shaft power required at the pump input coupling, higher than WHP by the pump's hydraulic efficiency: BHP = WHP / η_pump. The motor must deliver BHP to the pump shaft, and must itself be powered by input electrical power equal to BHP / η_motor. WHP is the useful output; BHP and input power represent the losses in the system.
VFDs reduce motor speed by reducing the output frequency below 60 Hz while maintaining a constant V/Hz ratio to keep flux constant. At speeds below base speed, a VFD motor delivers rated torque but reduced power (P = T × ω). Above base speed (field weakening zone), torque decreases as speed increases while power stays approximately constant. For constant torque loads like conveyors and positive displacement pumps, VFDs work well at any speed. For variable torque loads like centrifugal pumps and fans, the affinity laws (P ∝ N³) mean power drops dramatically at low speeds.
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