| Symbol | Variable | Imperial | SI |
|---|---|---|---|
| P | Power | Horsepower (HP) | Kilowatts (kW) |
| T | Torque | lb·ft | Newton-meters (N·m) |
| N | Rotational Speed | RPM | RPM |
| ω | Angular velocity | rad/s | rad/s |
| 5252 | Conversion constant | = 33,000 ft·lbf/min ÷ 2π | |
- Calculations assume 100% mechanical efficiency — real systems lose 2–15% to friction, heat, and drivetrain losses
- Horsepower values are theoretical (flywheel HP) — wheel/shaft HP will be lower after drivetrain losses
- The constant 5252 applies to brake horsepower (BHP) per SAE J1349 standard
- For electric motors, use shaft power output — input power will be higher based on motor efficiency (typically 85–95%)
- Torque curves vary with RPM — this calculator solves at a single operating point only
- 1 HP = 745.7 W | 1 lb·ft = 1.35582 N·m
Horsepower, Torque, and RPM — The Relationship
Horsepower and torque are two of the most frequently misunderstood quantities in mechanical engineering. Torque is the rotational force applied to a shaft — the twisting effort. Horsepower is the rate at which that work is done. Neither tells the full story alone: a high-torque motor that spins slowly produces the same power as a lower-torque motor that spins faster. Understanding the mathematical relationship between all three is essential for motor selection, drivetrain design, and powertrain analysis.
The Formulas
Worked Examples
Example 1 — Engine Power from Dyno Data
A performance engine produces peak torque of 420 lb·ft at 4,200 RPM and peak power at 6,100 RPM where torque is 365 lb·ft. Calculate peak power and the RPM where HP and torque curves cross.
Example 2 — Electric Motor Sizing for Conveyor
A conveyor requires 180 N·m of torque at the drive shaft running at 1,450 RPM. Select a standard motor frame size with 15% service factor.
Example 3 — Pump Drive Shaft Torque
A 25 HP pump motor runs at 3,550 RPM. What torque is developed at the shaft and what is the tangential force at the coupling face (coupling radius = 3 inches)?
Example 4 — Hydraulic Motor Output
A hydraulic motor operates at 2,000 psi with 5 GPM flow rate and 85% overall efficiency. What is the output power and torque at 1,200 RPM?
Real World Applications
Common Mistakes Engineers Make
Frequently Asked Questions
Brake horsepower (BHP) is measured at the engine crankshaft using a dynamometer brake. Wheel horsepower (WHP) is measured at the driven wheels after power has passed through the transmission, driveshaft, differential, and axles. Drivetrain losses typically consume 15–20% for RWD and 20–25% for AWD vehicles. A 400 BHP engine typically delivers 320–340 WHP at the wheels.
Diesel engines produce peak torque at lower RPM (1,400–2,200 RPM) due to higher compression ratios and longer power strokes. Gasoline engines produce peak torque at higher RPM (3,000–5,000 RPM). Since HP = T × RPM / 5252, a diesel can produce the same HP as a gasoline engine with less peak torque if it spins faster — but the diesel’s lower-RPM torque is more useful for towing and heavy work at low speeds.
There are several horsepower definitions: Mechanical HP = 550 ft·lbf/s = 745.7 W. Metric HP (PS) = 75 kgf·m/s = 735.5 W. Electrical HP = 746 W exactly. Boiler HP = 9,810 W (steam industry only). For mechanical engineering calculations always use mechanical HP (745.7 W). The difference between mechanical and electrical HP (0.04%) is negligible for most applications.
Acceleration torque: T_acc = I × α, where I is the mass moment of inertia (kg·m² or lb·ft²) and α is the angular acceleration in rad/s². For a solid cylinder: I = ½mr². For a hollow cylinder: I = ½m(r_outer² + r_inner²). The total torque required is the sum of load torque (steady state) plus acceleration torque during startup — this peak torque governs motor and coupling sizing.
Specific power (power-to-weight ratio) is power output divided by engine or motor mass, typically expressed in kW/kg or HP/lb. It’s a key metric for comparing powerplants in weight-sensitive applications like aircraft, racing vehicles, and portable equipment. Modern electric motors achieve 3–5 kW/kg, gasoline engines 0.5–1.5 kW/kg, and gas turbines up to 10 kW/kg.