What is Horsepower?
Horsepower (HP) is a unit of power — the rate at which work is done. James Watt defined it in the 1780s as the work output of a strong draft horse: lifting 33,000 pounds one foot in one minute, or 550 ft·lb per second. The unit stuck and still dominates US automotive and equipment specs.
Three Ways to Calculate Horsepower
- Mechanical: from torque × rotational speed. The engine bench-test formula.
- Power conversion: from any other power unit (W, kW, BTU/hr, PS).
- Electrical: from voltage × current with power factor and motor efficiency. Used to size electric motors.
Mechanical Horsepower (Torque & RPM)
HP = (Torque × RPM) / 5252
where torque is in lb·ft. The constant 5252 = 33,000 / (2π). For metric:
HP_metric = (Torque_N·m × RPM) / 7127
An interesting consequence: at 5252 RPM, torque (in lb·ft) and horsepower are numerically equal. That's the famous "horsepower and torque cross at 5252 RPM" on every dyno chart.
Power Unit Conversions
| From | To HP (mechanical) |
|---|---|
| 1 watt (W) | ÷ 745.7 = 0.001341 HP |
| 1 kilowatt (kW) | × 1.341 HP |
| 1 BTU/hr | × 0.000393 HP |
| 1 PS (metric HP) | × 0.9863 HP |
HP vs PS: European cars often quote PS (Pferdestärke). 1 PS = 75 kgf·m/s = 735.5 W, slightly less than 1 mechanical HP (745.7 W). A "200 PS" Mercedes is about 197 mechanical HP.
Electrical Horsepower
HP = (V × I × PF × η) / 746
where V = volts, I = amps, PF = power factor (1.0 for DC and resistive AC loads, 0.7–0.9 for inductive AC motors), and η = motor efficiency (typically 0.85–0.95). The 746 W per HP comes from the mechanical definition.
For three-phase systems multiply by √3 ≈ 1.732. This calculator handles single-phase only — for three-phase, multiply your final HP result by 1.732.
Worked Example
A V8 making 400 lb·ft of torque at 4,500 RPM:
- HP = (400 × 4,500) / 5252 = 342.7 HP
A 240 V single-phase motor drawing 10 A at PF 0.85 and 90% efficiency:
- HP = (240 × 10 × 0.85 × 0.90) / 746 = 2.46 HP
HP vs Torque — Which Matters?
Common automotive saying: "Torque is what you feel. Horsepower is what you brag about."
- Low-end torque matters for towing, off-roading, hauling — it's the rotational force at low RPM.
- Peak horsepower matters for top speed and high-RPM acceleration. It's torque × RPM, so engines that spin freely make more HP per lb·ft.
- Diesel: high torque, low peak HP. Truck-and-tow.
- Sport bike: lower torque, very high peak HP at 10,000+ RPM.