Horsepower Formulas Reference
Every horsepower and torque equation in one place — with the constants explained and a calculator linked for each.
This is a complete, printable reference of the formulas used across calchorsepower.com. Every equation here powers one of our calculators, so once you understand the math you can either compute it by hand or jump straight to the matching tool.
Core Horsepower Formulas
| What it finds | Formula | Calculator |
|---|---|---|
| Horsepower from torque & RPM | HP = (Torque × RPM) ÷ 5252 | HP from Torque & RPM |
| Torque from horsepower | Torque = (HP × 5252) ÷ RPM | HP to Torque |
| Wheel HP from crank HP | WHP = Crank HP × (1 − loss) | Wheel HP |
| Crank HP from wheel HP | Crank HP = WHP ÷ (1 − loss) | Flywheel HP |
The constant 5252 is the heart of engine math: it equals 33,000 ft-lb/min ÷ 2π. Because horsepower and torque share it, their dyno curves always cross at 5252 RPM — see the 5252 rule explained.
Unit Conversion Formulas
| Conversion | Formula / factor | Calculator |
|---|---|---|
| HP → kilowatts | kW = HP × 0.7457 | HP to kW |
| kW → HP | HP = kW × 1.341 | HP to kW |
| HP → amps (3-phase) | A = (HP × 746) ÷ (V × √3 × PF × Eff) | HP to Amps |
| Torque (lb-ft) → Nm | Nm = lb-ft × 1.3558 | Torque tools |
| HP → watts | W = HP × 745.7 | HP Unit Converter |
Racing & Performance Formulas
| What it finds | Formula | Calculator |
|---|---|---|
| HP from trap speed | HP = Weight × (MPH ÷ 234)³ | Quarter Mile |
| HP from ET | HP = Weight ÷ (ET ÷ 5.825)³ | HP from ET |
| Power-to-weight ratio | PWR = Power ÷ Weight | Power-to-Weight |
Industrial Formulas
- Three-phase motor HP: HP = (V × A × √3 × PF × Eff) ÷ 746 — see Electric Motor HP.
- Hydraulic (water) HP: HHP = (GPM × Head ft) ÷ 3960 — see Pump HP.
- Engine displacement: V = π × (Bore ÷ 2)² × Stroke × Cylinders — see Engine Displacement.
Frequently Asked Questions
The core formula is HP = (Torque in lb-ft × RPM) ÷ 5252. This converts rotational force and engine speed into power, and is the foundation of nearly every other horsepower calculation.
5252 comes from dividing 33,000 foot-pounds per minute (the definition of one horsepower) by 2π radians per revolution. The result, 5252.11, is the constant that links torque in pound-feet to horsepower.
Multiply horsepower by 0.7457 to get kilowatts (1 mechanical HP = 0.7457 kW). To go the other way, multiply kilowatts by 1.341.
The Hale trap-speed formula is HP = Weight × (MPH ÷ 234)³, where weight is in pounds (car plus driver) and MPH is the speed at the quarter-mile trap.
For a three-phase motor, HP = (Volts × Amps × √3 × Power Factor × Efficiency) ÷ 746. For single-phase, drop the √3 term. This gives shaft horsepower from electrical input.
Power-to-weight ratio = Power ÷ Weight. It is commonly expressed as hp per pound (hp/lb), hp per ton (hp/ton), or kilowatts per kilogram (kW/kg).