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.
Metric Formulas
Every imperial formula above has a metric twin with a different constant. Getting these mixed up is the most common source of wrong answers.
| What it finds | Formula | Calculator |
|---|---|---|
| kW from Nm & rpm | kW = (Nm × rpm) ÷ 9,549 | Nm to kW |
| HP from Nm & rpm | HP = (Nm × rpm) ÷ 7,121 | Nm to HP |
| PS from Nm & rpm | PS = (Nm × rpm) ÷ 7,023.5 | Nm to HP |
| Nm from kW & rpm | Nm = (kW × 9,549) ÷ rpm | kW to Nm |
| Metric power-to-weight | kW/t = kW ÷ (kg ÷ 1,000) | kW per Tonne |
| Metric fluid power | kW = (bar × L/min) ÷ 600 | PSI to HP |
HVAC & Refrigeration Formulas
| What it finds | Formula | Calculator |
|---|---|---|
| Aircon HP from BTU/hr | HP ≈ BTU/hr ÷ 9,000 | BTU to HP |
| Tons from BTU/hr | TR = BTU/hr ÷ 12,000 | Ton to HP |
| Cooling kW to aircon HP | HP = kW ÷ 2.638 | Cooling kW to HP |
| VRF HP to tons | TR = HP × 0.796 | VRF HP to TR |
| Aircon input watts | W = BTU/hr ÷ EER | Aircon HP to Watts |
| Boiler HP to BTU/hr | BTU/hr = BHP × 33,475 | Boiler HP |
Engine Building Formulas
| What it finds | Formula | Calculator |
|---|---|---|
| Carburetor CFM | CFM = (CID × rpm ÷ 3,456) × VE | Carb CFM |
| Compression ratio | CR = (Vswept + Vchamber) ÷ Vchamber | Compression Ratio |
| Volumetric efficiency | VE = actual airflow ÷ theoretical airflow | Volumetric Efficiency |
| Displacement in cc from CID | cc = CID × 16.387 | Engine Size Converter |
| Specific output | hp/L = HP ÷ (cc ÷ 1,000) | HP per Liter |
| Gear ratio rpm | rpm = (MPH × ratio × 336) ÷ tire diameter | Gear Ratio RPM |
Every Constant, and Where It Comes From
The constants look arbitrary until you see the unit arithmetic behind them. None are empirical fudge factors — each is a pure conversion between measuring systems.
| Constant | Used for | Derivation |
|---|---|---|
| 5,252 | HP from lb-ft & rpm | 33,000 ÷ 2π |
| 9,549.30 | kW from Nm & rpm | 60,000 ÷ 2π |
| 7,120.97 | HP from Nm & rpm | 9,549.30 ÷ 1.34102 |
| 7,023.55 | PS from Nm & rpm | 9,549.30 ÷ 1.35962 |
| 745.699872 W | 1 mechanical horsepower | 550 ft·lbf/s |
| 735.49875 W | 1 metric horsepower (PS) | 75 kgf·m/s at g = 9.80665 |
| 746 W | 1 electrical horsepower | Defined exactly |
| 2,544.43 | BTU/hr per mechanical HP | 745.6999 W in BTU/hr |
| 33,475 | BTU/hr per boiler HP | Evaporating 34.5 lb water/hr at 212 °F |
| 12,000 | BTU/hr per ton of refrigeration | Freezing 1 short ton of ice in 24 h |
| 1,714 | Hydraulic HP from PSI × GPM | 33,000 ÷ (231 in³/gal ÷ 12) |
| 3,960 | Water HP from GPM × head | 33,000 ÷ 8.33 lb/gal |
| 3,456 | Carb CFM | 1,728 in³/ft³ × 2 (four-stroke) |
| 336 | Gear ratio rpm from MPH | 1,056 in/min per MPH ÷ π |
| 375 | HP from thrust × mph | 550 ft·lbf/s ÷ 1.4667 ft/s per mph |
| 234 | Trap-speed HP estimate | Empirical (Hale) — not a unit conversion |
| 16.387064 | cc per cubic inch | 2.54³ exactly |
| 1.35582 | Nm per lb-ft | 0.45359237 kg × 9.80665 × 0.3048 |
Picking the Right Formula
| You know… | Use |
|---|---|
| Torque in lb-ft and rpm | HP = T × rpm ÷ 5,252 |
| Torque in Nm and rpm | HP = Nm × rpm ÷ 7,121 |
| Power in kW | HP = kW × 1.341 |
| Volts, amps, efficiency, PF | HP = V × A × √3 × PF × Eff ÷ 746 |
| Trap speed and weight | HP = W × (MPH ÷ 234)³ |
| Pressure and flow | HP = PSI × GPM ÷ 1,714 |
| Only cooling BTU/hr | Aircon HP ≈ BTU/hr ÷ 9,000 |
If you are unsure which applies, the how to calculate horsepower guide walks through all seven methods with their accuracy ranges.
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).