Automotive & Engines
Basic

Horsepower from Torque (Imperial)

Horsepower from torque (lb-ft) and engine rpm.

Formula

HP=τ×N5252HP = \frac{\tau \times N}{5252}

Variables

HPHorsepower
τTorque (lb-ft)
NSpeed (rpm)

Example

250 lb-ft at 5252 rpm: HP = 250

How it works

This formula converts engine torque and rotational speed into power in imperial horsepower. It works because power is the rate of doing work, and for a rotating shaft that depends on both how hard the engine twists the shaft (torque) and how fast it spins (rpm); the constant 5252 comes from the unit conversions between foot-pounds, revolutions per minute, and horsepower. In practical terms, an engine can make more horsepower by producing more torque, spinning faster, or both.

When to use it

Use this when you know an engine’s torque in lb-ft and its speed in rpm and want to estimate its horsepower at that operating point. It is commonly used for cars, motorcycles, dynos, and engine performance comparisons.

Worked example, step by step

Given: τ = 180 lb-ft N = 4000 rpm Step 1: Substitute into the formula HP = (τ × N) / 5252 HP = (180 × 4000) / 5252 Step 2: Multiply HP = 720000 / 5252 Step 3: Divide HP ≈ 137.1 Final answer: HP ≈ 137 horsepower

Common mistakes to avoid

  • Using torque in newton-meters instead of lb-ft without converting units first
  • Forgetting that rpm is part of the calculation and trying to use torque alone
  • Assuming 5252 is optional or changing it for different engine speeds

Did You Know?

Torque and horsepower curves always cross at exactly 5252 rpm — a quirk of the constant in this formula.

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Reviewed & maintained by the FormulaWon editorial teamLast reviewed September 2026