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Power from torque and rpm

Convert torque at an rpm into kW and horsepower.

Units
N·m
rpm

Result

Power130.17 kW
Power (mechanical hp)174.6
Power (metric PS / CV)177.0

How it is calculated, with your numbers
  1. Powerkw = torque × rpm × 2 × π / 60000113 × 11,000 × 2 × π / 60000 = 130.17 kW
  2. Power (mechanical hp)hp = torque × rpm × 2 × π / 60000 × 1.34102209113 × 11,000 × 2 × π / 60000 × 1.34102209 = 174.6
  3. Power (metric PS / CV)ps = torque × rpm × 2 × π / 60000 × 1.35962162113 × 11,000 × 2 × π / 60000 × 1.35962162 = 177.0

Working uses the metric units the formula is written in.

  • torque Torque (N·m)
  • rpm Engine speed (rpm)
  • kw Power
  • hp Power (mechanical hp)
  • ps Power (metric PS / CV)

What it means

Power is torque times rotational speed. With torque in newton-metres and speed in radians per second the answer is in watts; one revolution per minute is 2π/60 radians per second. In imperial units the same relation becomes hp = lb·ft × rpm / 5252, which is why torque and horsepower curves always cross at 5,252 rpm.

European spec sheets often use PS (metric horsepower), which is about 1.4% more than mechanical hp for the same engine.

Assumptions and limits

  • Torque and rpm at the same point on the curve.

Sources

  • Heywood, J. B., Internal Combustion Engine Fundamentals, McGraw-Hill, 1988.