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Torque describes rotational force, while horsepower describes the rate at which work is performed. For a rotating shaft, horsepower depends on both the torque being produced and the rotational speed. That relationship makes it possible to calculate horsepower when torque and RPM are known, or to calculate torque when horsepower and RPM are known.
When torque is expressed in pound-feet and speed is expressed in revolutions per minute:
Horsepower = Torque (lb-ft) × RPM ÷ 5252
This is the same relationship used by the horsepower-from-torque calculation in the Auto Engineering Tools engineering workspace.
The relationship can be rearranged when horsepower and RPM are known:
Torque (lb-ft) = Horsepower × 5252 ÷ RPM
RPM must be greater than zero for this inverse calculation.
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Calculation
Horsepower = 400 × 4000 ÷ 5252 ≈ 304.6 hp
So 400 lb-ft at 4,000 RPM corresponds to approximately 304.6 horsepower.
The value 5252 is a unit-conversion constant that connects rotational speed in RPM and torque in pound-feet to mechanical horsepower. It comes from the definition of horsepower together with the circumference of one revolution. Because of this unit relationship, a torque curve expressed in lb-ft and a horsepower curve expressed in hp have the same numerical value at approximately 5,252 RPM.
The constant is specific to this combination of units. Calculations using newton-meters, kilowatts or other unit systems require the corresponding conversions rather than simply reusing 5252.
Torque by itself does not include rotational speed. Horsepower incorporates both torque and RPM, so the same torque value produces more horsepower when it occurs at a higher rotational speed. Conversely, a given horsepower level requires more torque when it occurs at a lower RPM.
This mathematical relationship does not mean that torque and horsepower are interchangeable descriptions. Torque remains a rotational-force quantity, while horsepower is a power quantity.
If a dynamometer reports torque and RPM, horsepower can be calculated directly from those measured values. Likewise, torque can be calculated from measured horsepower and RPM. The formula itself does not determine whether the underlying measurement represents crankshaft output, wheel output or another point in the drivetrain.
Chassis-dyno measurements include drivetrain effects between the engine and driven wheels. Engine-dyno measurements are taken at the engine. Test equipment, correction methods and atmospheric conditions can also affect reported measurements. For meaningful comparisons, use values measured or corrected on a consistent basis.
The horsepower/torque relationship is useful for checking dyno data, converting a known torque value at a particular RPM into horsepower, recovering torque from horsepower data, and understanding how an engine's torque curve relates to its power curve.