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Torque to Horsepower Calculator

Convert rotational torque and RPM into power output, in horsepower and kilowatts, using Power = Torque × Angular Velocity.

Power
126.39 hp (94.25 kW)
Angular velocity
314.159 rad/s

How it works

Rotational power is torque times angular velocity: P = τ × ω, where ω converts a revolutions-per-minute reading into radians per second via ω = RPM × 2π ÷ 60. Torque is converted to newton-meters first (the SI unit the formula is applied in) before the calculation runs, the same convert-to-canonical-then-back pattern this site's other unit-toggled calculators use, and the resulting power in watts is then converted to both horsepower (÷ 745.699872, the exact wattage of 1 mechanical horsepower) and kilowatts for display.

A well-known consequence of this formula shows up on every automotive dyno chart: the torque (in lbf·ft) and horsepower curves always cross at exactly RPM = 33,000 ÷ (2π) ≈ 5,252.11, because that's the specific RPM at which horsepower numerically equals torque in lbf·ft. It isn't a coincidence of any one engine — it falls directly out of how the 550 ft·lbf/s horsepower definition relates to a minute's worth of revolutions, and this calculator reproduces that exact crossover when given a torque and that RPM.

FAQ

Why do torque and horsepower curves cross on a dyno chart?

Because of how the units are defined, not because of anything physically special happening in the engine at that RPM. Horsepower is proportional to torque × RPM, so at the one specific RPM (≈5,252 using lbf·ft and mechanical horsepower) where that proportionality constant works out to exactly 1, the two numbers must be numerically equal — below that RPM horsepower reads lower than torque, and above it, higher.

Does this account for drivetrain losses or engine efficiency?

No — this is the pure physics relationship between torque, rotational speed, and power at the point they're measured (e.g. at the crankshaft or at a dyno's rollers). Real-world losses between that point and, say, a vehicle's wheels (drivetrain friction, torque converter slip, accessory loads) reduce the power actually delivered, and aren't part of this formula.

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