Power from torque and rpm
Rotational power is torque times angular speed: P = τ × ω, with ω = 2π × rpm ÷ 60 in rad/s. With torque in N·m the result is in watts.
In US units the shortcut is hp = torque (lb·ft) × rpm ÷ 5,252. The constant is 33,000 ÷ 2π = 5,252.11, which is why torque and horsepower curves cross at 5,252 rpm. A 300 lb·ft engine at 5,252 rpm makes 300 hp.
Power from force, distance and time
Linear mechanical power is P = F × d ÷ t. Lifting a 550 lbf load 1 ft in 1 s is exactly 1 mechanical horsepower, which is 745.69987 W. Metric horsepower (PS) is 75 kgf·m/s, or 735.49875 W.
Engine horsepower from quarter-mile results (estimate)
Drag racers use two empirical rules of thumb. From trap speed: hp ≈ weight × (mph ÷ 234)³. From elapsed time: hp ≈ weight ÷ (ET ÷ 5.825)³, with weight in pounds including the driver.
A 3,500 lb car trapping 110 mph gives about 364 hp; the same car running 12.5 s gives about 354 hp. These are curve fits to real cars, not physics, so traction, gearing, weather, altitude and drivetrain losses all move the answer. Sources disagree on whether they estimate flywheel or wheel horsepower. Trap speed is less affected by a poor launch.