Power ⇄ Torque ⇄ RPM Calculator

Understanding the power, torque and rpm calculator — concept and principle

Power, torque and rotational speed are tied together by one simple relation. This calculator turns a power rating in kilowatts and a speed in revolutions per minute into shaft torque in N·m and lb·ft, and also shows the power in horsepower. It is used to read electric motor nameplates, size couplings and gearboxes, and compare engines.

At fixed power, torque and speed trade off: 7.5 kW at 1,450 rpm is 49.4 N·m.

How it is calculated

Torque: T (N·m) = 9,549 × P (kW) ÷ n (rpm).
Horsepower: hp = P (kW) ÷ 0.7457, using mechanical (imperial) horsepower of 745.7 W.
Torque in lb·ft: T (N·m) × 0.737562.

The principle

Power is the rate of doing work. For rotation, work per radian is torque, so power equals torque times angular velocity: P = T × ω, with ω in rad/s. One revolution is 2π radians and a minute is 60 seconds, so ω = 2πn/60. Rearranging, T = P × 60 ÷ (2πn). With P in kilowatts (× 1,000), the constant is 60,000 ÷ 2π ≈ 9,549.3, which is where the 9,549 comes from. At fixed power, torque falls as speed rises; that is why gearboxes trade speed for torque.

Worked example

Inputs: P = 7.5 kW, n = 1,450 rpm (a typical four-pole induction motor on a 50 Hz supply).
Torque: 9,549 × 7.5 ÷ 1,450 = 71,617.5 ÷ 1,450 = 49.39138 N·m.
Horsepower: 7.5 ÷ 0.7457 = 10.05766 hp.
Torque in lb·ft: 49.39138 × 0.737562 = 36.4292 lb·ft.

Each point is the calculator re-run with only “Speed (rpm)” changed; the gold point is the default example. Change the inputs above and this chart follows your numbers.

Speed (rpm)	Torque (N·m)
362	197.5655172
725	98.78275862
1,088	65.85517241
1,450	49.39137931
1,812	39.51310345
2,175	32.92758621
2,900	24.69568966

How to read the result

The torque is the continuous rated torque at that speed. Motors can deliver more briefly at start, and engines have a torque curve that changes with rpm, so a single pair of numbers describes only one operating point. If a gearbox reduces speed by a ratio i, output torque rises by about i times (minus gear losses) while power stays nearly the same.

Common mistakes

Using rad/s where rpm is expected, or the reverse.
Mixing mechanical horsepower (745.7 W) with metric horsepower (PS, about 735.5 W).
Assuming the nameplate power is the input power; motor ratings are mechanical output at the shaft.

Keep in mind: Results are ideal values without losses. Real drive selection should include service factors, starting torque and efficiency, following the manufacturer's data and applicable standards.

Frequently asked questions

How do I get power from torque and rpm?

P (kW) = T (N·m) × rpm ÷ 9,549.

Why does a 1,450 rpm motor not run at 1,500 rpm?

A four-pole motor's magnetic field turns at 1,500 rpm on 50 Hz; an induction motor runs slightly slower (slip) to produce torque.

What about horsepower and lb·ft directly?

hp = T (lb·ft) × rpm ÷ 5,252, so torque and power curves cross at 5,252 rpm when plotted in those units.

Sources: BIPM, The International System of Units (SI Brochure), 9th edition · R. G. Budynas and J. K. Nisbett, Shigley's Mechanical Engineering Design, McGraw-Hill

Checked 8 Nov 2026. Standard textbook formulas in SI units, computed in your browser. For learning and estimates — real designs must follow your local codes and be checked by a qualified engineer.

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