Power, torque and speed are three views of the same rotating machine, tied together by one equation: power = torque × rotational speed. Know any two and the third is fixed. The practical consequence is that for a given power, torque and speed trade off inversely — slow the shaft down and the torque climbs in exact proportion. That single fact is why a small high-revving motor plus a gearbox can move an enormous load, and why engine and motor data sheets always quote power, torque and the speed at which each occurs.
Reviewed: June 19, 2026 · Author: Naveen P N, Founder — AI Calculator · Verified against: P = T·ω rotational-power identity.
The power–torque equations
The constant 9550 is 60,000 ÷ 2π: it folds together the per-minute-to-per-second conversion and the 2π radians in a revolution, so you can work straight from kW and rpm. The fundamental identity underneath is P = T·ω with ω = 2πN/60 in rad/s. Because the relationship is linear in each variable, halving the speed at constant power exactly doubles the torque, and vice versa.
Worked example — sizing a motor
Scenario: A 22 kW motor runs at 1,450 rpm (a typical 4-pole induction motor). What torque does it deliver?
The motor produces about 145 N·m at full load. Put a 5:1 reduction gearbox after it and (ignoring losses) the output shaft turns at 290 rpm but delivers five times the torque — about 725 N·m — at the same 22 kW. That is the everyday trade an engineer makes: pick the power for the job, then gear it to land the torque and speed the load actually needs.
Frequently Asked Questions
T = 9550 × P(kW) / N(rpm) gives N·m. 22 kW at 1450 rpm ≈ 145 N·m. The 9550 is 60000/2π.
P = T·ω (ω = 2πN/60). At fixed power, torque and speed trade off inversely — the basis of gearing.
9550 = 60000/2π, folding rpm→rad/s and kW→W into one factor. Use 9.5488 for watts → N·m.
hp = kW ÷ 0.7457. 22 kW ≈ 29.5 hp. Metric PS uses 0.7355 kW each — check which is meant.
No — power = torque × speed. A slow high-torque winch can match a fast low-torque turbine's power. Compare power first.