Torque, speed and power calculator
Compute any one of the three quantities torque M, speed n and power P from the other two. The basis is rotational mechanics with ω = 2π·n/60 and P = M·ω. The calculator also shows the angular velocity ω and compares the exact result with the familiar 9550 short formula – live with every input, power in watts or kilowatts.
M-n-P universal calculator
Model: rotation with P = M·ω and ω = 2π·n/60. Pure converter without efficiency, inertias or motion profile. For a complete motor design use the drive sizing calculator.
Results
Calculating …
Formulas and fundamentals
The mechanical power of a rotation is the product of torque and angular velocity: P = M·ω. The angular velocity ω in rad/s follows from the speed n in rpm via ω = 2π·n/60, because one full revolution corresponds to the angle 2π and n revolutions per minute must be converted to revolutions per second. From these two relations any of the three quantities can be found from the other two: M = P/ω, n = 60·P/(2π·M) and P = M·2π·n/60.
The short formula M = 9550·P/n common in mechanical engineering (P in kilowatts, n in rpm) is not separate physics but the same relation in practical units. The number 9550 is rounded: exactly it would be 60000/(2π) = 9549.297. As a result the short formula lies about one per mille above the exact value. For rough estimates this is irrelevant; for a clean design the calculator uses the exact path via ω and reports the approximation only for comparison.
Consistent handling of units is essential. In SI base units M is in Nm, ω in rad/s and P in W; then P = M·ω holds with no conversion factor. Speeds are usually given in rpm and must be divided by 60 first to obtain ω. Power appears in W or kW depending on the application – the calculator works internally in watts and shows both representations so that drive and process quantities stay directly comparable.
Worked example
A motor runs at n = 1480 rpm and delivers P = 250 kW. The torque is sought. The angular velocity is ω = 2π·1480/60 = 154.99 rad/s. This gives the exact torque M = P/ω = 250000 W / 154.99 rad/s = 1613.06 Nm.
The 9550 short formula gives M = 9550·250/1480 = 1613.18 Nm, about 0.12 Nm more. The deviation of roughly 0.007 percent comes solely from rounding the factor 9550 and is negligible in practice.
Conversely: at M = 100 Nm and n = 1450 rpm the angular velocity is ω = 151.84 rad/s, hence P = M·ω = 100·151.84 = 15184 W = 15.18 kW. This lets you check drive data and required motor power quickly in both directions.
Frequently asked questions
From which quantities can the calculator compute?
From exactly two of the three quantities torque M, speed n and power P it determines the third. You choose which quantity is sought and enter the other two. The calculator additionally shows the angular velocity ω in rad/s.
Where does the factor 9550 in the short formula come from?
M = 9550·P/n (P in kW, n in rpm) is P = M·ω in practical units. Substituting ω = 2π·n/60 and converting kW to W yields the prefactor 60000/(2π) = 9549.297, which rounds to 9550. The short formula therefore lies about one per mille above the exact result.
Why is the angular velocity ω shown separately?
ω = 2π·n/60 is the actual physical quantity behind the speed and is needed for many follow-up calculations – for power P = M·ω, for kinetic energy or for moment of inertia. The speed in rpm is just an application-oriented notation of the same quantity.
Watts or kilowatts – which unit should I use?
Both are allowed. The calculator works internally in watts and always displays power in W and kW. For input you can switch between W and kW; 1 kW equals 1000 W.
Does this also apply to linear motion?
No, this concerns rotation with P = M·ω. For straight-line motion the analogue is P = F·v with force F and speed v. For a complete drive design with motion profile, gear ratio and inertias use the drive sizing calculator.
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