MechClarityMechanical Engineering Calculators

Power transmission · Browser-based calculation

RPM / Torque / Power Calculator

Calculate steady mechanical shaft power, torque, or RPM from the other two quantities, with metric and imperial unit conversion.

Reference calculator #004

Choose the quantity to calculate

Inputs stay in your browser. Values are normalized to canonical units before calculation.

Choose the result; enter the other two shaft quantities.

Enter steady shaft torque magnitude.

Enter positive rotational-speed magnitude in rpm.

Calculated output

Results

rotational-power/1.0.0
Calculated power15.707963 kW
Mechanical power
15.707963 kW
Shaft torque
100 N·m
Rotational speed
1500 rpm

Valid steady rotational-power result

Rotational power, torque, and speed relationshipA rotating shaft with power, torque, and speed result cards connected by the relationship power equals torque multiplied by angular speed.MECHANICAL POWER, P15.707963 kWSHAFT TORQUE, T100 N·mROTATIONAL SPEED, n1500 rpmP = T × 2πn / 60
Steady shaft magnitudes; losses, efficiency, and transient torque are outside this relationship.
Scope and assumptions
  • Power, torque, and rotational speed are steady positive shaft magnitudes.
  • The relationship is mechanical P = Tω with angular speed derived from rpm.
  • Efficiency, transmission losses, electrical input power, and power factor are not included.
  • Starting torque, acceleration, service factor, duty cycle, thermal limits, component strength, and motor selection are not evaluated.

Calculation engine: rotational-power/1.0.0

Rotational power, torque, and speed formulas

P = Tω    ·    ω = 2πn / 60

Rearranging the same physical relationship gives:

T = P / ω    ·    n = 60P / (2πT)
Symbol Meaning Canonical unit
P Steady mechanical shaft power W
T Shaft torque magnitude N·m
n Rotational-speed magnitude rpm
ω Angular speed rad/s

The commonly published approximation P(kW) = T(N·m) × n(rpm) / 9555 follows from the same equation. The engine uses 2π/60 directly rather than rounding the denominator to 9555.

Worked power example

For T = 100 N·m and n = 1500 rpm:

  1. Angular speed: ω = 2π × 1500 / 60 = 157.079633 rad/s.
  2. Power: P = 100 × 157.079633 = 15,707.963268 W.
  3. Displayed result: 15.707963 kW.

Worked torque example

For P = 15 kW and n = 1500 rpm:

  1. Convert power: 15 kW = 15,000 W.
  2. Angular speed: 157.079633 rad/s.
  3. Torque: T = 15,000 / 157.079633 = 95.492966 N·m.

How to use the calculator

Choose Power, Torque, or Speed as the unknown quantity. The two remaining fields and their unit options update automatically. Switching modes preserves the same physical operating point when the current calculation is valid. All inputs are normalized to watts, newton metres, and rpm before the pure TypeScript engine runs.

The share URL uses readable parameters for the active mode. Query parameters store calculator state only and never create separate canonical SEO pages.

Units and horsepower definition

Power inputs support W, kW, and mechanical hp. Torque supports N·m, N·mm, lbf·in, and lbf·ft. Speed is rpm in V1. Mechanical horsepower is explicitly distinguished because metric, electric, boiler, and water horsepower use different conversion factors.

Engineering scope and limitations

This tool represents a steady mechanical shaft operating point. It does not determine whether a motor, gearbox, shaft, coupling, bearing, or driven machine is suitable.

Complete application checks may also require:

  • motor and drive efficiency, power factor, and electrical input data;
  • starting, pull-up, breakdown, accelerating, and peak torque;
  • inertia, acceleration time, duty cycle, service factor, and thermal capacity;
  • gearbox, belt, chain, bearing, seal, and coupling losses;
  • shock loading, torsional vibration, fatigue, shaft strength, and critical speed.

Do not use steady rated power alone as a substitute for starting or transient torque analysis.

Frequently asked questions

How do you calculate power from torque and RPM?

Convert torque to newton metres, multiply by 2π and RPM, then divide by 60. The result is mechanical shaft power in watts.

How do you calculate torque from power and RPM?

Convert power to watts and divide it by angular speed, where angular speed is 2π times RPM divided by 60.

How do you calculate RPM from power and torque?

Multiply power in watts by 60, then divide by 2π times torque in newton metres.

Is horsepower the same as kilowatts?

No. This calculator defines hp as mechanical horsepower based on 550 foot-pound-force per second. It is converted independently from electric, metric, boiler, or water horsepower definitions.

Does calculated shaft power include motor efficiency?

No. The result is the ideal steady mechanical relationship at one shaft. Electrical input, motor efficiency, transmission losses, starting torque, and duty-cycle limits require separate data.

References and review status

Reviewed . References provide formula and unit-conversion checks; they do not imply endorsement or application approval.