Torque - Work done and Power transmitted

Work done and power transmitted by constant torque

Work done

Work done is force multiplied with the distance moved by the force and can be expressed as

W = F s         (1)


W = work done (J, Nm)

F = force (N)

s = distance moved by force (s)

For an angular motion

force torque moment work power

the work done can be expressed as

W = F θ r

   = T θ         (2)


W = work (Joules)

θ = angle (radians)

r = radius (m)

T = torque or moment (Nm)

Power transmitted

Power is the ratio between work done and time taken and can be expressed as

 P = W / dt

    = T θ / dt

    = T ω

    = 2 π n T 

    = 2 π (nrpm / 60) T

    = 0.105 nrpm T      (3)


P = power (Watts)

dt = time taken (s)

ω =  θ / dt = 2 π n = angular velocity (rad/s)

n = speed (rev/s)

nrpm = speed (rev/min, rpm)

Note! - a machine must rotate to produce power!

A machine with no rotation can deliver torque - like an electric motor - but since no distance is moved by force no power is produced. As soon as the machine starts to rotate power is produced.

Example - Required Power

A machine rotating with speed 3000 rev/min (rpm) consumes 5 kW. The torque at the shaft can be calculated by modifying (3) to

T = P / 2 π n

    = (5 kW) (1000 W/kW) / 2 π (3000 rev/min) / (60 sek/min)

    = 15.9 Nm 

Related Topics

  • Mechanics - Kinematics, forces, vectors, motion, momentum, energy and the dynamics of objects

Related Documents

Tag Search

  • en: torque power work force radians angle distance moved
  • es: distancia ángulo de apriete de potencia fuerza de trabajo radianes trasladó
  • de: Drehmoment Leistung Arbeitskräfte Radiant Winkelabstand bewegt

Search the Engineering ToolBox

- "Search is the most efficient way to navigate the Engineering ToolBox!"

Engineering ToolBox - SketchUp Extension - Online 3D modeling!

3D Engineering ToolBox Extension to SketchUp - add parametric components to your SketchUp model

Add standard and customized parametric components - like flange beams, lumbers, piping, stairs and more - to your SketchUp model with the Engineering ToolBox - SketchUp Extension/Plugin - enabled for use with the amazing, fun and free SketchUp Make and SketchUp Pro . Add the Engineering ToolBox extension to your SketchUp from the Sketchup Extension Warehouse!

Translate the Engineering ToolBox!
About the Engineering ToolBox!

Support the ToolBox

If you find the Engineering ToolBox useful and want this website to be available tomorrow - and the days after tomorrow - enable ads or make a contribution!

Contribute to the Engineering ToolBox