Engineering ToolBox - Resources, Tools and Basic Information for Engineering and Design of Technical Applications!

Work done by Force

Work done by a force acting on an object.

Sponsored Links

When a body is moved as a result of a force being applied to it - work is done.

Work - constant force and distance diagram - spring force and distance diagram

Work done by a Constant Force

The amount of work done by a constant force can be expressed as

WF = F s                                         (1)


WF = work done (J, ft lbf)

F = constant force acting on object (N, lbf)

s = distance object is moved in direction of force (m, ft)

The unit of work in SI units is joule (J) which is defined as the amount of work done when a force of 1 Newton acts for distance of 1 m in the direction of the force.

  • 1 J (Joule) = 0.1020 kpm = 2.778x10-7 kWh = 2.389x10-4 kcal = 0.7376 ft lbf = 1 (kg m2)/s2 = 1 watt second = 1 Nm = 1 ft lb = 9.478x10-4 Btu
  • 1 ft lbf (foot pound force) = 1.3558 J = 0.1383 kp m = 3.766x10-7 kWh = 3.238x10-4 kcal = 1.285x10-3 Btu

This is the same unit as energy.

The work done by a constant force is visualized in the chart above. The work is the product force x distance and represented by the area as indicated in the chart.

Example - Constant Force and Work

A constant force of 20 N is acting a distance of 30 m. The work done can be calculated as

WF = (20 N) (30 m)

    = 600 (J, Nm)

Example - Work done when lifting a Brick of mass 2 kg a height of 20 m above ground

The force acting on the brick is the weight and the work can be calculated as

WF = F s

     = m ag s                               (2)

     = (2 kg) (9.81 m/s2) (20 m)

     = 392 (J, Nm)

Example - Work when Climbing Stair - Imperial units

The work made by a person of 150 lb climbing a stair of 100 ft can be calculated as

WF = (150 lb) (100 ft)

    = 15000 ft lb

Work done by a Spring Force

The force exerted by springs varies with the extension or compression of the spring and can be expressed with Hooke's Law as

Fspring = - k s                        (3)


Fspring = spring force (N, lbf)

k = spring constant

The work done by a spring force is visualized in the chart above. The force is zero with no extension or compression and the work is the half the product force x distance and represented by the area as indicated. The work done when a spring is compressed or stretched can be expressed as

Wspring = 1/2 Fspring_max s                     

     = 1/2 k s2                             (4)


Wspring = work done (J, ft lbf)

Fspring_max = maximum spring force (N, lbf)

Example - Spring Force and Work

A spring is extended 1 m. The spring force is variable - from 0 N to 1 N as indicated in the figure above - and the work done can be calculated as

Wspring = 1/2 (1 N/m) (1 m)2 

   = 0.5 (J, Nm)

The spring constant can be calculated by modifying eq. 4 to

k = 2 (0.5 J)/ (1 m)2                                             

  = 1 N/m

Work done by Moment and Rotational Displacement

Rotational work can be calculated as

WM = T θ                        (5)


WM = rotational work done (J, ft lb)

T = torque or moment (Nm, ft lb)

θ = displacement angle (radians)

Example - Rotational Work

A machine shaft acts with moment 300 Nm. The work done per revolution (2 π radians) can be calculated as

WM = (300 Nm) (2 π)

     = 1884 J  

Representations of Work 

Force can be exerted by weight or pressure:

W = ∫ F ds

    = ∫ m ag dh

    =∫ p A ds

    =∫ p dV                                             (6)


W = work (J, Nm)

F = force (N)

ds = distance moved for acting force, or acting pressure (m)

m = mass (kg)

ag = acceleration of gravity (m/s2)

dh = elevation for acting gravity (m)

p = pressure on a surface A, or in a volume (Pa, N/m2)

A = surface for acting pressure (m2)

dV = change in volume for acting pressure p (m3)

Power vs. Work

Power is the ratio of work done to used time - or work done per unit time.

Sponsored Links

Related Topics

Related Documents

Sponsored Links

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 - 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 Pro Sketchup Extension Warehouse!

About the Engineering ToolBox!


We don't collect information from our users. Only emails and answers are saved in our archive. Cookies are only used in the browser to improve user experience.

Some of our calculators and applications let you save application data to your local computer. These applications will - due to browser restrictions - send data between your browser and our server. We don't save this data.

Google use cookies for serving our ads and handling visitor statistics. Please read Google Privacy & Terms for more information about how you can control adserving and the information collected.

AddThis use cookies for handling links to social media. Please read AddThis Privacy for more information.


This page can be cited as

  • Engineering ToolBox, (2007). Work done by Force. [online] Available at: [Accessed Day Mo. Year].

Modify access date.

. .


3D Engineering ToolBox - draw and model technical applications! 2D Engineering ToolBox - create and share online diagram drawing templates! Engineering ToolBox Apps - mobile online and offline engineering applications!

Scientific Online Calculator

Scientific Calculator

3 30

Sponsored Links