The joule

The idea

The SI unit of work is the joule (J): 1 J is the work done when a 1 N force displaces an object 1 m in the direction of the force; 1 J = 1 kg m² s⁻².

A unit for work

Length is measured in metres and force in newtons. Work is made from a force and a displacement.

What do you think the unit of work could be built from?

• The newton and the metre together
• The kilogram alone
• The second alone

Build the unit

Press Next step to build the joule.

A newton times a metre

One newton pushing through one metre makes one joule. Because a newton is itself 1 kg m s⁻², the joule can be written in kilograms, metres and seconds.

The SI unit of work is the joule (J). 1 J is the work done when a 1 N force displaces an object 1 m in the direction of the force: 1 J = 1 N × 1 m = 1 kg m² s⁻².

Notes

1 J = 1 N × 1 m = 1 kg m² s⁻²: the work done when a 1 N force displaces an object 1 m in its direction.

Check yourself

What is the SI unit of work?

A constant force of 20 N moves an object 3 m in the direction of the force. How much work is done, in joules?

Answer: 60 J

W = 20 N × 3 m = 60 J.

1 joule of work is done when…

In terms of kg, m and s, 1 J is equal to…

• The newton (N). The newton is the SI unit of force, not of work.
• The joule (J) — correct. Yes!
• The metre (m). The metre is the SI unit of displacement, not of work.
• a force of 1 N acts for 1 second. The joule is defined by the force and the displacement. Time is not part of the definition.
• an object of mass 1 kg is displaced by 1 m. The work depends on the force applied and the displacement, not on the mass alone.
• a constant force of 1 N displaces an object by 1 m in the direction of the force — correct. Yes!
• 1 kg m² s⁻² — correct. Yes!
• 1 kg m s⁻². That is 1 newton, the unit of force. Multiplying by 1 m gives 1 kg m² s⁻².
• 1 kg m² s⁻¹. The newton contains s⁻², so 1 J = 1 kg m s⁻² × 1 m = 1 kg m² s⁻², not s⁻¹.