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Work done by an angled force calculator
Energy and power
Work done by a force that acts at an angle to the direction of movement.
W = F s cos(θ)
This free calculator is for A-level physics. Choose the quantity you want to find, enter the other values with their units, and it shows the working in the layout used in exams, with the answer to the number of significant figures you choose. The values shown are an example. Change them to your own.
Quantity to find
Working
- Write the equationW = F s cos(θ)
- Substitute the valuesW = 50 × 8 × cos(30°)
- CalculateW = 346.41 J
- Give the answer to 3 significant figuresW = 346 J
Worked example
Find W, the work done. Given: force F = 50.0 N; distance moved s = 8.00 m; angle between the force and the movement θ = 30.0°.
- Write the equationW = F s cos(θ)
- Substitute the valuesW = 50 × 8 × cos(30°)
- CalculateW = 346.41 J
- Give the answer to 3 significant figuresW = 346 J
Symbols and units
| Symbol | Quantity | SI unit |
|---|---|---|
| W | Work done | J |
| F | Force | N |
| s | Distance moved | m |
| θ | Angle between the force and the movement | ° |
Work done by an angled force: rearranged
- To find work done: W = F s cos(θ)
- To find force: F = W / (s cos(θ))
- To find distance moved: s = W / (F cos(θ))
- To find angle between the force and the movement: θ = cos−1(W / (F s))
Exam tip
Only the component of the force along the movement does work. At 90° the work done is zero.
Common questions
What is the formula for work done by an angled force?
The equation is W = F s cos(θ), where W is the work done (J); F is the force (N); s is the distance moved (m); θ is the angle between the force and the movement (°).
What units should I use for work done by an angled force?
In SI units: work done in J, force in N, distance moved in m, angle between the force and the movement in °. The calculator also accepts common alternatives such as kilometres, grams or minutes, and converts them for you.
How do I rearrange W = F s cos(θ)?
Rearranging gives these forms: to find work done: W = F s cos(θ). to find force: F = W / (s cos(θ)). to find distance moved: s = W / (F cos(θ)). to find angle between the force and the movement: θ = cos⁻¹(W / (F s)).
Practise work done by an angled force questions
Press the button for a question with random numbers. Work it out on paper first, then type your answer.
Related
More energy and power equations: Work done, Elastic potential energy, Power from force and speed, Kinetic energy, Gravitational potential energy, Power, Energy transferred, Efficiency. See the full list on the a-level physics equation calculator page.