Work Done Calculator
Work in physics has a precise meaning: force applied in the direction of motion, over a distance — push something sideways while it moves forward and you're doing less work than if you pushed directly along its path.
Inputs
Result
600 J
0.00016667 kWh
How it works
W = F·d·cos θ
How the work done calculator works
W = F × d × cos θ, where θ is the angle between the applied force direction and the direction of motion.
Worked example: 120 N pushed 5 m, force aligned with motion (0°)
- W = 120 × 5 × cos(0°) = 120 × 5 × 1 = 600 J.
- The same force and distance at a 60° angle instead gives 120 × 5 × cos(60°) = 120 × 5 × 0.5 = 300 J — exactly half, purely from the angle.
Common mistakes to avoid
Assuming work is just force times distance regardless of angle
That's only true when force is applied exactly in the direction of motion (θ = 0°). At any other angle, only the component of force in the direction of motion contributes to work, which is what cos θ accounts for.
Forgetting that a force perpendicular to motion does zero work
At exactly 90°, cos(90°) = 0, meaning that force contributes no work at all — this is why carrying a heavy bag while walking horizontally (force is vertical, motion is horizontal) technically involves zero physics-definition 'work' from the carrying force, even though it feels effortful.
Frequently asked questions
Why does carrying something horizontally feel like work but technically isn't?
The muscular effort to support the weight against gravity involves internal biological energy use, but in the strict physics definition, work requires force in the direction of displacement — supporting weight while moving horizontally involves a vertical force and horizontal motion, which are perpendicular.
How is work related to energy?
Work done on an object equals the energy transferred to or from it — this is the fundamental connection between force, motion, and energy change captured in the work-energy theorem.
What does negative work mean?
When the angle exceeds 90° (force has a component opposing motion, like braking friction), cos θ becomes negative — negative work means energy is being removed from the object's motion rather than added.
Why is the result also shown in kWh?
kWh is a more familiar large-scale energy unit (used for electricity billing) — showing the joule result converted to kWh helps put mechanical work into a more everyday-recognisable scale, even though the actual number is usually tiny in kWh terms.
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