Work & Energy Calculator
Work500.000 J
Work (kJ)0.500 kJ
The Work & Energy Calculator computes the mechanical work done when a constant force pushes an object through a distance, including the case where the force acts at an angle to the motion. By the work–energy relationship, this work equals the energy transferred to or from the object. Results are given in joules and kilojoules so you can size everything from a quick lift to a long haul.
Formula
W = F · d · cos(θ)
- F
- Applied force in newtons (N)
- d
- Distance moved in metres (m)
- θ
- Angle between the force and the direction of motion, in degrees
- W
- Work done in joules (J)
How it works
- Enter the force in newtons, the distance moved in metres, and the angle (in degrees) between the force and the direction of motion.
- The calculator takes the cosine of the angle, because only the component of force along the motion does work, then multiplies force × distance × cos(angle).
- The result is reported in joules (rounded to three decimals) and in kilojoules. Force and distance must both be non-negative.
Worked examples
A 50 N force pushes a box 10 m in the same direction as the force (angle 0°).
- cos(0°) = 1.
- W = 50 × 10 × 1 = 500 J.
500 joules (0.5 kJ) of work done.
A 100 N force pulls a sled 5 m while angled 60° above the direction of travel.
- cos(60°) = 0.5.
- W = 100 × 5 × 0.5 = 250 J.
250 joules (0.25 kJ) of work done.
Frequently asked questions
- What is mechanical work?
- Work is energy transferred when a force moves an object along its line of action. It equals the force times the displacement times the cosine of the angle between them, measured in joules.
- Why does the angle matter?
- Only the part of the force that lies along the direction of motion does work. The cosine factor extracts that component, so a force perpendicular to the motion (90°) does zero work.
- How is work related to energy?
- By the work–energy theorem, the net work done on an object equals its change in kinetic energy. More generally, work measures the energy transferred to or from the object, both in joules.
- What units does this calculator use?
- It uses SI units: force in newtons and distance in metres, giving work in joules. The result is also expressed in kilojoules (1 kJ = 1000 J) for larger values.