What next?
Work done over time is power. Work stored in motion is kinetic energy.
How to use this calculator
- Enter the force applied, in newtons.
- Enter the distance the object moves, in metres.
- Set the angle between the force and the direction of motion (0° if they line up).
What your result means
Work is energy transferred when a force moves something — measured in joules. Only the part of the force acting along the direction of motion does work, which is why the angle matters: push at 90° to the motion and no work is done.
Why this one is different
The angle between the force and the movement is part of the sum, not an afterthought, and its consequence is spelled out: at ninety degrees the cosine is zero, so carrying a bag along a level floor does no work at all. Past ninety the figure goes negative, because the force is now taking energy out of the motion, and that is labelled too.
Holding a heavy box does no work
In physics, work needs movement. Straining to hold a box still feels like effort, but with zero distance the work done is zero. Carry it across the room and you finally do measurable work — force multiplied by the distance travelled.
How it works
Work equals force times distance times the cosine of the angle between them. When force and motion point the same way (θ = 0°), cosθ = 1 and work is simply force × distance. At 90°, cosθ = 0 and no work is done.
Formula
Worked example
Dragging a crate 8 m with a 150 N force applied at 30° to the floor:
W = 150 × 8 × cos 30°
W = 150 × 8 × 0.8660
W = 1,039 J (about 1.04 kJ)
Pulling horizontally instead (θ = 0°) would do 1,200 J — the vertical component of an angled pull does no useful work along the floor.
Frequently asked questions
What are the units of work?＋
Work is measured in joules (J) in SI units. One joule is one newton of force moving something one metre. It is the same unit used for energy.
Why does the angle reduce the work?＋
Only the component of force along the direction of motion does work. At an angle, that component is F×cosθ, so the steeper the angle the less work is done — reaching zero at 90°.
Is work the same thing as energy?＋
They share a unit and, in this context, a value: work is energy transferred by a force. Doing 1,000 J of work on an object hands it 1,000 J of energy. The distinction is that energy is a quantity a system has, while work is the process of moving it from one place to another.
Why is no work done when I hold something still?＋
Because work requires displacement. Holding a heavy box is tiring because muscles consume energy maintaining tension, but in the mechanical sense nothing moves, so no work is done on the box.
How does work relate to power?＋
Power is work divided by the time taken. Lifting the same load up the same stairs does identical work whether you walk or run; running simply demands more power.
Does work depend on the path taken?＋
For conservative forces such as gravity, no: only the start and end heights matter. Against friction it very much does, which is why a longer route costs more energy even when it ends in the same place.
Related calculators
Assumptions & limitations
Engineering formulas are exact; the situations they model are not. Read your result with these limits in mind:
- Assumes a constant force acting over the whole displacement. A varying force needs the integral of force with respect to distance.
- Only the component of force along the direction of motion does work, which is what the cos θ term handles.
- A force perpendicular to motion does zero work — carrying a box across level ground does no work on the box in the physics sense.
- Ignores energy lost to friction and heat unless you enter the friction force yourself.