Work equals force times distance times the cosine of the angle between them — W = Fd cos θ. Plug in your values and get the answer instantly, with the formula shown.
A work calculator lets you instantly find the work done by a force acting on an object using the fundamental physics formula W = Fd cosθ, where force is measured in newtons, distance in meters, angle in degrees, and the result in joules. Work is one of the most important bridge concepts in physics, connecting force and motion to energy — whenever a force causes an object to move, it transfers energy, and that transferred energy is precisely what we call work.
This calculator handles the full formula, including the often-overlooked angle term: enter the force applied, the distance the object moves, and the angle between the force direction and the direction of motion, and the calculator computes both the total work done and the effective force (the component of force actually contributing to motion). This makes it far more accurate than simplified force-times-distance calculations that ignore angle, which is essential for real-world scenarios like pulling a sled at an angle or carrying a load while walking.
Work calculations appear throughout physics, engineering, and everyday activities: mechanical engineers calculate work done by motors and actuators, biomechanics researchers study the work performed by muscles during exercise, construction engineers calculate the work required to lift materials, and physics students use it as a stepping stone to understanding energy conservation and the work-energy theorem. Because work depends on the angle between force and displacement, it captures an important nuance that simple force calculations miss — the same force can do maximum work, zero work, or even negative work depending purely on direction.
A person pulls a sled with a rope at a 30° angle above the ground, applying 100 N of force while the sled moves 10 m across the snow. The work done is W = 100 × 10 × cos(30°) = 100 × 10 × 0.866 = 866 joules. If the same person instead pulled the rope perfectly horizontal (0°), the work would increase to W = 100 × 10 × cos(0°) = 1,000 joules — the full force would contribute to motion, since none of it is 'wasted' lifting the rope at an angle.
The work value from this calculator tells you how much energy was transferred to (or from) an object by the applied force over the given distance. A positive result means the force added energy to the object's motion, while a negative result (which occurs when the angle exceeds 90°) means the force removed energy, such as friction slowing an object down. Pay close attention to the effective force shown alongside your result — this is the portion of your applied force that actually did the work. If the effective force is much smaller than the total applied force, it means most of your effort is being 'wasted' at an unfavorable angle rather than contributing to motion. This has practical implications: when pulling a heavy object, a rope angle closer to horizontal (0°) transfers more of your pulling force into useful motion than a steep angle. When your result shows zero work despite force being applied and the object moving, check your angle input — a 90° angle between force and motion (like carrying a bag while walking, or the tension in a satellite's orbital motion) always produces zero work in the physics sense, even though it may not match everyday intuition about effort and fatigue.
Enter the force, the distance moved, and the angle between the force and the direction of motion (0° if they're aligned).
| Activity | Force | Distance | Angle | Work Done |
|---|---|---|---|---|
| Lifting a 10 kg box 1.5 m | 98 N | 1.5 m | 0° | 147 J |
| Pushing a shopping cart 20 m | 50 N | 20 m | 0° | 1,000 J |
| Carrying a bag 20 m (horizontal) | 50 N | 20 m | 90° | 0 J |
| Pulling a sled 10 m at 30° | 100 N | 10 m | 30° | 866 J |
| Deadlifting a barbell 0.6 m | 800 N | 0.6 m | 0° | 480 J |