How much work does a force really do?
Work is force times distance in the direction of motion: W = F x d x cos(theta). Enter a force, a distance and the angle between them and see the work in joules, kilojoules, foot-pounds and calories, plus how it changes with distance and angle.
The setup
What this work means
How work changes
Work grows in a straight line with distance while the force and angle stay fixed.
Work scorecard
Work at several distances
Same force and angle, different distances. Work scales directly with distance.
Work in physics, explained
When Work Equals Zero
Physics work is zero when the force is perpendicular to the motion (angle = 90 degrees). This is why carrying a heavy box across a flat floor does no physics work, even though it feels tiring, gravity acts downward while motion is horizontal. The body still uses chemical energy to maintain muscle tension, but no work is done in the physics sense.
The Work-Energy Theorem
Net work done on an object equals its change in kinetic energy: W = ΔKE = 0.5m(v_f² - v_i²). Doing 1000 J of work on a stationary mass gives it 1000 J of kinetic energy. This connects work, force, distance, and motion into a single relationship.
Real-World Work Examples
Lifting a 10 kg weight 1 meter: ~98 J of work. Pushing a 1500 kg car 10 m on a flat road against rolling resistance (~150 N): 1500 J. Climbing one flight of stairs (3 m vertical, 70 kg person): ~2058 J. Human total daily energy expenditure: ~10 million joules, only a tiny fraction goes to mechanical work.
Angle Between Force and Motion
When force and motion are aligned (angle = 0), work is maximum: W = F × d. When perpendicular (angle = 90°), work is zero. Pulling a sled with a rope angled upward, only the horizontal component does work, the vertical component just reduces friction. The cosine factor handles all of this automatically.
Common questions
Why use degrees instead of radians?
Degrees are more intuitive for most users. The calculator converts internally before applying the cosine function, enter degrees, get correct results.
How is physics work different from everyday 'work'?
Physics work requires displacement in the direction of force. Holding a heavy weight without moving it does zero physics work, even though your muscles fatigue. Carrying groceries horizontally also does zero work against gravity.
What if the force varies along the path?
This calculator handles constant force. For varying force, you would integrate F(x) over the distance path. For simple cases (springs, gravity), specialized formulas exist.
Can work be negative?
Yes, when force opposes motion (angle > 90°). Friction is the most common example: it acts opposite to motion, doing negative work that removes kinetic energy from the moving object.
How does this relate to energy?
Work transfers energy between objects or forms. Work done on an object adds to its kinetic energy (or potential energy if lifting against gravity). The unit (joule) is the same for both work and energy.
Results assume a constant force and a straight-line displacement. Real machines lose energy to friction, heat and deformation, so the useful work delivered is usually less than the ideal figure shown here.