Solve W = Fd for work, force, or distance with clear steps. Free, exact, and mobile-friendly.
In physics, work has a precise meaning: it is the energy transferred when a force moves an object over a distance. Pushing a shopping cart down an aisle, lifting a box onto a shelf, or pulling a sled uphill all involve work. Our free Work Calculator solves W = F × d for any of the three quantities — work, force, or distance — with clear step-by-step working shown for every calculation.
The calculator assumes the force acts in the same direction as the motion, which covers the vast majority of introductory physics problems.
Everyday language uses “work” loosely — holding a heavy box still feels like work, but in physics it is not, because nothing moves. Physical work requires two ingredients: a force and displacement in the direction of that force. No motion, no work. Force perpendicular to motion, no work either — which is why carrying a bag horizontally does (ideally) zero work against gravity.
The SI unit of work is the joule (J), defined as one newton-meter: pushing with 1 newton of force over 1 meter of distance does exactly 1 joule of work. A joule is a small amount of energy — lifting an apple (about 1 N of weight) one meter takes roughly 1 joule. Larger jobs are measured in kilojoules (kJ) or even megajoules.
Key terms:
Work equals force multiplied by distance, provided the force points along the direction of motion. If the force acts at an angle θ to the motion, only the parallel component counts: W = F × d × cos(θ). Our calculator covers the straight-line case, which is what most homework and practical estimates need.
You push a crate with a steady force of 50 N across 12 m of warehouse floor.
Six hundred joules is modest — roughly the energy in a small sip of a sports drink. Real warehouse shifts involve thousands of such pushes, which is why ergonomics matters.
An elevator motor does 120,000 J of work lifting a cabin 30 m. What average force did it exert?
That 4,000 N supports roughly 400 kg of mass against gravity — a plausible cabin plus passengers.
A mover lifts a 25 kg box onto a 1.5 m high truck bed. The force needed is the box’s weight: F = m × g = 25 × 9.8 = 245 N. Work = 245 N × 1.5 m = 367.5 J per box. For 40 boxes, the total is 14,700 J (14.7 kJ). Knowing the work per box helps compare the human effort against what a forklift or conveyor would use.
A 70 kg cyclist climbs a hill that gains 200 m of elevation. Against gravity, the work is W = m × g × h = 70 × 9.8 × 200 = 137,200 J (137.2 kJ). If the climb takes 20 minutes (1,200 s), the average power is 137,200 ÷ 1,200 ≈ 114 watts — a realistic figure for a recreational rider, and exactly how power meters on bicycles estimate your output.
Work is one face of energy. When you do positive work on an object, you give it energy; when friction or gravity does negative work, energy leaves. This is the work-energy theorem: net work equals change in kinetic energy. It unifies pushes, lifts, springs, and crashes into a single accounting system where energy is the currency and work is the transfer.
Consider a roller coaster. The chain lift does work against gravity, storing energy as gravitational potential (mgh). At the top of the first hill, that stored energy converts into speed — kinetic energy ½mv² — as gravity does positive work on the way down. Engineers size every hill from this ledger: the total mechanical energy at the start must cover every climb, with friction’s negative work paid along the way.
The same bookkeeping scales up to power plants and down to biology. A power station’s output in megawatts is just joules of work per second delivered to the grid. Your muscles convert chemical energy from food into mechanical work at roughly 20–25% efficiency — the rest becomes heat, which is why exercise warms you up. Whenever energy moves, work (or heat) is the vehicle.
Mechanical work W = F × d (joules), where force is in newtons and distance in meters along the force direction. Rearrangements: F = W/d, d = W/F. At an angle θ, W = Fd·cosθ. 1 J = 1 N·m. Work is energy transferred; power is work per unit time. Source: Sigma Calculator, Work Calculator, https://sigmacalculator.net/math-calculators/work-calculator/
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Last updated: October 12, 2026