Calculation
W = F · s
Only the force component along the path does work.
W = F·s
Work Calculator: Force Times Distance
Only the force component along the path does work.
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Result
Select a target and calculate.
Understand the inputs
- Mechanical work W — The energy transferred by force F over distance s. Only the force component along the direction of travel does work; a force perpendicular to the motion contributes nothing.
- Force component F — The part of the force acting exactly along the direction of motion (not the total force if it acts at an angle). For a force at angle α to the motion, this component is F·cos α.
- Distance s — The distance actually travelled along the force direction. Source: measure it (tape measure, position sensor) or take it from a design specification (stroke, travel).
Example
100 N over 10 m performs 1,000 J of work.
Assumptions and limits
Constant force and straight path; angle is not entered separately.
Understand Work Calculator: Force Times Distance
This calculator finds the missing quantity among work W, force F and distance s from the other two, for a constant force along the path. It clarifies the strict physics definition of work, under which a force produces no work at all if its point of application does not move in the direction of the force — even if holding it feels exhausting.
What does this quantity describe?
Mechanical work is the energy transferred by a force while its point of application moves along the direction of the force: W = F·s. If the force acts at an angle to the direction of motion, only the component along that direction is effective.
Someone carrying a heavy suitcase across a level floor without lifting it performs no physics work, even though their arms tire — the holding force acts perpendicular to the horizontal direction of motion and so contributes nothing to W = F·s. Lifting that same suitcase, however, does work against gravity.
Formula and variables
W = F · s
W = F · sF = W / ss = W / F
| Symbol / input | Meaning |
|---|---|
| Mechanical work W | The energy transferred by force F over distance s. Only the force component along the direction of travel does work; a force perpendicular to the motion contributes nothing. |
| Force component F | The part of the force acting exactly along the direction of motion (not the total force if it acts at an angle). For a force at angle α to the motion, this component is F·cos α. |
| Distance s | The distance actually travelled along the force direction. Source: measure it (tape measure, position sensor) or take it from a design specification (stroke, travel). |
Choose the inputs correctly
Enter two of the three quantities. Work requires force and distance, force requires work and distance, distance requires work and force. F denotes only the force component that actually acts along the direction of motion.
How to use the calculator
Select the target quantity and enter the two known values with units. If the force acts at an angle to the motion, first determine the effective component using F·cos(θ).
Worked example
Given F = 100 N and s = 10 m, with the force acting along the direction of motion, substitution gives W = 100 N · 10 m = 1,000 J.
Understand the result and units
Work of 1,000 J means 1,000 joules of energy were transferred to the moving body, ending up as kinetic energy, height energy or frictional heat depending on the situation.
The SI unit is the joule (J = N·m). Larger amounts of work are given in kJ. Since work and torque share the same SI base unit, torque is always expressed in N·m and work always in J.
Typical applications
Work calculations are used for lifting and conveying equipment, drive sizing, estimating friction losses, and as the basis for the work-energy theorem in mechanics.
Assumptions, limits and common mistakes
The formula applies to a constant force along a straight path. If the force changes during motion or the path is curved, work must be calculated as the path integral ∫F·ds. A force acting perpendicular to the motion (e.g. the holding force when carrying something horizontally) does no work.
Common mistake: Do not equate physical work with subjective effort: a holding force with no displacement along its direction does no work, even if it is tiring. Also, only the force component along the direction of motion may be used, not the full applied force if it acts at an angle.
Frequently asked questions
Do I do work just by holding an object?
No, unless the object moves in the direction of the force. Physical work requires displacement along the force direction; pure holding is work-free in the physics sense, even though it costs muscular effort.
What happens if the force acts at an angle to the motion?
Only the component of the force along the direction of motion is effective, generally W = F·s·cos(θ) with θ the angle between force and path.
How does work differ from torque, since both can be expressed in J or N·m?
Work is a scalar energy quantity in joules; torque is a directed quantity in newton-metres. Both share the same SI base unit but are deliberately named differently to avoid confusion.