Calculators
Work Calculator
Solve mechanical work, force, or distance with W = Fd cos(θ).
Work Calculator tool
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About This Tool
Mechanical work measures energy transferred when a force has a component along an object's displacement. For a constant force and straight displacement, W = Fd cos(θ), where θ is the angle between the force and displacement vectors. This calculator solves for work, force magnitude along the stated direction, or displacement distance while accounting for that angle and common units. All calculations run locally in your browser.
How To Use It
- Choose whether to solve for work, force, or displacement distance.
- Enter the known force, displacement, and/or work values with their units.
- Enter the angle in degrees between the force direction and displacement direction. Use 0° for parallel directions, 90° for perpendicular directions, and 180° for opposite directions.
- Choose the result unit and interpret the sign of work using your chosen direction and angle.
Examples
Parallel force
A constant 10 N force acting along a 3 m displacement does W = 10 × 3 × cos(0°) = 30 J of work.
Force at 60 degrees
A 10 N force over 3 m at 60° does 15 J of work because only the force component along the displacement contributes.
Perpendicular force
At 90°, cos(90°) = 0, so a force perpendicular to displacement does zero mechanical work in this model.
Opposing force
A 10 N force opposite a 3 m displacement has θ = 180° and does -30 J of work, indicating energy transfer opposite the displacement.
Useful Notes
Work formula
For a constant force and straight-line displacement, W = Fd cos(θ). Rearrangements are F = W/[d cos(θ)] and d = W/[F cos(θ)] when their divisors are non-zero.
Why the angle matters
Only the component of force parallel to displacement contributes to this form of mechanical work. The cosine factor projects the force onto the displacement direction.
Units
The SI unit of work is the joule (J), equal to one newton-metre. The calculator also supports kilojoules and foot-pounds force, plus common force and distance units.
Positive, zero, and negative work
Work is positive when the force component points with the displacement, zero when it is perpendicular, and negative when it points against the displacement.
Model limitations
This calculator assumes a constant force and straight displacement with a fixed angle. Variable forces, curved paths, rotational work, and multi-stage motion generally require integration or a more detailed model.
FAQ
Is work the same as force times distance?
Only when force is parallel to displacement. In general, constant-force work is Fd cos(θ), so the angle between force and displacement matters.
Why can work be negative?
Negative work occurs when the force component along the displacement points opposite the displacement, such as some friction or braking situations.
Why is work zero at 90 degrees?
A perpendicular force has no component along the displacement, so its dot product with displacement is zero.
Is a joule the same as a newton-metre?
For work and energy, 1 joule equals 1 newton-metre. Torque also uses newton-metres dimensionally, but torque and energy are different physical quantities.