Work Formula – W = F × d Explained
The work formula in physics: W = F × d. Explained with examples, units, and the angle variant W = Fd cos θ. Generate it for Word instantly.
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The work formula in physics - definition, variables, and worked examples
The work formula calculates the energy transferred when a force moves an object over a distance. In its simplest form, the work equation is W = F × d, where W is work in joules (J), F is the applied force in newtons (N), and d is the displacement in metres (m). This version applies when the force acts in the same direction as the motion - for example, pushing a box across a flat floor.
When the force is applied at an angle θ to the direction of displacement, the work formula becomes W = F × d × cos θ. The cosine factor isolates the component of force that actually contributes to movement. At θ = 0° the full force does work; at θ = 90° (force perpendicular to motion) no work is done - which is why carrying a suitcase horizontally does zero work against gravity.
A quick worked example: a 50 N force pushes a crate 4 metres along a ramp inclined at 30° to the horizontal. The work done is W = 50 × 4 × cos 30° = 50 × 4 × 0.866 ≈ 173.2 J. If the same force were applied parallel to the displacement (θ = 0°), the work would be 200 J - the cosine term accounts for the 'lost' component of force that pushes into the ramp surface rather than along it.
The work formula connects directly to kinetic energy through the work-energy theorem: the net work done on an object equals the change in its kinetic energy (W_net = ΔKE = ½mv₂² − ½mv₁²). This relationship is fundamental in mechanics, from calculating braking distances to designing roller coasters. Use the generator above to get the work formula - or any of its variants - formatted and ready for your Word document or lab report.
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Frequently asked questions
What is the work formula in physics?
The work formula is W = F × d, where W is work measured in joules, F is force in newtons, and d is displacement in metres. When the force is applied at an angle θ to the direction of motion, the formula becomes W = F × d × cos θ.
What is the equation for work?
The standard equation for work is W = Fd. It calculates the energy transferred when a force moves an object over a distance. If the force acts at an angle, you multiply by cos θ to account for only the component of force along the displacement.
How do I calculate work with the work formula?
Identify the force (F) in newtons and the displacement (d) in metres. If the force is parallel to the motion, multiply them: W = Fd. If the force is at an angle θ, use W = Fd cos θ. The result is in joules (J).
What are the units of the work formula?
Work is measured in joules (J). One joule equals one newton-metre (1 J = 1 N·m). In CGS units, work is measured in ergs (1 erg = 1 dyne·cm).
How do I insert the work formula into Word?
Use FormulAI to generate the work formula, then paste it directly into Microsoft Word as a native equation. You can also download it as a DOCX file or copy the LaTeX source.
When is work zero even if a force is applied?
Work is zero when the force is perpendicular to the displacement (θ = 90°), because cos 90° = 0. For example, carrying a box horizontally does no work against gravity, since gravity acts downward whilst the displacement is horizontal.