Work Energy Calculator
Calculate work done by a force using W = Fd cos(θ). Includes Work-Energy Theorem (ΔKE = W), gravitational PE, friction work, efficiency, and mechanical advantage.
N
m
°
Work Done (J)
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Work Done (kJ) —
Work Done (ft-lb) —
Extended More scenarios, charts & detailed breakdown ▾
N
m
°
Work (J)
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Work (kJ) —
Effective Force Component —
Professional Full parameters & maximum detail ▾
N
m
°
kg
J
Work Components
Work by Applied Force (J) —
Work Against Friction (J) —
Net Work (J) —
Efficiency & Type
Efficiency (%) —
Force Type —
How to Use This Calculator
- Enter Force (N), Distance (m), and the Angle between force and displacement.
- Click Calculate to see work in Joules, kJ, and ft-lb.
- Use the Work-Energy Theorem tab to find net work from velocity change.
- Use the Gravitational PE tab to compute mgh work.
- The Professional tab adds friction work, net work, and efficiency calculation.
Formula
W = F × d × cos(θ) | ΔKE = W_net = ½mv₂² − ½mv₁² | W_gravity = mgh
Example
F=50 N, d=10 m, θ=0° → W = 50×10×cos(0°) = 500 J = 0.5 kJ = 368.78 ft-lb.
Frequently Asked Questions
- Work = Force × Distance × cos(θ), where θ is the angle between the force direction and displacement. When force and displacement are parallel (θ=0°), cos(0°)=1, so W = F × d.
- The Work-Energy Theorem states that the net work done on an object equals its change in kinetic energy: W_net = ΔKE = ½mv₂² − ½mv₁². This means work and energy are interchangeable.
- The SI unit of work is the Joule (J), where 1 J = 1 N·m = 1 kg·m²/s². In imperial units, work is measured in foot-pounds (ft-lb). 1 J ≈ 0.7376 ft-lb.
- Only the component of force parallel to displacement does work. At 0° (force parallel to motion), all force contributes: W = Fd. At 90° (force perpendicular), cos(90°)=0, so no work is done despite the force.
- Work is the energy transferred (W = Fd cos θ, in Joules). Power is the rate at which work is done (P = W/t, in Watts). Same work done faster requires more power.