Work Calculator
Mechanical work measures the scalar energy transferred when an applied force displaces an object along a spatial path (W = F × d × cos θ). If the force acts perpendicular to motion, zero work is accomplished. This calculator calculates total work accomplished alongside instantaneous mechanical power generated over time in both SI (Joules, Watts) and Imperial (foot-pounds, horsepower) units.
Magnitude of force applied in Newtons (N)
Distance the object travels while force is applied in metres (m)
Angle in degrees between applied force vector and direction of motion (0° = parallel)
Duration in seconds taken to perform the displacement (for power calculation)
Total mechanical work accomplished in Joules (1 J = 1 N·m)
How to Use This Calculator
- Enter the applied force in Newtons.
- Enter the total distance the object was displaced along its trajectory.
- Specify the angle between the pulling/pushing direction and the motion axis.
- Input the time taken to evaluate power generation in Watts and mechanical horsepower.
Formula & Calculation Methodology
Work equals the dot product of the force vector and the displacement vector. When the angle θ is 0°, cos(0°) = 1 yielding maximum work. If θ is 90°, cos(90°) = 0 meaning no work is done. Power is work divided by time elapsed.
Worked Example
Pulling a sled with 200 N force at a 30° angle over 50 metres in 25 seconds
Frequently Asked Questions
Can mechanical work be negative?↓
Yes. When force opposes displacement (such as kinetic friction or braking deceleration where 90° < θ ≤ 180°), cos(θ) is negative, indicating energy is being removed from the moving body.
Why does carrying a heavy box horizontally perform zero gravitational work?↓
Lifting force acts vertically upward against gravity (90° relative to horizontal travel). Because cos(90°) = 0, gravity does zero work on the box during purely horizontal displacement.
How does one Joule relate to electrical power units?↓
One Joule is equal to one Watt-second (1 W·s). Consequently, 1 kilowatt-hour (kWh) equals exactly 3,600,000 Joules (3.6 MJ).
What limitation applies if the applied force changes over the path?↓
This formula assumes a constant force magnitude and steady vector angle over the entire distance. If force varies with position (e.g. compressing an elastic spring), work must be calculated via calculus integration: W = ∫ F(x) dx.
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Source Citation & Disclaimer
Informational tool only; not licensed tax, legal, or financial advice.