Work Calculator (Physics): Work, Energy, and Power
Work, energy, and power in one calculator: work (W = F d cos θ), power, kinetic energy, gravitational PE, and the work-energy theorem, each with its formula and convention shown.
Result
Enter the values above to compute work.
| Quantity | Value |
|---|
W = F d cos θ; KE = ½ m v²; PE = m g h; P = W / t; P = F v cos θ
How?
How this is calculated
Work for a constant force is W = F d cos θ, where θ is the angle between the force and the displacement. Kinetic energy is KE = ½ m v², and the work-energy theorem ties the two together: the net work done on an object equals its change in kinetic energy, W_net = KE_final - KE_initial. Gravitational potential energy near Earth's surface is PE = m g h. Average power is work over time, P = W / t; instantaneous power from a force and a velocity is P = F v cos θ, which reduces to P = F v when the force acts along the direction of motion.
At exactly 90 degrees, cos θ is not quite zero in floating-point arithmetic (Math.cos(π/2) evaluates to about 6 × 10-17), and that residue scales with the size of the inputs. This tool snaps the cosine itself to zero whenever its magnitude is below 1e-12, so a 90-degree angle always reports exactly zero work or power, at any magnitude, rather than a stray fraction of a joule or watt. Values display to 4 significant figures; the calculation runs at full precision in SI units, with US-customary input converted to SI before anything is computed.
Formula: W = F d cos θ; KE = ½ m v²; PE = m g h; P = W / t; P = F v cos θ
How to calculate power in physics
Power is the rate energy is transferred. When you know the work done and how long it took, P = W / t. When you know the force and the speed of the object it is acting on, P = F v cos θ, using the angle between the force and the velocity. The two methods agree: work over a time interval divided by that interval is the same average power that F v cos θ gives you instant to instant, for a constant force.
The work-energy theorem
The work-energy theorem says the net work done on an object equals the change in its kinetic energy, W_net = KE_final - KE_initial. Give this page an initial and a final velocity and a mass, and it returns both kinetic energies and the net work between them, without you needing to know the force or the distance it acted over.
Force times distance, and the angle that changes everything
"Force times distance" is only the full story when the force pushes straight along the motion. The moment there is an angle, the effective force along the direction of travel shrinks by a factor of cos θ, and past 90 degrees the force removes energy instead of adding it. That is the entire content of W = F d cos θ, and it is why this page always asks for the angle rather than assuming it is zero.
Joules, watts, and horsepower
Work and energy are reported in joules; power in watts, one joule per second. The power mode also converts to mechanical horsepower (745.699872 W per hp) as a secondary figure, since a lot of power ratings in the wild are still quoted in horsepower.
Where kinetic energy fits
Kinetic energy, KE = ½ m v², is the energy an object has because it is moving. It shows up on its own in the kinetic-energy mode, and it is the quantity the work-energy theorem tracks the change in. For the spring's own stored energy, ½ k x², see the Hooke's law calculator, which owns elastic potential energy.
Assumptions and model
- Constant force along a straight path; a position-dependent force needs W = ∫F·ds.
- Gravity near Earth's surface, g stated beside every potential-energy result.
- Force and distance are entered as magnitudes; the angle carries direction.
- Mechanical horsepower (745.699872 W), not metric horsepower (735.49875 W).
Sources
- OpenStax College Physics 2e, 7.1 Work - The Scientific Definition. OpenStax. Retrieved .
- OpenStax College Physics 2e, 7.2 Kinetic Energy and the Work-Energy Theorem. OpenStax. Retrieved .
- OpenStax College Physics 2e, 7.3 Gravitational Potential Energy. OpenStax. Retrieved .
- OpenStax College Physics 2e, 7.7 Power. OpenStax. Retrieved .