Work-Energy Theorem Calculator
The work-energy theorem is one of the most useful tools in classical mechanics: the net work done on an object equals the change in its kinetic energy, W = (1/2) m v2² - (1/2) m v1². Enter the object's mass, initial velocity, and final velocity to find the net work done. A positive result means work was done on the object (it sped up); a negative result means the object lost kinetic energy (it slowed down, with work done against the motion). The calculator also shows initial and final kinetic energies for reference.
Work-energy theorem formula
W = ΔKE = (1/2) m v2² - (1/2) m v1²
Where m is mass (kg), v1 is initial velocity (m/s), v2 is final velocity (m/s), and W is net work done in Joules (J). The sign of W indicates whether energy was added to (+) or removed from (-) the object.
Understanding work and energy
- Work done by gravity on a falling object is positive (object gains KE); work done by friction is always negative (object loses KE).
- If the net work on an object is zero (e.g., circular motion on a level surface with no friction), its speed stays constant.
- The theorem applies even when force is not constant, because it integrates F ds = d(KE).
- Power is the rate of doing work: P = W / t = F v (Watts = Joules per second).
- For gravity, W = -mgh (negative when going up, positive when going down), directly giving the gravitational potential energy change.
Work-energy theorem: frequently asked questions
What is the work-energy theorem?
The work-energy theorem states that the net work done on an object equals the change in its kinetic energy: W_net = delta KE = (1/2) m v2² - (1/2) m v1². It directly links force, displacement, mass, and velocity, providing a powerful alternative to Newton's second law for many problems.
What is the unit of work?
The SI unit of work (and energy) is the Joule (J), equal to one Newton times one meter (N m = kg m² / s²). In the imperial system, work is measured in foot-pounds (ft lb). One foot-pound equals approximately 1.356 J.
How is work related to force and displacement?
For a constant force F acting over displacement d at angle theta to the displacement direction: W = F d cos(theta). This equals the change in kinetic energy only if the force is the net force. If multiple forces act, you add their individual work contributions.
Can work be negative?
Yes. If the velocity decreases (v2 less than v1), the change in kinetic energy is negative, meaning work done on the object is negative. For example, friction does negative work on a sliding object, removing kinetic energy and converting it to heat.
How is the work-energy theorem used in practice?
It is used to find the speed of an object after a known force acts over a known distance without needing to know the time. For example, calculating how fast a car accelerates after a known engine force acts over a given distance, or how far a bullet travels in a gun barrel.
Official sources
- OpenStax University Physics Volume 1: Kinetic Energy and the Work-Energy Theorem.
- NIST Reference on Constants, Units, and Uncertainty: NIST Physics.
Reviewed by the CalculatorHub team, edited by James Graham, 15 June 2026. See our methodology.