Work-Energy Theorem Calculator
Calculate net work done on an object from its change in kinetic energy.
Enter mass and initial and final velocities to apply the work-energy theorem.
The work-energy theorem states that the net work done on an object equals its change in kinetic energy. It does not matter how many forces act or in what direction — only the net result matters.
W_net = ΔKE = (1/2)mv² - (1/2)mv₀²
Where v₀ is the initial speed and v is the final speed. If the object speeds up, net work is positive (energy added to the system). If it slows down, net work is negative (energy removed, typically by friction or braking).
A 1,500 kg car accelerating from 0 to 30 m/s (roughly 0 to 67 mph): W = (1/2)(1500)(30²) - 0 = 675,000 J = 675 kJ
That work comes from the engine minus losses to rolling resistance and air drag. If the engine does 800 kJ and only 675 kJ appears as kinetic energy, the difference (125 kJ) went to heat in the drivetrain and tires.
The theorem is also useful in reverse: if you know how much work friction does (from force times distance), you can predict exactly how much an object slows down.
For constant force at an angle: W = F × d × cos(θ) A 50 N force applied at 30° over 10 m does W = 50 × 10 × cos(30°) = 433 J of work.
This calculator uses the velocity approach. Enter mass and before/after speeds for the object. Alternatively, it calculates from force, distance, and angle if you prefer the direct-force approach.