Calculators
Work-Energy Theorem Calculator
Solve net work or speed changes with the work-energy theorem.
Work-Energy Theorem Calculator tool
Loading tool…
Jump to a section
About This Tool
The work-energy theorem says the net work done on an object equals its change in kinetic energy. For constant mass translational motion, Wnet = 1/2 m(vf^2 - vi^2). This calculator solves net work, final speed, initial speed, or mass from the other values, with common mass, speed, and energy units. All calculations run locally in your browser.
How To Use It
- Choose whether to solve for net work, final speed, initial speed, or mass.
- Enter the known mass, speeds, and/or net work with their units.
- Use positive net work when the object's kinetic energy increases and negative net work when it decreases.
- Read the result with the model assumptions, especially when solving inverse cases that require physically consistent signs.
Examples
Speeding up
A 2 kg object speeding up from 3 m/s to 5 m/s has Wnet = 1/2 x 2 x (25 - 9) = 16 J.
Slowing down
The same 2 kg object slowing from 5 m/s to 3 m/s has Wnet = -16 J because kinetic energy decreases.
Find final speed
For a 2 kg object starting at 3 m/s with 16 J of positive net work, vf = sqrt(3^2 + 2 x 16 / 2) = 5 m/s.
Find mass
If speed changes from 3 m/s to 5 m/s while net work is 16 J, m = 2Wnet / (vf^2 - vi^2) = 2 kg.
Useful Notes
Core relationship
The calculator uses Wnet = delta KE = 1/2 m(vf^2 - vi^2). Net work is the total work from all forces, not necessarily the work from one individual force.
Sign convention
Positive net work increases kinetic energy. Negative net work decreases kinetic energy. When solving for mass, the sign of net work must match the sign of vf^2 - vi^2.
Speeds, not velocity components
Kinetic energy depends on speed magnitude, not direction. This calculator does not track vector direction, displacement, force angle, or rotational motion.
Units
Mass values are converted to kilograms, speeds to metres per second, and work or energy to joules before the formula is applied. Results can be shown in common metric, imperial, and energy units.
Model limitations
This educational calculator assumes constant mass and translational kinetic energy. It does not replace a full force, path, friction, potential energy, or safety analysis for real systems.
FAQ
Is net work the same as kinetic energy?
No. Net work is the change in kinetic energy. The final kinetic energy equals the initial kinetic energy plus net work.
Can net work be negative?
Yes. Negative net work means the object's kinetic energy decreases, such as during braking or when resistive forces dominate.
Why does the calculator reject some speed and work combinations?
Some inverse inputs would require a negative value under a square root or a negative mass. Those combinations are not physically consistent in this simplified model.
Does this include gravitational potential energy?
Not directly. The theorem can be used with total net work from all forces, but this calculator focuses on the kinetic energy change between two speeds.