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 = KE_final − KE_initial = ½mv² − ½mv₀². It links the mechanical work done by all forces acting on an object to the resulting change in its speed.

What units does this calculator use?

Mass is in kilograms (kg), speed is in meters per second (m/s), and work/energy is in joules (J). One joule equals one newton-meter (N·m) or one kg·m²/s².

Can net work be negative?

Yes. Negative net work means the object slowed down — the net force acted opposite to the direction of motion, removing kinetic energy. For example, friction does negative work on a sliding box.

What is the difference between net work and total work?

They are the same thing. "Net work" emphasizes that W is the result of all forces combined, not just one. Individual forces (friction, gravity, applied force) each do their own work, and their sum is the net work equal to ΔKE.

How is the work-energy theorem related to Newton's second law?

The work-energy theorem is derived from Newton's second law (F = ma). By integrating F·dx = ma·dx over displacement and using kinematics (v² = v₀² + 2as), you arrive directly at W_net = ½mv² − ½mv₀². The theorem is therefore not a separate law but a useful restatement of Newton's second law.

Does this tool account for rotational kinetic energy?

No. This calculator uses translational (linear) kinetic energy only: KE = ½mv². For rotating objects such as wheels or spinning tops, rotational kinetic energy (½Iω²) must be added separately.

Work-Energy Theorem Calculator

Name: Work-Energy Theorem Calculator
Availability: InStock
Author: Nham Vu

Apply the work-energy theorem (W = ½mv² − ½mv₀²) to find net work, final speed, initial speed, or mass given the other three values.

Solve for

Select the unknown, then enter the three known values.

W = ½mv² − ½mv₀²

Mass (m) (kg)

Must be greater than 0.

Initial Speed (v₀) (m/s)

Speed at the start (use 0 for starting from rest).

Final Speed (v) (m/s)

Speed at the end of the interval.

Result

Enter values on the left and click Calculate.

Formula Reference

Solve for	Rearranged formula
Net Work (W)	W = ½mv² − ½mv₀²
Final Speed (v)	v = √(v₀² + 2W/m)
Initial Speed (v₀)	v₀ = √(v² − 2W/m)
Mass (m)	m = 2W / (v² − v₀²)

W = net work (J), m = mass (kg), v = final speed (m/s), v₀ = initial speed (m/s).

Summary

Apply the work-energy theorem (W = ½mv² − ½mv₀²) to find net work, final speed, initial speed, or mass given the other three values.

How it works

Select which variable you want to solve for: Net Work (W), Final Speed (v), Initial Speed (v₀), or Mass (m).
Enter the three known values into the input fields that appear.
Click Calculate (or press Enter) to apply the work-energy theorem formula.
The result is shown with a full equation trace so you can verify each step.
Change the solve-for variable at any time and recalculate without clearing your inputs.

Use cases

Physics homework: find the net work done on a car that accelerates from rest to highway speed.
Engineering: determine how much energy a braking system must absorb to stop a moving load.
Sports science: estimate the work done by muscles to bring an athlete from a jog to a sprint.
Classroom demos: explore how doubling speed quadruples the kinetic energy change.
Lab reports: back-calculate the net force over a known distance using measured velocities and mass.
Safety analysis: compute the stopping energy required for a vehicle at various impact speeds.

Frequently Asked Questions

Last updated: 2026-06-11 · Reviewed by Nham Vu