Work-Energy Theorem Calculator

The Work-Energy Theorem Calculator applies the principle Wnet = ΔKE = ½m(vf² − vi²) to solve physics problems. Enter an object's mass, initial velocity, and final velocity — or switch to Work from Force mode using force, displacement, and angle. Get back net work done, change in kinetic energy, initial and final KE values, plus a visual energy breakdown.

kg

Mass of the object in kilograms

m/s

Speed of the object before the force acts

m/s

Speed of the object after the force acts

N

Magnitude of the force applied to the object

m

Distance the object moves in the direction of interest

°

Angle in degrees between the force vector and the direction of motion. Use 0° if force is parallel to motion.

Results

Net Work Done (W)

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Change in Kinetic Energy (ΔKE)

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Initial Kinetic Energy (KEᵢ)

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Final Kinetic Energy (KE_f)

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Kinetic Energy Comparison (J)

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 = ΔKE = ½m·v_f² − ½m·v_i². If the net work is positive, the object speeds up; if negative, it slows down.

How do I calculate work done by a force?

Work done by a constant force is calculated as W = F·d·cos(θ), where F is the applied force in newtons, d is the displacement in metres, and θ is the angle between the force and the direction of motion. When the force is parallel to the motion (θ = 0°), cos(θ) = 1 and the formula simplifies to W = F·d.

What units are used in the work-energy theorem?

The SI unit for both work and energy is the joule (J), where 1 J = 1 N·m = 1 kg·m²/s². Force is measured in newtons (N), mass in kilograms (kg), velocity in metres per second (m/s), and displacement in metres (m).

Under what conditions is work done zero?

Work is zero when: (1) no displacement occurs, (2) the force is perpendicular to the displacement (θ = 90°, so cos 90° = 0), or (3) the applied force is zero. For example, carrying a box horizontally while the gravitational force acts downward does zero work against gravity.

Can work be negative?

Yes. When the force component acts opposite to the direction of motion (θ > 90°), the work done is negative. Friction is a classic example — it always does negative work on a sliding object, removing kinetic energy and slowing it down.

How does a work-energy theorem calculator work?

You provide either (a) mass, initial velocity, and final velocity so the calculator computes ΔKE = ½m(v_f² − v_i²) and equates it to net work, or (b) force, displacement, and angle so it computes W = F·d·cos(θ). Both modes show initial KE, final KE, and the net work or energy change.

Can this calculator be used for all types of physics problems?

This calculator covers the most common work-energy scenarios: work from kinematics (velocity change) and work from a constant force at an angle. It does not cover variable forces, rotational work, or thermodynamic work, which require more advanced integration or separate tools.

What is the difference between work and kinetic energy?

Kinetic energy (KE = ½mv²) is the energy an object possesses due to its motion — it is a state quantity. Work is the process of transferring energy via a force over a displacement. The work-energy theorem links them: the net work done on an object equals the change in its kinetic energy.

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