Energy & Power Calculator — Kinetic, Potential, Work

Compute kinetic energy, potential energy, work, power and conservation of energy.

About this calculator

An energy and work calculator computes kinetic energy, gravitational and elastic potential energy, work done by forces, and power delivered. Energy is the universal currency of physics — it can change form (kinetic to potential, electrical to thermal) but is conserved in any closed system.

The work-energy theorem states that the net work done on an object equals the change in its kinetic energy. This single equation solves problems that would be tedious with kinematics + Newton's laws alone.

Formula

KE = \tfrac{1}{2}mv^2 \;;\; PE = mgh \;;\; W = F \cdot d

  • KE — Kinetic energy (J)
  • PE — Gravitational potential energy at height h
  • W — Work = force × distance (parallel components only)
  • P — Power = W/t = F·v

Worked example

Inputs: 2 kg ball dropped from 10 m height (g = 9.81)

  1. Initial PE = mgh = 2 × 9.81 × 10 = 196.2 J
  2. At ground: all PE → KE, so KE = 196.2 J
  3. Impact velocity: ½mv² = 196.2 → v² = 196.2, v = 14.0 m/s
  4. Verifies kinematic answer: v = √(2gh) = √196.2 = 14.0 m/s

Frequently asked questions

Is energy really always conserved?

In a closed, isolated system: yes, exactly. In real-world problems we often see "energy loss" — but it is really energy being transferred out of the system (sound waves, heat dissipation, deformation of materials). When you account for ALL forms of energy (kinetic, potential, thermal, electromagnetic, chemical, nuclear), the total is always conserved.

What is the relationship between work, power, and force?

Work is energy transferred when a force moves an object: W = F·d (if force is constant and along the direction of motion). Power is the rate of work: P = W/t. For motion at constant velocity, P = F·v — used to spec motors, engines, and athletes' output (cyclists at 250 W sustained = pro level).

Related calculators

Kinematics Newton's Laws Thermodynamics

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