STEMHub.tools
Energy · Mechanics

Kinetic & Potential Energy Calculator

Calculate kinetic energy, gravitational potential energy, and their mechanical total from mass, speed, height, and local gravitational acceleration.

Formula shown Runs locally Reviewed Aug 11, 2026
Follow us on Google
Equation guide

Near-Earth translational energy with constant gravitational acceleration

Kinetic energy

Eₖ = ½mv²

Gravitational potential

Ug = mgh

Mechanical total

Emech = Eₖ + Ug
Mechanical energy

Compare motion and position energy

Height is measured upward from the chosen level h = 0 and cannot be negative in this calculator. The approximation Ug = mgh assumes nearly constant g over the height range. In conservation mode, each edited value determines the other while Emech stays fixed. Inputs, derived inputs, and displayed results use at most three decimal places.

Emech = ½mv² + mgh

Enter one state to compare its kinetic and potential energy.

Using the model

Symbols, assumptions and limitations

Interpretation notes

The user-selected level h = 0 is the zero of gravitational potential energy, and this calculator restricts h to non-negative values above it. The approximation Ug = mgh assumes nearly constant gravitational acceleration over the height range. Conservation mode fixes mass, gravity, and total energy while kinetic and potential energy exchange. The model excludes rotational, elastic, thermal, and dissipative energy.

Worked examples

See the method in practice

01

Moving above Earth’s surface

A 2 kg object moving at 4 m/s at a height of 3 m has 16 J of kinetic energy and about 58.84 J of gravitational potential energy.

02

Maximum height

When all available mechanical energy is potential energy, speed is zero and hmax = Emech/(mg).

Questions

Frequently asked

Can height or potential energy be negative?

Potential energy depends on the chosen zero level. This calculator defines the entered reference as h = 0 and models only h ≥ 0, so its displayed mgh term is non-negative; another valid reference convention could produce negative values.

Should velocity be negative?

Enter speed as a non-negative magnitude. Kinetic energy depends on v² and therefore does not encode direction.

Is mechanical energy always conserved?

Only when the modeled system has no energy transfer through friction, drag, external work, deformation, or other non-conservative effects.

Sources & review

Equations and examples are checked against the references below. Results are educational and should be independently verified for safety-critical work.

OpenStax University Physics — Potential Energy and Conservation of Energy

Written by the STEM Hub editorial team · Reviewed August 11, 2026 · Review methodology