Kinetic & Potential Energy — KE, PE, Conservation

Compute KE (½mv²), PE (mgh), and total mechanical energy. Use the conservation solver to find speed at height, drop speed, or max height. Private by design — runs entirely in your browser.

Inputs

Tip: Press Ctrl/Cmd + Enter to calculate. The URL updates so you can bookmark or share your inputs.

Results

Understanding Kinetic & Potential Energy

Kinetic energy measures the energy of motion and is given by KE = ½ m v², where m is mass (kg) and v is speed (m/s). Gravitational potential energy in a uniform field is PE = m g h, with g the local gravitational acceleration (m/s²) and h height relative to a chosen zero level. The sum E = KE + PE is the mechanical energy. When non-conservative forces like air drag are negligible, E stays constant — this is the principle of conservation of mechanical energy.

This calculator lets you compute KE and PE directly for any mass, speed, height, and gravity, or use conservation to predict speeds and heights as energy trades between kinetic and potential forms. For example, an object dropped from rest at height h₀ has v = √(2 g (h₀ − h)) when it falls to height h, and a launch straight up with speed v₀ reaches a maximum height hmax = v₀²/(2 g) + h₀ (ignoring drag).

Assumptions & Tips

  • Uniform g: We assume gravity is constant over the height range. For large altitudes, use a variable-g model like our Gravity tool.
  • Reference level: Set h = 0 wherever you like; only differences in height matter for PE.
  • Units: Inputs are SI; results show Joules (J) and derived values. Copy results with one click.

Disclaimer: Educational tool only. Ignores air resistance, rotation, and real-world losses.

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