Energy Calculator
Three Kinds of Energy, One Calculator
Mechanical energy shows up in different forms depending on what's holding it: height above the ground, motion, or mass itself. This calculator covers three distinct energy formulas — gravitational potential energy, kinetic energy, and Einstein's mass-energy equivalence — each solving a different physical question with the same underlying idea that energy can be measured, converted, and conserved.
The Formulas
Kinetic Energy: KE = ½ × m × v²
Mass-Energy Equivalence: E = m × c²
Here g is standard gravity (9.81 m/s²) and c is the speed of light in a vacuum (3×10&sup8; m/s, used in this calculator's rounded form). All energy results are in joules.
Where Each Form Applies
- Potential energy — used for anything raised against gravity: a dam's stored water, a roller coaster crest, a dropped object's impact energy.
- Kinetic energy — used for anything in motion: vehicle crash energy, projectile impact, flywheel storage.
- Mass-energy equivalence — used in nuclear physics to find the energy released or absorbed when a small amount of mass converts to energy, such as in fission or fusion reactions.
How Fast Kinetic Energy Grows
Because kinetic energy scales with the square of velocity, doubling speed quadruples the energy. This is exactly why braking distances and crash forces increase so sharply with speed:
| Speed | Kinetic Energy |
|---|---|
| 30 km/h | 52,083 J |
| 50 km/h | 144,676 J |
| 90 km/h | 468,750 J |
| 120 km/h | 833,333 J |
Values computed with KE = ½mv² using m = 1,500 kg and speed converted to m/s.
How to Use This Calculator
- Choose a mode: Gravitational Potential Energy, Kinetic Energy, or Mass-Energy Equivalence.
- For potential energy, enter Mass (kg) and Height (m).
- For kinetic energy, enter Mass (kg) and Velocity (m/s).
- For mass-energy equivalence, enter only Mass (kg).
- Select Calculate to see the energy result in joules with the full worked formula.
Related Calculations
For a dedicated single-purpose version of the motion case, see the Kinetic Energy Calculator, or work backward from energy to force with the Work Calculator.