Apple on a tree
Inputs: 0.20 kg, 3 m, Earth gravity. Formula: PE = mgh. Result: 5.88 J. The apple has stored gravitational energy relative to the ground.
Potential energy
Kinetic and Potential Energy Calculator
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Tip: Press Ctrl/Cmd + Enter to calculate. The URL updates so you can bookmark or share your inputs.
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Formula Reference
| Use case | Formula | Known values |
|---|---|---|
| Kinetic energy | KE = 1/2 mv^2 | Mass and speed |
| Potential energy | PE = mgh | Mass, gravity, and height |
| Total mechanical energy | E = KE + PE | Kinetic and potential energy |
| Speed from kinetic energy | v = sqrt(2KE / m) | Kinetic energy and mass |
| Mass from kinetic energy | m = 2KE / v^2 | Kinetic energy and speed |
| Height from potential energy | h = PE / (mg) | Potential energy, mass, and gravity |
| Gravity from potential energy | g = PE / (mh) | Potential energy, mass, and height |
| Speed from height change | v1 = sqrt(v0^2 + 2g(h0 - h1)) | Initial speed, heights, and gravity |
| Maximum height | hmax = h0 + v0^2 / (2g) | Initial height, speed, and gravity |
Understanding Kinetic and Potential Energy
This calculator helps you explore one of the most useful ideas in physics: energy can change form while the total stays the same. It lets you find kinetic energy (energy of motion) and gravitational potential energy (energy stored by height), then compare them to see how an object speeds up, slows down, or rises and falls. Whether you are studying a rolling ball, a thrown object, or a moving vehicle, the tool makes the math quick and clear.
In simple terms, kinetic energy depends on mass and speed: KE = ½ m v². Double the speed and the kinetic energy grows by a factor of four. Gravitational potential energy depends on mass, gravity, and height: PE = m g h. The height is measured relative to any reference level you choose. The sum, E = KE + PE, is called mechanical energy. If air resistance and friction are small, that total stays nearly constant, which is the idea behind the conservation of mechanical energy.
To use the calculator, enter the object’s mass, its speed, the height, and the local value of gravity. The tool will compute kinetic energy, potential energy, and the total. If you know the energy instead, choose a reverse-solve tab to find mass, speed, height, or gravity. If you are working a conservation problem, choose the requested output and let the calculator show how energy converts between forms. For example, an object dropped from rest at height h₀ has v = √(2 g (h₀ − h)) when it falls to height h. A launch straight up with speed v₀ reaches a maximum height hmax = v₀²/(2 g) + h₀ (ignoring drag).
Step by step: choose a reference height, then enter mass in kilograms, speed in meters per second, and height in meters. If you are on Earth, you can leave gravity at 9.81 m/s², or adjust it for other planets or elevations. Click calculate to see energy in joules. If you only know some values, use the conservation idea to solve for a missing speed or height by comparing the energy before and after.
Real-world uses include estimating the energy of a skateboarder on a ramp, the speed of a roller coaster at different points, or the potential energy stored in a lifted load. Students use these formulas in physics homework, and engineers use the same concepts when analyzing motion, safety, and energy efficiency in systems like elevators, cranes, or regenerative braking.
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 can be metric or US customary. The calculator converts internally to SI units, then displays results in your selected units.
Disclaimer: Educational tool only. Ignores air resistance, rotation, and real-world losses.
Example Problems
Baseball in motion
Inputs: 0.145 kg, 40 m/s. Formula: KE = 1/2mv². Result: 116 J. Speed matters strongly because it is squared.
Kinetic energy
Dropped object
Inputs: drop from 10 m with v0 = 0. Formula: v = sqrt(2gh). Result: 14.0 m/s before impact, ignoring air resistance.
PE to KE
Roller coaster hill
Inputs: v0 = 20 m/s at 30 m, target height 10 m. Formula: v1 = sqrt(v0² + 2g(h0 - h1)). Result: 28.1 m/s.
Conservation
Formula Review and Sources
Last updatedJune 30, 2026
Reviewed for formulasKE = 1/2mv², PE = mgh, and ideal mechanical-energy conservation.
AssumptionsUniform gravity, no air resistance, no rotational energy, and no losses unless friction loss is selected.
ReferencesOpenStax College Physics, Khan Academy physics lessons, and The Physics Classroom energy tutorials.
Kinetic and Potential Energy FAQ
How do you calculate kinetic energy?
Use KE = 1/2mv². Convert mass to kilograms and speed to meters per second, square the speed, then multiply by one half times the mass.
How do you calculate potential energy?
Use PE = mgh. Convert mass to kilograms, gravity to meters per second squared, and height to meters. Height is measured from your chosen zero level.
How do you find velocity from kinetic energy?
Rearrange KE = 1/2mv² to v = sqrt(2KE/m). Enter kinetic energy and mass in the Find speed tab.
How do you find height from potential energy?
Rearrange PE = mgh to h = PE/(mg). Enter potential energy, mass, and gravity in the Find height tab.
What units should I use?
You can enter kg, g, lb, oz, m/s, km/h, mph, ft/s, meters, feet, centimeters, inches, J, kJ, calories, kWh, ft-lbf, eV, and more. The calculator converts to SI units before applying the formulas.
Does mass cancel in conservation problems?
For ideal gravity-only speed and height calculations, mass cancels from both sides of the conservation equation. Mass is still needed to report actual energy values or friction loss in joules.
Why can potential energy be negative?
Potential energy depends on the zero height you choose. If an object is below that reference level, height is negative, so PE = mgh is negative.
Is my data private?
Yes. The calculator runs in your browser and does not upload your inputs.