Compute KE (½mv²), PE (mgh), total mechanical energy, missing variables, and conservation results with common metric and US units. Private by design - runs entirely in your browser.
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.
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.
