Kinetic & Potential Energy — KE, PE, Conservation

Understanding Kinetic & 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 are working a conservation problem, enter the known values 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 h_max = 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 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.