Kinetic and Potential Energy Calculator
Calculate kinetic energy, gravitational potential energy, and total mechanical energy of a moving object at height. Use it for physics problems involving falling objects, roller coasters, or pendulums.
About this calculator
Mechanical energy is the sum of kinetic energy (energy of motion) and gravitational potential energy (energy of position). Kinetic energy is KE = ½mv², where m is mass in kg and v is speed in m/s. Gravitational potential energy is PE = mgh, where g is gravitational field strength (9.81 m/s² on Earth) and h is height in meters above the reference level. Total mechanical energy is therefore E = ½mv² + mgh. In a closed system with no friction or air resistance, E remains constant — energy converts between KE and PE as the object moves, but their sum stays the same (conservation of mechanical energy). This principle lets you predict the speed at any height if you know the speed and height at another point, making it foundational in classical mechanics, engineering, and sports science.
How to use
A 5 kg ball rolls along a track at 4 m/s when it is 3 m above the ground. Using g = 9.81 m/s²: KE = ½ × 5 × 4² = ½ × 5 × 16 = 40 J. PE = 5 × 9.81 × 3 = 147.15 J. Total mechanical energy E = 40 + 147.15 = 187.15 J. Enter mass = 5, velocity = 4, height = 3, and gravity = 9.81 into the calculator to confirm. If the ball then rolls down to ground level (h = 0) without friction, all 187.15 J converts to KE, giving a final speed of v = √(2×187.15/5) ≈ 8.65 m/s.
Frequently asked questions
What is the difference between kinetic energy and potential energy?
Kinetic energy is the energy an object possesses because of its motion — a faster or heavier moving object has more KE. Potential energy, in the gravitational sense, is stored energy due to an object's height above a reference point — lifting an object higher increases its PE regardless of its speed. The two forms are interchangeable in a frictionless system: a pendulum bob continuously trades PE for KE and back again with each swing. In real systems, friction converts some mechanical energy into heat, so the total KE + PE gradually decreases over time.
How does conservation of mechanical energy apply to roller coasters?
At the top of the first hill, a roller coaster car has maximum potential energy and relatively low kinetic energy. As it descends, PE converts to KE and the car accelerates. At the bottom of a dip, nearly all energy is kinetic and speed is at its peak. Going up the next hill converts KE back to PE, slowing the car. In an ideal (frictionless) coaster, total mechanical energy would be perfectly conserved, but real coasters lose some energy to friction and air drag — which is why subsequent hills must always be shorter than the first.
How do you calculate the speed of a falling object using energy conservation?
If an object starts from rest at height h, all its initial energy is potential: E = mgh. When it reaches the ground (h = 0), all energy is kinetic: E = ½mv². Setting them equal: mgh = ½mv², so v = √(2gh). For example, an object dropped from 10 m reaches v = √(2 × 9.81 × 10) = √196.2 ≈ 14 m/s just before impact. Notice mass cancels out — every object, regardless of weight, reaches the same speed when dropped from the same height in a vacuum. Air resistance breaks this equality in real falls.