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Multiply mass in kilograms by gravity in metres per second squared and by height in metres. A 2 kg ball on a 3 m shelf on Earth stores 58.86 joules, which converts to kinetic energy if it falls, ignoring air resistance.
Gravitational potential energy (GPE) is mass times gravity times height, the mgh formula. To calculate potential energy, multiply mass by gravity by height. Use kilograms for mass, metres per second squared for gravity, and metres for height, and the answer comes out in joules. A 10 kg object at 5 m on Earth stores 10 × 9.81 × 5 = 490.5 joules.
Gravitational energy comes from height in a gravity field, while elastic energy comes from stretching or compressing a spring, with Ee = 1/2 × k × x², where k is the spring constant and × is the extension. This calculator covers gravitational potential energy only, so use a spring calculator for elastic energy problems.
A 2 kg ball on a shelf 3 m above the floor stores Ep = 2 × 9.81 × 3 = 58.86 joules. If it falls with no air resistance, that energy becomes kinetic energy, giving a speed of the square root of (2 × 9.81 × 3) = 7.67 metres per second at the floor. More potential energy examples follow in the conversion table below.
Using gravity 9.81, the table values are: 1 kg at 2 m gives 19.62 joules, 3 kg at 1 m gives 29.43 joules, 2 kg at 4 m gives 78.48 joules, and 0.5 kg at 10 m gives 49.05 joules. For conversion, divide joules by 1000 to get kilojoules, so 490.5 joules is 0.491 kilojoules, allowing for rounding.
Gravity changes the result for the same mass and height. The Moon has gravity 1.62, Mars has 3.72, and Jupiter has 24.79. A 10 kg object at 5 m stores 81 joules on the Moon and 186 joules on Mars, against 490.5 joules on Earth, which is why the gravity input is adjustable.
Rearrange the mgh formula for the missing value: height = potential energy / (mass × gravity), and mass = potential energy / (gravity × height). An object with 147.15 joules, mass 3 kg and gravity 9.81 sits at 147.15 / (3 × 9.81) = 5 m, a rearrangement commonly tested in GCSE physics.
Potential energy is stored energy from position, while kinetic energy is energy of motion, given by 1/2 × mass × speed². As an object falls, potential energy converts to kinetic energy, and total mechanical energy stays constant if friction and air resistance are ignored. In real falls some energy becomes thermal energy through air resistance.
Do not enter weight in newtons as mass in kilograms, since weight already includes gravity and inflates the result by about 9.81 times. Convert centimetres to metres by dividing by 100, pick one reference point and keep it, and remember that using 10 instead of 9.81 for gravity adds about 2 percent error. For satellites and large distances, the mgh formula does not apply, since gravity is no longer constant.
Ep = m × g × h, where Ep is energy in joules, m is mass in kilograms, g is gravity in metres per second squared, and h is height in metres. Rearrangements are m = Ep / (g × h), g = Ep / (m × h), and h = Ep / (m × g).
On Earth g is 9.81 metres per second squared, often rounded to 9.8 or 10 in GCSE questions for simpler arithmetic. Use the value given in your question when one is supplied.
Elastic potential energy is Ee = 1/2 × k × x², where k is the spring constant in newtons per metre and × is the extension in metres. It equals the work done stretching or compressing the spring within its elastic limit.
When an object falls, gravitational potential energy converts to kinetic energy: m × g × h = 1/2 × m × speed², giving speed = square root of (2 × g × h) at the bottom, ignoring air resistance. A 1 kg ball dropped from 5 m reaches about 9.9 metres per second.
Potential energy is measured from a chosen reference point, usually the ground or lowest position, where it is zero. Energy above the point is positive and below it can be negative, but the change between two positions is what matters.
Yes, below the chosen reference point, and in the universal gravity formula where zero is set at infinite distance. Only differences in potential energy are physically meaningful for motion near Earth.
Use h = Ep / (m × g). For example, if a 2 kg object has 98.1 joules of potential energy, its height is 98.1 / (2 × 9.81) = 5 m.
The unit is the joule (J), equal to one kilogram metre squared per second squared. One kilojoule is 1000 joules.
9.81 is the accepted average value of Earth gravity, while 10 is a quick GCSE approximation that adds about 2 percent error. Use 9.81 for precise work and 10 only when a question asks for it.
No, not for orbits. The mgh formula assumes gravity is constant over a small height change near Earth. For satellites use the universal formula with distance from Earth centre, where energy is negative relative to infinity.