What is the formula for gravitational potential energy?

Gravitational potential energy is PE = mgh, where m is mass in kilograms, g is gravitational acceleration (9.81 m/s2 on Earth), and h is height in metres above a reference point. The result is in Joules. When an object falls, this potential energy converts to kinetic energy.

What reference point should I use for height?

Height h is always measured relative to a chosen reference point, which you define as zero. Commonly this is the ground, the floor of a room, or sea level, depending on the problem. The actual choice does not matter as long as you are consistent, because only differences in potential energy have physical significance.

Is potential energy converted to kinetic energy during free fall?

Yes. In the absence of air resistance, the total mechanical energy (potential plus kinetic) is conserved. As an object falls, it loses potential energy (PE = mgh decreases as h decreases) and gains kinetic energy (KE = half mv squared increases). At the moment of impact, all the initial potential energy has converted to kinetic energy, giving v = sqrt(2gh).

Potential Energy Calculator

This calculator computes gravitational potential energy using the formula PE = mgh, where m is mass in kilograms, g is gravitational acceleration, and h is height in metres above a chosen reference level. Gravitational potential energy is the energy stored in an object by virtue of its position in a gravitational field. The higher an object is raised, the more potential energy it has, and when it falls, that energy converts to kinetic energy and eventually to other forms such as heat or sound on impact. You choose whether to solve for potential energy, mass, or height. When solving for potential energy, you provide mass, height, and gravity (defaulting to 9.81 m/s squared for Earth), and receive the energy in Joules, kilojoules, and kilowatt-hours. When solving for mass, you provide the energy and height. When solving for height, you provide the energy and mass. You can adjust the gravity value to model other planets; for example, the Moon has g = 1.62 m/s squared and Mars has g = 3.72 m/s squared. This tool is useful for physics students, civil engineers assessing hydroelectric power potential, and anyone working through energy conservation problems. The formula gives potential energy relative to the reference height; only differences in PE are physically meaningful.

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Solve for

Mass (m)

Height (h)

Gravity (g)

m/s²

Potential Energy (PE)

490.50 J

potential energy

Kilojoules0.49 kJ

kWh0.000136 kWh

Equiv. fall speed9.90 m/s

How it works

The three rearrangements of the potential energy equation are: PE = mgh (energy), m = PE / (gh) (mass), and h = PE / (mg) (height). Select the variable you want to find, enter the other values, and the calculator applies the appropriate formula. The equivalent fall speed shows the velocity a dropped object would reach after converting all that potential energy to kinetic energy: v = sqrt(2PE / m) = sqrt(2gh).

Worked example

A 10 kg object is raised 5 m above the ground. PE = 10 × 9.81 × 5 = 490.50 J = 0.49 kJ. If dropped from that height, it would hit the ground at v = sqrt(2 × 9.81 × 5) = 9.90 m/s. These match the defaults pre-filled above.

Related calculators

Kinetic Energy Calculator: the complementary energy form for moving objects (KE = half mv squared).
Free Fall Calculator: find velocity and time for an object converting PE to KE.
Force Calculator: find the weight force (F = mg) used to raise the object.
SUVAT Calculator: model the full kinematics of a falling object.

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