MotionLab

Potential Energy Calculator

PE = m · g · h, in joules.

Mass (kg)

Height (m)

Gravity (m/s²)

Potential energy (J)

196.2

PE = m · g · h

What you entered

Mass (kg): 2Height (m): 10Gravity (m/s²): 9.81

1
Gravitational PE: PE = m × g × h
2 × 9.81 × 10= 196.2

Result

Potential energy (J): 196.2

A 2kg mass raised 10m off the ground stores 196.2 joules of gravitational potential energy.

Gravitational potential energy by mass and height

Potential energy is mass times g times height, using 9.81 m/s2. It measures energy stored by position in a gravitational field.

Mass (kg)	Height (m)	Potential energy (J)	Context
0.5	2	9.81	Book on a shelf
1	1	9.81	1 kg lifted 1 m
1	10	98.10	1 kg on a 10 m roof
70	10	6867.00	Person on a 10 m board
70	100	68670.00	Person on a 100 m cliff
1000	5	49050.00	Car on a 5 m ramp

The first two rows both give 9.81 J from different combinations, since only the product of mass and height matters. Potential energy is always measured relative to a chosen reference height - there is no absolute zero point, so the useful figure is the difference between two positions, which is why the ground is normally taken as zero. Fall from that height and the potential energy converts to kinetic: a 70 kg person falling 10 m arrives with 6,867 J, which is why the free fall calculator gives an impact speed of 14 m/s.

Stored energy of position

An object raised above the ground stores energy purely by virtue of its height — drop it, and that stored potential energy converts into kinetic energy as it falls, which is exactly why falling from higher up hurts more.

Why 9.81 m/s²

That's the standard acceleration due to gravity at Earth's surface — the field defaults to it, but you can change it to model the Moon (1.62), Mars (3.71), or any other gravitational environment.

Frequently asked questions

A 75 kg hiker climbs 500 meters of elevation gain. How much potential energy did they gain?

PE = mgh = 75 × 9.81 × 500 = 367,875 J ≈ 368 kJ. That's roughly 88 food calories of energy. In reality, the body is ~25% efficient, so the hiker burns about 350 calories just from the elevation gain.

How does potential energy convert to kinetic energy?

When an object falls, PE converts to KE: mgh becomes ½mv². At the bottom, all PE has become KE (ignoring air resistance). A ball dropped from 20 m hits the ground at v = √(2×9.81×20) = 19.8 m/s. See the kinetic energy calculator.

What is the potential energy of water behind a dam?

PE = mgh. A reservoir holding 1 million cubic meters of water (1 billion kg) at 100 m height stores PE = 10⁹ × 9.81 × 100 = 981 billion joules ≈ 272,500 kWh. Hydroelectric dams convert this stored energy into electricity as water falls through turbines.