How do you calculate potential energy?

Multiply the mass in kilograms by 9.81 m/s² by the height in metres: PE = mgh. A 60 kg person at the top of a 3 m ladder has 60 × 9.81 × 3 ≈ 1,766 J. In pounds and feet, convert first (0.4536 kg per lb, 0.3048 m per ft) — the page does it for you.

What is g, and why 9.80665?

g is the acceleration due to gravity at the Earth's surface, about 9.8 m/s². 9.80665 is the internationally agreed 'standard gravity'; the real value varies from about 9.78 at the equator to 9.83 at the poles. OpenStax rounds it to 9.80. Change the g box for the Moon (1.62) or Mars (3.72).

Can potential energy be negative?

Yes, whenever the object is below the reference level you picked. A stone at the bottom of a 5 m well has −m × g × 5 relative to the ground. Nothing physical changes; the sign just records which side of the reference it is on.

How is potential energy related to kinetic energy?

When something falls without air resistance, the potential energy it loses becomes kinetic energy it gains: mgh at the top equals ½mv² at the bottom, so v = √(2gh) — independent of the mass, which is why a bowling ball and a marble hit the ground at the same speed in a vacuum. The page shows that speed under the result.

Gravitational Potential Energy Calculator (PE = mgh)

Potential energy from mass and height in kg or lb and m or ft, with the speed a drop from that height would give.

Inputs

Mass

0.0011,000,000,000

Mass unit

Height above the reference

-1,000,0001,000,000

Height unit

Gravity (g)(m/s²)

0.1 m/s²100 m/s²

9.80665 is standard gravity. Moon 1.62, Mars 3.72.

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Gravitational PE

196.13 J

Working (SI): 2 kg × 9.80665 m/s² × 10 m = 196.133 J
Mass: 2 kg
Height: 10 m
In kJ / kcal: 0.1961 kJ / 0.0469 kcal
Speed if dropped from this height (no air): √(2 × 9.80665 × 10) = 14.00 m/s

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What each Gravitational Potential Energy input means

Mass: The object's mass, in kilograms or pounds.
Mass unit: kg or lb; pounds are converted at 0.45359237 kg.
Height above the reference: How far above your chosen reference level it is — the floor, the ground, the bottom of the drop. Negative if it is below that level.
Height unit: Metres or feet; feet are converted at exactly 0.3048 m.
Gravity (g): Gravitational acceleration, 9.80665 m/s² by default. Use 1.62 for the Moon or 3.72 for Mars.

Gravitational Potential Energy formula

PE = m × g × h (m in kg, g in m/s², h in m above your chosen reference; PE in joules) · speed if released, no air: v = √(2gh)

PE_g = m g h \qquad v = \sqrt{2 g h}

Gravitational potential energy is the work it took to lift something against gravity, stored ready to come back out: the weight (mass × g) times the height lifted. It is always measured from a reference level you choose — the floor, the ground, sea level — so only differences in height carry meaning, and a height below the reference gives a negative value, which is fine. Pounds and feet are converted to kilograms and metres first, since the formula wants SI, and the working shows the conversion. If the object is released, all of that energy becomes kinetic energy on the way down (ignoring air), which is why the page also shows √(2gh), the speed at the bottom — the same figure the free-fall calculator reaches from the kinematics.

Gravitational Potential Energy worked example

A 2 kg mass lifted 10 m: 2 × 9.80665 × 10 = 196.1 J. Dropped from there it would reach √(2 × 9.80665 × 10) = 14.0 m/s just before landing, with 196.1 J of kinetic energy. Ten pounds lifted 20 feet is 4.54 kg × 9.80665 × 6.096 m = 271.2 J.

More Gravitational Potential Energy examples

A 60 kg person at the top of a 3 m ladder: 60 × 9.80665 × 3 = 1,765.2 J above the floor. Falling from there, they would land at 7.67 m/s, about 28 km/h.

Where the Gravitational Potential Energy calculator can give the wrong answer

The reference level is yours to choose, and the answer changes with it. A book on a table has 20 J relative to the table's surface and much more relative to the floor; both are correct, and only the difference between two positions is physically meaningful.
mgh assumes g is constant, which holds near the Earth's surface. For heights of hundreds of kilometres — satellites — gravity weakens with distance and the formula −GMm/r replaces it.
The drop speed shown ignores air resistance. A dense object from a few metres matches it closely; a feather or a person from a height does not, because drag takes energy out of the fall.
Pounds are converted as mass (0.45359237 kg per lb). Feet are 0.3048 m exactly.
This is gravitational potential energy only. Springs store elastic potential energy, ½kx²; charges store electrical potential energy; neither is on this page.

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Gravitational Potential Energy reference table

Per kilogram: the potential energy at a height, and the speed of a drop from it
Height	Potential energy of 1 kg	Speed at the bottom (no air)
1 m	9.81 J	4.43 m/s (15.9 km/h)
2 m	19.61 J	6.26 m/s (22.5 km/h)
5 m	49.03 J	9.9 m/s (35.7 km/h)
10 m	98.07 J	14 m/s (50.4 km/h)
20 m	196.13 J	19.81 m/s (71.3 km/h)
50 m	490.33 J	31.32 m/s (112.7 km/h)
100 m	980.67 J	44.29 m/s (159.4 km/h)

Source: Arithmetic: PE = mgh and v = √(2gh) with g = 9.80665 m/s² (OpenStax College Physics 2e, §7.3); multiply the energy column by the mass

Gravitational Potential Energy FAQ

: Multiply the mass in kilograms by 9.81 m/s² by the height in metres: PE = mgh. A 60 kg person at the top of a 3 m ladder has 60 × 9.81 × 3 ≈ 1,766 J. In pounds and feet, convert first (0.4536 kg per lb, 0.3048 m per ft) — the page does it for you.
: g is the acceleration due to gravity at the Earth's surface, about 9.8 m/s². 9.80665 is the internationally agreed 'standard gravity'; the real value varies from about 9.78 at the equator to 9.83 at the poles. OpenStax rounds it to 9.80. Change the g box for the Moon (1.62) or Mars (3.72).
: Yes, whenever the object is below the reference level you picked. A stone at the bottom of a 5 m well has −m × g × 5 relative to the ground. Nothing physical changes; the sign just records which side of the reference it is on.
: When something falls without air resistance, the potential energy it loses becomes kinetic energy it gains: mgh at the top equals ½mv² at the bottom, so v = √(2gh) — independent of the mass, which is why a bowling ball and a marble hit the ground at the same speed in a vacuum. The page shows that speed under the result.