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Potential Energy Calculator

Enter any two of mass, height and energy and find the third with PE = mgh. Shows the energy in joules and kJ, and the impact speed if the object is dropped.

PE = m·g·h
Solve any of PE, m, h
Joules & kJ
Impact speed
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Potential energy — Quick answer

Gravitational PE is the energy stored by lifting: weight times height. Drop it and that energy becomes motion.

PE = m·g·h · m = PE/(g·h) · h = PE/(m·g)
if dropped: ½mv² = mgh → v = √(2gh)

Worked example: m = 10 kg, h = 5 m, g = 9.81. PE = 10×9.81×5 = 490.5 J; dropped, it lands at 9.9 m/s.

PE of a 10 kg mass by height

HeightPEImpact speed
2 m196.2 J6.3 m/s
5 m490.5 J9.9 m/s
10 m981 J14.0 m/s

Used for: energy conservation, hydro & pendulums, drop tests, homework.

🔭 Potential Energy Calculator

Enter any two of energy, mass and height — leave the one you want blank. g defaults to 9.81.

Potential energy
Mass
Height
Impact speed if dropped

⚠️ Gravitational PE relative to your chosen zero height — only changes in height matter. Impact speed assumes a vacuum drop with all PE converting to kinetic energy (½mv² = mgh).

Lift something and you store energy in it. That stored energy — gravitational potential energy — is exactly the work you did against gravity: the object's weight (mass × g) multiplied by the height you raised it. Let it go and the store empties: the PE converts into kinetic energy as it falls, so that the speed it lands at depends only on the drop height, never the mass. PE = mgh is one of the simplest and most useful equations in physics, behind everything from hydro dams to a swinging pendulum.

Reviewed: June 19, 2026 · Author: Naveen P N, Founder — AI Calculator · Verified against: gravitational potential energy and energy conservation.

The potential-energy equations

Gravitational PE
PE = m × g × h
Mass & height
m = PE / (g × h) · h = PE / (m × g)
Conversion to motion
½·m·v² = m·g·h → v = √(2·g·h)

With mass in kilograms, g in metres per second squared and height in metres, PE comes out in joules. The energy-conservation link is the elegant part: set the kinetic energy at the bottom equal to the potential energy at the top and the mass cancels, leaving v = √(2gh) — the same impact speed a free-fall calculation gives. Only the change in height matters, so you measure PE from whatever zero level is convenient.

Worked example — lifting and dropping

Scenario: A 10 kg mass is raised 5 m, then released (g = 9.81 m/s²).

Potential energy
PE = 10 × 9.81 × 5 = 490.5 J
Impact speed
v = √(2 × 9.81 × 5) = √98.1 ≈ 9.9 m/s

Lifting the mass stored 490.5 J. When dropped, all of that becomes kinetic energy and it hits the ground at 9.9 m/s — and a 20 kg mass from the same height would land at the same speed, just with twice the energy (981 J). On the Moon (g = 1.62) the stored energy and impact speed are far smaller, which is the whole reason things feel "lighter" there: less weight means less PE for the same height.

Frequently Asked Questions

How do you calculate potential energy?

PE = m × g × h. A 10 kg mass at 5 m has 10 × 9.81 × 5 = 490.5 J. It's the energy stored by lifting.

What are the units?

Joules (J); 1 kJ = 1000 J. kg × m/s² × m gives joules directly.

How is PE related to kinetic energy?

They convert: falling turns PE into KE. ½mv² = mgh, so impact speed v = √(2gh) — mass cancels.

Does it depend on the reference height?

Yes — PE is relative to a chosen zero (floor, table). Only the height change matters physically.

Energy to lift something?

Equals the PE gained: mgh. A 20 kg box up 2 m needs 392.4 J, regardless of how fast you lift it.

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