# Gravitational Potential Energy Calculator

Calculate gravitational potential energy with PE = mgh. Find the energy stored by height and the equivalent free-fall velocity.

## What this calculates

Gravitational potential energy is the energy an object possesses due to its position in a gravitational field. Calculated as PE = mgh, it depends on the object's mass, height above a reference point, and the strength of gravity. This calculator also shows the equivalent velocity the object would reach if all potential energy converted to kinetic energy during a fall.

## Inputs

- **Mass** (kg) — min 0 — Mass of the object.
- **Height** (m) — min 0 — Height above the reference point.
- **Gravitational Acceleration (g)** (m/s²) — min 0 — Gravitational acceleration. Default is Earth's surface (9.81 m/s²).

## Outputs

- **Potential Energy** (J) — PE = mgh
- **Potential Energy** (kJ) — Potential energy in kilojoules
- **Equivalent Kinetic Velocity** (m/s) — v = sqrt(2gh), the velocity if all PE converts to KE

## Details

The formula PE = mgh gives the gravitational potential energy relative to a chosen reference level (usually the ground). Here m is mass in kilograms, g is gravitational acceleration (9.81 m/s² on Earth’s surface), and h is height in meters. Potential energy is always measured relative to some reference point, so the choice of “zero height” is arbitrary.

By conservation of energy, an object falling from height h (starting from rest) converts all its potential energy to kinetic energy: mgh = ½mv². Solving for velocity gives v = √(2gh), independent of mass. This is why all objects in free fall (ignoring air resistance) hit the ground at the same speed regardless of weight.

Gravitational potential energy is central to hydroelectric power (water falling from a reservoir), roller coaster design, pendulum physics, and orbital mechanics. For very large heights where g is not constant, the more general formula PE = -GMm/r is used instead.

## Frequently Asked Questions

**Q: What is gravitational potential energy?**

A: Gravitational potential energy is the energy stored in an object due to its height above a reference point in a gravitational field. It equals mgh, where m is mass, g is gravitational acceleration, and h is height. This energy can be converted to kinetic energy when the object falls.

**Q: Why does the equivalent velocity not depend on mass?**

A: When PE converts to KE (mgh = ½mv²), mass cancels from both sides, giving v = sqrt(2gh). This is Galileo's famous result: all objects fall at the same rate in a vacuum, reaching the same speed from the same height regardless of mass.

**Q: Is potential energy always positive?**

A: With PE = mgh, it is positive when the object is above the reference point and zero at the reference level. In the more general formula PE = -GMm/r used in orbital mechanics, potential energy is negative, approaching zero at infinite distance.

**Q: How is potential energy used in hydroelectric power?**

A: Water stored at height in a reservoir has gravitational PE. When released, it flows downhill, converting PE to kinetic energy of flowing water, which spins turbines to generate electricity. The power depends on the height (head) and flow rate of the water.

**Q: Can I use this for other planets?**

A: Yes. Change the gravitational acceleration to match the planet's surface gravity. For example, Mars has g ≈ 3.72 m/s² and the Moon has g ≈ 1.62 m/s². The formula PE = mgh remains valid for heights where g is approximately constant.

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Source: https://vastcalc.com/calculators/physics/potential-energy
Category: Physics
Last updated: 2026-04-21