# Potential Energy Calculator (PE = mgh)

Compute gravitational potential energy, mass, or height from the other two, with impact velocity

> Canonical page: https://elysiatools.com/en/tools/potential-energy-calculator

- **Category:** Math & Numbers

- **Keywords:** potential energy, energy, mass, height, gravity, gravitational, joule, physics, mechanics, pe=mgh

## Overview

Gravitational potential energy is the energy stored in an object due to its height in a gravity field.

Equations (three-way solver):
- Potential energy: PE = m · g · h (J)
- Mass:              m  = PE / (g · h)
- Height:            h  = PE / (m · g)

Weight W = m · g. Impact velocity v = √(2·g·h). Gravity defaults to 9.80665 m/s².

## Inputs

- **Solve For** (select)
- **Potential Energy (PE, J)** (number): leave blank when solving for potential energy
- **Mass (m, kg)** (number): leave blank when solving for mass
- **Height (h, m)** (number): leave blank when solving for height
- **Gravity (g, m/s²)** (number): 9.80665 (Earth). Moon ≈ 1.62, Mars ≈ 3.71

## When to use

- When solving physics homework problems involving gravitational potential energy, mass, or height.
- When estimating the impact velocity of a falling object from a specific height.
- When calculating potential energy or weight under different gravitational fields, such as on the Moon or Mars.

## How it works

- Select the variable you want to solve for: Potential Energy (PE), Mass (m), or Height (h).
- Enter the two known values in their respective fields (Joules, kilograms, or meters).
- Adjust the local acceleration due to gravity (g) if calculating for a body other than Earth.
- Click calculate to instantly view the solved variable, the object's weight, and its final impact velocity.

## Use cases

- Physics students verifying textbook calculations for mechanical energy conservation.
- Engineers estimating the potential energy stored in elevated industrial components or weights.
- Space enthusiasts comparing gravitational potential energy and impact velocities across different planets.

## Frequently asked questions

### What formula does this calculator use?

It uses the gravitational potential energy formula: PE = m · g · h, where m is mass, g is gravitational acceleration, and h is height.

### Can I calculate the impact velocity of a falling object?

Yes, the calculator automatically computes the theoretical impact velocity using the formula v = √(2 · g · h).

### How do I calculate potential energy on Mars or the Moon?

Change the gravity input field from Earth's default (9.80665 m/s²) to Mars (3.71 m/s²) or the Moon (1.62 m/s²).

### What units of measurement are used?

Mass is measured in kilograms (kg), height in meters (m), potential energy in Joules (J), and gravity in meters per second squared (m/s²).

### Can I solve for mass or height instead of energy?

Yes, select 'Mass' or 'Height' from the 'Solve For' dropdown menu and input the remaining known variables.

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