Potential Energy Calculator (PE = mgh)

Potential Energy Calculator (PE = mgh) | Online Free Tool | Elysia Tools

Tool usage guide

Learn when to use this tool, what it supports, and how real users apply it.

Key facts

Category: Math & Numbers
Input types: select, number
Output type: html
Sample coverage: 4
API ready: Yes

Overview

The Potential Energy Calculator is a physics utility designed to solve the gravitational potential energy equation (PE = mgh). It functions as a three-way solver, allowing you to calculate potential energy, mass, or height when given the other two variables, while also computing weight and theoretical impact velocity under customizable gravity settings.

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

1Select the variable you want to solve for: Potential Energy (PE), Mass (m), or Height (h).
2Enter the two known values in their respective fields (Joules, kilograms, or meters).
3Adjust the local acceleration due to gravity (g) if calculating for a body other than Earth.
4Click 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.

Examples

1. Calculating Potential Energy of a Book

Physics Student

Background

A student needs to find the potential energy of a textbook resting on a high shelf for a lab report.

Problem

Calculate the potential energy of a 2 kg book placed on a shelf 1.5 meters above the ground on Earth.

How to use

Set 'Solve For' to 'Potential Energy (PE)', enter 2 for mass, 1.5 for height, and keep the default gravity at 9.80665.

solveFor: pe, mass: 2, height: 1.5, gravity: 9.80665

Outcome

The calculator outputs a potential energy of approximately 29.42 Joules and an impact velocity of 5.42 m/s.

2. Finding the Required Height for a Drop Test

Safety Engineer

Background

An engineer is designing a drop test to simulate a 1000 Joule impact using a 5 kg test weight.

Problem

Determine the exact height from which the 5 kg weight must be dropped to achieve 1000 Joules of potential energy.

How to use

Set 'Solve For' to 'Height (h)', enter 1000 for potential energy, 5 for mass, and keep gravity at 9.80665.

FAQ

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.

solveFor: height, pe: 1000, mass: 5, gravity: 9.80665

What this tool helps you do

Run this tool

Prepared example runs

Inputs

Result

Examples that match this tool

Continue with connected tools and hubs

Prepared example runs

Inputs

Result

Learn when to use this tool, what it supports, and how real users apply it.

Key facts

Overview

When to use

How it works

Use cases

Examples

1. Calculating Potential Energy of a Book

2. Finding the Required Height for a Drop Test

FAQ

Web Image Processing Python Samples

Android Image Processing Java Samples

Android Image Processing Kotlin Samples

macOS Image Processing Objective-C Samples

Buoyancy Calculator (Archimedes, F = ρ·V·g)

Density Calculator (ρ = m/V)

Free Fall Calculator (h = ½gt²)

Image Palette to Design Tokens

Physics Classroom and Lab Calculators

Audio Encoding and Format Conversion Tools

Image Format Conversion and Animated Export Tools

JSON Interchange and Format Translation Tools