# Potential Energy Calculator - Calculate Gravitational PE (PE = mgh)

Free online gravitational potential energy calculator. Compute potential energy using the formula PE = mgh. Supports multiple mass and height units (kg, g, lb, oz, m, cm, km, ft, in, mi) and energy units (J, kJ, cal, kcal, Wh, kWh). Perfect for physics students, engineers, and anyone working with energy calculations.

### Input Values (PE = mgh)

Mass (m)

_Enter mass value_

Mass Unit

Height (h)

_Enter height value_

Height Unit

Gravity (g) - m/s²

Earth (9.81 m/s²)  Moon (1.62 m/s²)  Mars (3.71 m/s²)  Jupiter (24.79 m/s²)

Saturn (10.44 m/s²)  Venus (8.87 m/s²)  Mercury (3.70 m/s²)  Neptune (11.15 m/s²)  Sun (274 m/s²)

_Enter custom gravity (default: 9.81)_

Calculate Potential Energy  Clear All

### Calculated Potential Energy

Energy Unit

Result

Enter mass and height to calculate potential energy

### What Is a Potential Energy Calculator and Why Do You Need One?

A **potential energy calculator** (also called a gravitational potential energy calculator or mgh calculator) is an online tool that computes the gravitational potential energy of an object using the fundamental physics equation **PE = mgh**, where PE is potential energy (in joules), m is mass (in kilograms), g is the acceleration due to gravity (in m/s²), and h is the height above a reference point (in meters). This formula is one of the cornerstones of classical mechanics, derived from the work done against gravity to lift an object.

Gravitational potential energy depends on position relative to a chosen reference height; an object can have both potential and kinetic energy at the same time. Lifting a book from the floor to a shelf increases its potential energy relative to the floor. If it falls, some of that energy becomes kinetic energy, while losses such as air resistance may transfer energy elsewhere.

As an example, 2 kg raised 5 m at 9.81 m/s² gains 98.1 J relative to the starting height. The mgh calculation assumes gravity is approximately constant over that height. To explore energy associated with motion, use the [kinetic energy calculator](https://www.toolcomb.com/kinetic-energy-calculator); for work performed over time, try the [power calculator](https://www.toolcomb.com/power-calculator).

This **free online potential energy tool** operates entirely within your browser - no data is sent to any server, ensuring your privacy and enabling offline use. It supports 4 mass units (kg, g, lb, oz), 6 height units (m, cm, km, ft, in, mi), 6 energy output units (J, kJ, cal, kcal, Wh, kWh), and includes quick‑select gravity presets for Earth, Moon, Mars, Jupiter, and other planets, plus a custom field. Whether you are a student solving physics homework, an engineer calculating energy storage, or a science enthusiast, this calculator is your go‑to solution.

### How to Use This Free Online Potential Energy Calculator

Using this **mgh calculator** is simple. Follow these steps:

1. **Enter the mass** of the object in the first input field.
2. **Select the mass unit** from the dropdown (kg, g, lb, oz).
3. **Enter the height** of the object above the reference point.
4. **Select the height unit** from the dropdown (m, cm, km, ft, in, mi).
5. **Select or enter gravity** - choose a preset for Earth (9.81 m/s²), Moon (1.62 m/s²), Mars (3.71 m/s²), Jupiter (24.79 m/s²), etc., or enter a custom value.
6. The **potential energy is automatically calculated** as you type.
7. **Select your desired energy unit** from the output dropdown (J, kJ, cal, kcal, Wh, kWh).
8. **Copy the result** using the copy button, or use Clear All to reset.

### The Potential Energy Formula - PE = mgh Explained

PE = m × g × h

Potential Energy = Mass × Gravitational Acceleration × Height

The gravitational potential energy formula is derived from the definition of work (W = F × d). The force needed to lift an object at constant speed against gravity is **F = mg** (where g ≈ 9.81 m/s² on Earth). The work done is then **W = F × h = mgh**. This work is stored as gravitational potential energy. Because energy is conserved, the object can later release that stored energy - for example, as kinetic energy when falling or as heat if it hits the ground.

The formula can also be rearranged by hand to solve for another variable. This calculator's inputs solve for potential energy only:

- **Potential Energy:** PE = mgh
- **Mass:** m = PE / (g × h)
- **Gravity:** g = PE / (m × h)
- **Height:** h = PE / (m × g)

### All Supported Units - Complete Reference Tables

#### Mass Units

| Unit | Symbol | Value in kg | Common Uses |
| --- | --- | --- | --- |
| Ounce | oz | 0.0283495 | Cooking, small objects, postal weight |
| Gram | g | 0.001 | Cooking, food labels, small packages |
| Pound | lb | 0.453592 | Body weight, groceries, gym weights |
| Kilogram | kg | 1 | SI base unit, most common worldwide |

#### Height (Distance) Units

| Unit | Symbol | Value in m | Common Uses |
| --- | --- | --- | --- |
| Inch | in | 0.0254 | Screen sizes, small measurements (US) |
| Centimeter | cm | 0.01 | Body measurements, small objects |
| Foot | ft | 0.3048 | Room dimensions, altitude (US) |
| Meter | m | 1 | SI base unit, most common worldwide |
| Kilometer | km | 1000 | Long distances, geography |
| Mile | mi | 1609.344 | Road distances (US/UK) |

#### Energy Units

| Unit | Symbol | Value in J | Common Uses |
| --- | --- | --- | --- |
| Calorie | cal | 4.184 | Chemistry, small heat measurements |
| Joule | J | 1 | SI base unit, physics, engineering |
| Watt‑hour | Wh | 3600 | Electricity, battery capacity |
| Kilojoule | kJ | 1000 | Mechanical work, food labels |
| Kilocalorie | kcal | 4184 | Nutrition ("Calories" with capital C) |
| Kilowatt‑hour | kWh | 3,600,000 | Electricity billing |

### Gravitational Acceleration Values - Across the Solar System

The acceleration due to gravity (g) varies depending on the celestial body. Below are the standard surface gravity values for planets and other bodies in the solar system:

| Body | Surface Gravity (m/s²) | Fraction of Earth's Gravity | Typical Uses |
| --- | --- | --- | --- |
| Sun | 274.0 | 27.9 G | Solar physics, heliocentric calculations |
| Jupiter | 24.79 | 2.53 G | Gas giant studies, orbital mechanics |
| Neptune | 11.15 | 1.14 G | Outer planet missions |
| Saturn | 10.44 | 1.06 G | Ring system studies |
| Earth | 9.81 | 1 G | Standard physics, engineering, everyday life |
| Venus | 8.87 | 0.904 G | Atmospheric studies |
| Mars | 3.71 | 0.378 G | Rover missions, space exploration |
| Mercury | 3.70 | 0.377 G | Inner planet missions |
| Moon | 1.62 | 0.165 G | Lunar exploration, Apollo missions |

### Gravitational Potential Energy vs. Kinetic Energy - Key Differences

| Property | Gravitational Potential Energy (PE) | Kinetic Energy (KE) |
| --- | --- | --- |
| Definition | Energy stored due to position in a gravitational field | Energy of an object due to its motion |
| Formula | PE = mgh | KE = ½mv² |
| Depends on | Mass, gravity, height | Mass, velocity |
| Zero point | Reference height (often ground level) | At rest (v = 0) |
| Example | Book on a shelf, water behind a dam | Falling object, car in motion |
| Conservation | In a closed system, PE + KE is constant (ignoring friction) | Same |

The total mechanical energy of an object is the sum of its kinetic and potential energies: **E_total = KE + PE**. In the absence of friction or air resistance, total mechanical energy is conserved. When an object falls, its potential energy decreases and its kinetic energy increases by the same amount - explaining why a falling object speeds up.

### Real‑World Examples of Potential Energy Calculations

#### Example 1 - Lifting a Weight

What is the gravitational potential energy of a 10 kg box sitting on a shelf 2 m above the ground (on Earth)?

PE = mgh = 10 kg × 9.81 m/s² × 2 m = **196.2 J**

#### Example 2 - Hydroelectric Power

Water behind a dam: 1000 kg of water at a height of 50 m. How much potential energy is stored?

PE = 1000 kg × 9.81 m/s² × 50 m = **490,500 J (490.5 kJ)**

#### Example 3 - On the Moon

A 15 kg rock is raised 5 m on the Moon (g = 1.62 m/s²). What is its PE?

PE = 15 kg × 1.62 m/s² × 5 m = **121.5 J**

#### Example 4 - Finding Height from Energy by Hand

A ball has 50 J of PE and a mass of 2 kg. How high is it (on Earth)?

h = PE / (mg) = 50 J / (2 kg × 9.81 m/s²) = **2.55 m**

### Real‑World Applications of Gravitational Potential Energy

#### 1. Hydroelectric Dams

Water stored behind a dam has gravitational potential energy proportional to its height. When released, this energy converts to kinetic energy, turning turbines to generate electricity - one of the largest sources of renewable energy worldwide.

#### 2. Roller Coasters

The first hill of a roller coaster is always the tallest because the cars are pulled up to convert electrical energy into gravitational potential energy. As the cars descend, that stored energy converts to kinetic energy, propelling them through the rest of the track.

#### 3. Gravity Energy Storage

Modern gravity storage systems lift heavy blocks using excess electricity and lower them to generate power when needed. This offers an environmentally friendly, long‑duration storage solution that could complement battery systems.

#### 4. Spacecraft Launches

Rockets must provide enough kinetic energy to overcome Earth's gravity and achieve orbital height. The gravitational potential energy at orbital altitude is a significant portion of the total energy required.

### Frequently Asked Questions (FAQ) About Potential Energy

#### What is gravitational potential energy?

Gravitational potential energy is the energy stored in an object due to its position in a gravitational field. It is given by the formula **PE = mgh**, where m is mass, g is gravity, and h is height.

#### How do I calculate potential energy from mass and height?

Use the formula **PE = m × g × h**. Make sure mass is in kilograms, height in meters, and gravity in m/s² to get the result in Joules. Our calculator handles all unit conversions automatically.

#### What is the difference between gravitational and elastic potential energy?

Gravitational potential energy (PE = mgh) depends on an object's mass and height in a gravitational field. Elastic potential energy (PE = ½kx²) is stored in stretched or compressed springs and depends on the spring constant and displacement. This calculator focuses on gravitational potential energy.

#### What is the value of g on Earth?

The standard acceleration due to gravity at Earth's surface is approximately **9.81 m/s²**. For the Moon, g ≈ 1.62 m/s²; for Mars, g ≈ 3.71 m/s²; and for Jupiter, g ≈ 24.79 m/s².

#### How accurate is this potential energy calculator?

The calculator uses exact conversion factors (e.g., 1 lb = 0.45359237 kg) and the formula PE = mgh with results to 6 decimal places. It is more than accurate enough for educational, engineering, and scientific applications.

#### Is my data secure when using this online potential energy calculator?

Absolutely. All calculations happen locally in your browser using JavaScript. No data is transmitted to any server - your inputs remain on your own device. This ensures your privacy and also means the tool works offline after the initial page load.

#### Can I use this calculator offline?

Yes. Once the page has loaded, all conversion and calculation logic runs locally in your browser. No internet connection is required after the first load - perfect for use in classrooms, labs, or anywhere without Wi‑Fi.

### Why Choose Our Potential Energy Calculator Over Others?

- **Completely free, no registration.** Unlimited calculations with no hidden costs.
- **Privacy‑first design.** All calculations happen locally in your browser. Your data never leaves your device.
- **Supports 4 mass units, 6 height units, and 6 energy units** - covering both metric and imperial measurement systems.
- **Quick‑select gravity presets** for Earth, Moon, Mars, Jupiter, and other planets, plus a custom field.
- **High precision** with results to 6 decimal places, suitable for educational, engineering, and scientific applications.
- **Works offline** after initial page load.
- **Fully responsive design** with resizable panels on desktop for custom workflow.

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### Related guides

Read the how-to, then come back to this tool when you are ready to run it locally.

- [How to Calculate Kinetic Energy KE = ½mv² explained, with unit conversion notes and a browser calculator.](https://www.toolcomb.com/blog/how-to-calculate-kinetic-energy)
- [How to Calculate Potential Energy Gravitational potential energy problems and a local calculator for classwork.](https://www.toolcomb.com/blog/how-to-calculate-potential-energy)
- [Potential Energy vs Kinetic Energy: Which Page? PE = mgh vs KE = ½mv², energy conservation, and a comparison table for picking the right ToolComb physics tool.](https://www.toolcomb.com/blog/potential-energy-vs-kinetic-energy-which-page)

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