JUMP TO TOPIC

# Gravitational Potential Energy Calculator + Online Solver With Free Steps

The **Gravitational Potential Energy Calculator** is used to calculate the gravitational potential energy of an object.

The user must understand the concept of **potential energy** to understand gravitational potential energy. The object placed on the **ground** has zero potential energy as it is not displaced to a certain height.

If an external **force** is applied to the object in the upward vertical direction, it covers a height **h** and stores energy as it can come down on its own if it is dropped. The **energy** stored in the object is due to the height **h** or the displacement covered by the body due to work done on it.

A kind of energy stored in the object due to a change in **position** of the object is known as **potential energy**. The potential energy stored in the object in the presence of a **gravitational field** is known as gravitational potential energy. This means that the position of the body is in the gravitational field.

## What Is a Gravitational Potential Energy Calculator?

**The Gravitational Potential Energy Calculator is an online tool used to calculate the gravitational potential energy U of an object of mass m at a height h with the gravitational acceleration g.**

The gravitational potential energy comes from the formula of **work done** W. The work done on the object after displacing the object to a height h is:

**W = F.h **

The **force** F applied by the earth in the downward direction due to the weight of the object is given by:

**F = mg **

Replacing F by mg in the work equation as it is equal to the applied force on the object to cover a height h.

**W = mgh**

The amount of **work done** in lifting the object to a certain height will be transformed into **potential energy**. So,

**W = P.E = U **

So, the **gravitational potential energy** is given by,

**U = mgh**

## How To Use the Gravitational Potential Energy Calculator

The user can use the Gravitational Potential Energy Calculator by following the steps given below.

### Step 1

The user must first enter the object’s mass m in the input window of the calculator. It should be entered in the block labeled “**Mass**.” The user must enter the mass in units of **kilograms** kg.

The calculator takes the mass as 10kg for the default example.

### Step 2

The object is displaced to a certain height h. The user must now enter the height of the object in the calculator’s input window.

It should be entered in the block titled “**Height**”. The calculator takes the height in units of **meters** m.

The calculator takes the height as 10 meters for the **default** example.

### Step 3

The gravitational acceleration g is the **acceleration **due to** gravity** on the surface of the earth. The standard value of g is 9.807 $m s^{-2}$.

The calculator **multiplies** the value of g with the number entered in the “**Gravity**” block.

For the** default** example, the value for Gravity is taken as 1.

### Step 4

The user must now “**Submit**” the input values for the calculator to compute the output.

### Output

The calculator displays the output in the three windows given below.

#### Input Information

The calculator shows the input values in this window. It displays the mass, height, and gravitational acceleration entered by the user.

#### Result

The calculator computes the gravitational potential energy U and shows the result in this window. It displays U in units of kilo-Joules kJ, Watt-hours Wh, and Giga electron volts GeV.

For the **default** example, it calculates the gravitational potential energy as follows:

**U = mgh**

**U = (10 kg)(1 × 9.807 $m s^{-2}$ )( 10 m)**

**U = 980.7 kg $m^{2}$ $s^{-2}$ = 980.7 J **

As

**1 J = $\frac{1}{1000}$ kJ **

So, the calculator shows the gravitational potential energy in** kilo-Joules** kJ as follows:

**U = $\frac{980.7}{1000}$kJ = 0.980kJ**

As

**1 kJ = 0.278 Wh **

So, the calculator shows the gravitational potential energy in **Watt-hours** Wh as follows:

**U = 0.9807 × 0.278 Wh = 0.2724 Wh**

As

**1 Wh = 2.247 × $10^{13}$ GeV**

So, the calculator shows the gravitational potential energy in **Giga electron-volts** GeV as follows:

**U = 0.2724 × ( 2.247 × $10^{13}$ ) GeV = 6.121 × $10^{12}$ GeV **

#### Equation

The calculator also displays the equation for gravitational potential energy U as follows:

**U = mgh**

## Solved Example

The following example is solved through the Gravitational Potential Energy Calculator.

### Example 1

An object with **mass** 15kg is displaced at the **height** of 25m with **twice** the earth’s gravitational acceleration. Calculate the gravitational potential energy U of the object.

### Solution

The user must first enter the mass, height, and gravitational acceleration in the **input** window of the calculator as given below.

**Mass = 15 kg **

**Height = 25 m **

**Gravity = 2 $m s^{-2}$**

After submitting the input values, the calculator displays the **input information** entered by the user as given above.

The calculator computes the gravitational potential energy U and displays the **result** as follows:

**U = 7.355 kJ **

This gravitational potential energy is in **kilo-Joules** kJ. It also calculates the value of U in **watt-hours** Wh and shows it as follows:

**U = 2.043 Wh **

It also displays the value of U in **Giga electron-volts** GeV as follows:

**U = 4.591 × $10^{13}$ GeV**

The calculator also shows the **equation** for the potential energy of an object due to gravity near the surface of a gravitating body as follows:

**U = mgh**