# 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 energyThe 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