Height for a Potential Energy

The Height for a Potential Energy  calculator computes the required height to create a potential energy for a body at rest with a certain mass (m).

INSTRUCTIONS: Choose the preferred units and enter the following:

• (m)  This is the mass of the object.
• (U)  This is the Potential Energy of the object.
• (g)  This is the acceleration due to gravity.

Height for Potential Energy (y):  The calculator returns the height (y) required to achieve the potential energy in meters (m).  However this can be automatically converted to compatible units via the pull-down menu.

The Math / Science

The formula for Potential Energy is:

• U(y) = m • g • y

Where the inputs are acceleration due to gravity (g), mass (m) and vertical displacement (y). The default units for Potential Energy are Joules (J) for potential energy, meters per second (m/s²) for acceleration due to gravity, and meters (m) for vertical displacement.  

This formula solves for the height:

• y =  U(y)/( m • g )

The default acceleration due to gravity (g) is that of surface of the Earth at Sea Level (9.80665 m/s² ) .  The user can override the default with other values.

Education Resources:

• More information is available regarding Potential Energy in Light and Matter chapter 12.2 Potential energy: energy of distance or closeness
• YouTube video on Potential Energy