Height to Achieve Potential Energy

The Height to Achieve Potential Energy  calculator computes the vertical displacement needed to attain a potential energy of a body with a certain mass (m).

INSTRUCTIONS: Choose units and enter the following:

• (m) Mass of the object.
• (U)  Potential Energy
• (g)  Acceleration due to gravity.

Vertical Displacement(y):  The calculator returns the vertical displacement in meters.  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:

• U(y) is potential energy.
• g is the acceleration due to gravity
• m is the mass and
• y is the vertical displacement

Therefor, the formula for the height to achieve potential energy is: 

   y =  U(y) / (m • g)

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.  

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.

Energy Calculators:

• Kinetic Energy (change of velocity) : K = ½⋅m⋅(V₁-V₂)²
• Kinetic Energy: KE= ½⋅m⋅v²
• Relativistic Kinetic Energy
• Potential Energy
• Potential Energy of Gravity (two bodies)
• Force of Gravity
• Nuclear Binding Energy (BE)

• 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