Gravitational Potential Energy Formula

The Formula to Calculate Gravitational Potential Energy

The work done on an object against the pull of gravity, can be estimated from its potential energy. The computation formula for the same, has been explained in this article.
Gravity is the all-pervading, inescapable force that keeps us glued to Earth. This force of nature has been under scrutiny since the dawn of human civilization, but it was in the 17th century that a theory explaining the force was developed by Sir Isaac Newton. In its theoretical formulation, an important concept is the gravitational potential energy. It's the inert energy stored in any object due to its specific configuration and position in presence of a force. Motion is made possible when this inert energy, gets converted into kinetic energy. All forms of energy can be classified as either potential or kinetic.

What is Gravitational Potential Energy?

The energy of an object associated with its position in a gravitational field, is called gravitational potential energy. Gravitation affects each and everything that occurs in this universe, where there is presence of matter. When you lift anything from the surface of the Earth to a higher position, you need to perform work against the gravitational force. When work is done in such a way, to lift an object, its potential energy increases.

The gravitational force exerted on an object is directly proportional to its mass. More the mass of the object being raised, more will be the work done to lift that object and higher will be its potential energy at the raised position. When such an object is lowered in height in a gravitational field, its potential energy decreases and gets converted into kinetic energy. Stronger the gravitational field or pull of gravity, more will be the work done in raising it, against the force. Thus, the gravitational potential energy is dependent on three factors, which include the mass of an object, its height from the surface of the Earth, and the magnitude of gravitational force exerted near the planet's surface.

Gravity being an infinite-range force following an inverse square law, a gravitational field can extend till infinity. As one goes away from Earth, the gravitational pull exerted by our planet, decreases but never goes to zero, except at infinity. Any value of potential energy at a distance lesser than infinity is taken to be a negative value. So when an object is raised, it attains a higher negative value of potential energy.

Consider a ball tossed in air. When the ball is thrown up, with a force exerted by our muscles, it gains potential energy as it rises higher. It goes high until its propellant force is balanced by the pull of gravity. At this point, it has the highest gravitational potential. Once the pull of gravity overcomes the force of propulsion, the ball falls back due to the conversion of gravitational potential energy into kinetic energy, which aids its fall. At impact with the ground, it has maximum kinetic energy, which gets converted into sound energy (the 'thud') and other forms of energy including heat.

Formula

As we saw before, the gravitational potential energy of an object is affected by three factors, which include mass of the object, height to which it is raised, and the pull of gravity at that point. The associated formula is the following:

Gravitational Potential Energy = mgh

Here 'm' is the mass of the object, 'g' is the acceleration due to gravity (9.81 m/s2), and 'h' is the height of the object above Earth's surface. The value is always written with a negative sign.

Units

According to SI units, energy is measured in Joules. So the units for the calculated value will be joules. While calculating, mass should be in kilograms, acceleration should be in meter/s2, and height in meters.