Inverse square law

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The inverse square law predicts the intensity of a field at a given distance from a point source. In general, it applies to 'force-fields' forces such as gravitational, magnetic and electrical. This law states that force gets weaker as you move away from its source by a factor of four (i.e. two squared) when the distance from source is doubled.[1]

Take a point source that is propagating something (light, sound, gravity, electric field, etc..) out.

The inverse square law can be derived by looking at the surface area of a sphere of radius . The surface area of a sphere is As the radius increases, the surface area of the sphere goes up with the square of the radius and the intensity of the phenomena will be inversely proportional to the surface area.

With gravity, the inverse square law can be seen as:


Using the inverse square law and knowing the strength of the phenomena, it is possible to calculate the distance to the source. Knowing how bright a light bulb is and measuring how bright it appears to be. This can also be used with sound or radiation.

The inverse square law can also be used with gravitation to determine the mass of an unknown. Measuring the mass of one object, the force gravity exerts on the other object, and the distance between the two objects one can calculate the mass of the unknown. This is how the mass of the Moon is measured.[2]



  1. Edgar Anrews (2010). Who made God? Searching for a theory of everything.. Carlisle, PA, USA: EP Books, 149. ISBN 978-0-85234-707-2. 
  2. How do we know the mass of the Earth and the Moon?