Gravitational Force Calculator

Created by Luis Hoyos
Last updated: Jul 08, 2022

Welcome to the gravitational force calculator. With this tool, you'll calculate the gravitational force between two objects of known mass. Besides calculating the force of gravity, the calculation of the mass of one of the objects is also possible if you know the force and one mass.

But why is the force of gravity equation necessary? Well, we need the gravitational force to understand the interaction between celestial objects and be able to design space systems. For example, with the gravity formula, we can derive the formula for escape velocity, which is the velocity an object must have to leave the surface of any celestial object (like a space shift that leaves the earth, for example).

Another common application of the law of universal gravitation is the free fall, in which an object moves under the influence of gravitational force only.

🔎 You can look at our force converter to learn more about the different force units.

Law of universal gravitation

Newton's law of universal gravitation states that every object of nonzero mass attracts every other object in the universe. This attractive force is called gravity and exists between all objects.

For example, if you're in your room reading this article, a tiny force arises between you and your bed (but please, don't take this as an excuse). Thanks to the gravitational force formula, you'll notice this force is too small to cause any visible effect. Still, the effects will be significant if you apply the principle of gravitational force to massive objects, like planets or stars.

Now we're ready for the force of gravity equation!

Gravitational force formula

The formula to calculate the gravitational force between two objects is:

F = GMm/R²

where:

  • F — Force of gravity;
  • G — The gravitational constant, which equals G = 6.674×10⁻¹¹ N·m²/kg² in the previous gravity formula;
  • M — Mass of the first object;
  • m — Mass of the second object; and
  • R — Distance between the centers of both objects;

As you can see, the 10⁻¹¹ coefficient is a tiny number, which causes the gravitational force between two objects to also be tiny, unless we use very massive objects, like planets.

Luis Hoyos
F = GMm/R²
Mass 1 (M)
lb
Mass 2 (m)
lb
Distance (R)
ft
Gravitational force (F)
lbf
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