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Gravitational Force Calculator

Created by Bogna Szyk
Reviewed by Steven Wooding
Last updated: Jan 18, 2024


This gravitational force calculator lets you find the force between any two objects. Read on to get a better understanding of the gravitational force definition and learn how to apply the gravity formula.

Gravitational force definition

Newton's law of universal gravitation states that everybody of nonzero mass attracts every other object in the universe. This attractive force is called gravity. It exists between all objects, even though it may seem ridiculous.

For example, while you read these words, a tiny force arises between you and the computer screen. This force is too small to cause any visible effect, but if you apply the principle of gravitational force to planets or stars, its effects will begin to show.

Our free fall calculator is one of the most common examples illustrating the principle of gravitational force.

What is the gravity equation?

Use the following formula to calculate the gravitational force between any two objects:

F = GMm/R²

where:

  • F — Gravitational force, measured in newtons (N) (our force converter can convert it to other units). It is always positive, which means that two objects of a certain mass always attract (and never repel) each other;
  • M and m — Masses of two objects in question, in kilograms (kg);
  • R — Distance between the centers of these two objects, in meters (m); and
  • G — Gravitational constant. It is equal to 6.674×10⁻¹¹ N·m²/kg².

Did you notice that this equation resembles the formula in our Coulomb's law calculator? While Newton's law of gravity deals with masses, Coulomb's law describes the attractive or repulsive force between electric charges.

The attractive nature of gravity is also connected with a new definition of mass. The theory of General Relativity, introduced by Albert Einstein in 1915, establishes that curvature = mass, which means that any massive object — including the Sun, the Earth, and you — deforms or curves the spacetime, creating a gravity well. You can see an example of a gravity well in the picture below.

Plot of a two-dimensional slice of the gravitational potential in and around a uniform spherical body.
AllenMcC., CC BY-SA 3.0, via Wikimedia Commons.

How to use this gravity formula calculator

  1. Find out the mass of the first object. Let's choose Earth — its mass is equal to 5.972×10²⁴ kg. You can enter this large number into the calculator by typing 5.972e24.

  2. Find out the mass of the second object. Let's choose the Sun — it weighs 1.989×10³⁰ kg, approximately the same as 330,000 Earths.

  3. Determine the distance between two objects. We will choose the distance from Earth to Sun — about 149,600,000 km.

  4. Enter all of these values into the gravitational force calculator. It will use the gravity equation to find the force.

  5. You can now read the result. For example, the force between Earth and Sun is as high as 3.54×10²² N.

FAQ

What is gravitational force?

Gravitational force is an attractive force, one of the four fundamental forces of nature, which acts between massive objects. Every object with a mass attracts other massive things, with intensity inversely proportional to the square distance between them. Gravitational force is a manifestation of the deformation of the space-time fabric due to the mass of the object, which creates a gravity well: picture a bowling ball on a trampoline.

How do I calculate gravitational force?

To calculate the gravitational force between two objects, you can use the formula found by Newton, whose discovery is easily one of the most important moments in Science. Follow these easy steps:

  1. Find the mass of the two objects. Use kilograms for the sake of conformity.
  2. Multiply the masses, and multiply the result by the gravitational constant G = 6.6743×10-11 m3/(kg·s2).
  3. Divide the result by the square of the distance between the masses, in meters.

The result is the gravitational force in newtons.

What is the gravitational force between the Earth and the Moon?

The gravitational force between Earth and the Moon is 1.982×1020 N. To find this result:

  1. Identify the mass of Earth: ME = 5.972×1024 kg.

  2. Find the mass of the Moon: MM = 7.348×1022 kg.

  3. Calculate ME · MM · G = 5.972×1024 kg · 7.348 ×1022 kg · 6.6743×10-11 m3/(kg·s2) = 2.92883×1037 m3·kg/s2.

  4. Divide by the square of the distance between the Earth and the Moon:

    r = 3.844×108 m

    F = 2.92883×1037 m3·kg/s2 / (3.844×108 m)2 = 1.982×1020 N

Does the gravitational force of the planets affect humans?

No! Faraway planets don't affect humans: the only celestial bodies that do so are the Sun and the Moon, but not directly. Only tides show us a daily reminder of the presence of gravitational force.

Don't trust horoscopes that tell you Saturn affects your love life: the only thing planets do is keep Earth in its orbit. The gravitational force between you and Saturn is about 0.00000197 N, similar to the force between you and an apple a few centimeters away, and we're sure the fruit doesn't affect your love life.

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