# Gravitational Force Calculator

Calculate the gravitational force, the mass of an object, or the distance between objects using the calculator below.

**Calculate:**

## Gravitational Force:

### Force Formula

_{1}m

_{2}/ r²

### Mass Formula

_{2}= Fr² / Gm

_{1}

### Distance Formula

_{1}m

_{2}/ F

## On this page:

## How to Calculate Gravitational Force

Newton’s Law of Universal Gravitation is a fundamental principle in physics that describes the gravitational attraction between two masses. This law can be used to calculate the force of gravity acting between any two objects.

### Newton’s Law of Universal Gravitation

Newton’s Law of Universal Gravitation states that every point mass attracts every other point mass in the universe with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers. This can be expressed mathematically as:

F = Gm_{1}m_{2} / r²

**Where:**

*F* = gravitational force between the two masses

*G* = gravitational constant

*m _{1}* &

*m*= masses of the two objects

_{2}*r*= distance between the centers of the two masses

The gravitational force *F* is equal to the gravitational constant *G* times the masses of the two objects *m _{1}* &

*m*, divided by the distance between them

_{2}*r*squared. This is nearly identical to the calculation for the electrostatic force of two charges defined by Coulomb’s Law.

#### The Gravitational Constant

The gravitational constant *G* is a key part of the equation, serving as the proportionality factor that makes the equation work across the board. The gravitational constant is approximately equal to 6.674 × 10^{-11} N(m² /kg²), which is remarkably small.

This indicates that the gravitational force is a weak force, only noticeable when at least one of the objects has a large mass (like a planet).

**For example,** let’s apply Newton’s Law of Universal Gravitation to calculate the gravitational force between the Earth and an object on its surface. For simplicity, we’ll consider the object to have a mass of 1 kg, and we’ll use the Earth’s average mass of 5.972 × 10^{24} kg and radius of 6.371 × 10^{6} m.

Substitute the values and the gravitational constant into Newton’s Law of Universal Gravitation.

F = 6.674 × 10^{-11} N(m² /kg²) · 5.972 × 10^{24} kg · 1 kg / (6.371 × 10^{6} m)^{2}

Then solve.

F = 6.674 × 10^{-11} N(m² /kg²) · 5.972 × 10^{24} kg / (6.371 × 10^{6} m)^{2}

F = 9.8195 N

Thus, the gravitational force between the Earth and a 1 kg object on its surface is approximately *9.82 N*. Observe that this is quite close to the acceleration due to gravity (9.81 m/s²), which is what we observe as the “weight” of the object due to Earth’s gravity.