Gravitational Force Calculator

Last updated: June 2026

Mass 1

Mass 2

Distance between centres

Gravitational force

6.874e+2 N

Decimal force

687.367 N

Earth weight equivalent

70.092 kg

Formula

F = G x m1 x m2 / r^2, where G = 6.674 x 10^-11 N m2/kg2 and r is the distance between mass centres.

Planet gravity reference

Body	g (m/s2)	Weight of 70kg
Mercury	3.70	259 N
Venus	8.87	621 N
Earth	9.81	687 N
Mars	3.72	260 N
Jupiter	24.79	1,735 N
Moon	1.62	113 N

About this calculator

The Gravitational Force Calculator estimates the attractive force between two masses using Newton law of universal gravitation. It is useful for astronomy examples, Earth-weight comparisons, and understanding why distance has a squared effect.

Newton gravitation formula

Gravitational force depends on both masses and the square of the distance between their centres.

F = G x m1 x m2 / r^2
G = 6.674 x 10^-11 N m2/kg2

How to use the gravitational force calculator

Enter the first mass in kilograms.
Enter the second mass in kilograms.
Enter the distance between the centres of the masses.
Use scientific notation for very large or small values.
Review the force in newtons.
Compare the force with an Earth weight equivalent.

Worked examples

Person near Earth surface

Input: Earth mass, 70 kg person, Earth radius

Calculation: F = Gm1m2/r^2

Result: About 687 N, similar to 70 kg weight on Earth.

Distance doubled

Input: Same masses, double the distance

Calculation: Force divides by 2^2

Result: Force becomes one quarter as large.

Why distance matters

Distance is squared in the denominator, so gravitational force falls quickly as objects move apart.

Planet gravity reference

Body	g
Earth	9.81 m/s2
Moon	1.62 m/s2
Mars	3.72 m/s2
Jupiter	24.79 m/s2

Gravity model limitation

This calculator treats masses as point masses or spheres measured from centre to centre. It does not model orbital mechanics, tides, relativity, or non-uniform mass distributions.

Frequently asked questions

What is G?

G is the universal gravitational constant.

Why use centre-to-centre distance?

The formula treats spherical bodies as if mass were concentrated at the centre.

Is this the same as weight?

Weight is gravitational force near a body such as Earth.

What happens if distance doubles?

Force becomes one quarter as large.

Does this handle orbits?

No. It only calculates force between two masses.

Related calculators

force-calculator
acceleration-calculator
scientific-notation-calculator

What does this mean?

This calculator is designed to help you understand the likely number before you make a decision or start an application.

Your result should be checked against official UK guidance, especially if your circumstances include dependants, exemptions, prior leave, or a complex immigration history.

Treat the figure as a planning tool rather than legal advice. Where the answer affects an application deadline or major payment, speak to an authorised adviser.