Gravitational Force Calculator

Every pair of masses attracts along the line joining their centres with a force F = G times m1 times m2 divided by r squared, where r is the centre-to-centre distance. The pull on each body is equal in size and opposite in direction.

It uses G = 6.674 x 10^-11 N m^2 / kg^2, the standard CODATA value. The API accepts an optional G override if you need a different precision or a scaled model, but the web form always uses the standard constant.

Mass in kilograms, distance in metres and the resulting force in newtons. These SI units keep G at its usual value, so convert grams, pounds, miles or kilometres before you type them in.

The force scales with 1 divided by r squared, so a distance of zero would imply an infinite, unphysical force. The calculator rejects a zero or negative distance and only accepts positive separations.

Newton's law uses the distance between the centres of mass, not the gap between surfaces. For the Earth surface example, r is Earth's radius of about 6.371 million metres, measured from the planet's centre.

Because G is extremely small, gravity is only noticeable when at least one mass is enormous, such as a planet or star. Two 1000 kg cars two metres apart pull on each other with only about 1.67 x 10^-5 N, far too weak to feel.

The web form solves for force, but the underlying engine also has functions that rearrange the same law to solve for a mass or a separation. Those inverse forms are available through the tool's code rather than the on-page inputs.

It treats each mass as a point, or equivalently as a uniform sphere, so the force acts as if all the mass sits at the centre. For irregular or very close bodies the real force can differ from this idealised result.

No. The force is computed in your browser as you type, so the masses and distance you enter never leave your device.