Gravitational Force Calculator

What the gravitational force calculator does

Every mass in the universe pulls on every other. This calculator finds the gravitational force between two objects from their masses and the distance separating them, using Newton's law of universal gravitation. You can also solve for one of the masses or for the distance when you know the force, and switch on an advanced mode to set the gravitational constant yourself.

Below is what gravitational force is, the equation behind it, why it follows an inverse-square law, and a worked example.

How to use it

1. Choose what to calculate: the force, one of the two masses, or the distance.
2. Enter the known values, each with its unit. The unit menus run from grams to the mass of stars, and from nanometres to astronomical units, so you can work at any scale.
3. Press Calculate for the result, or Reset to clear it. Advanced mode lets you adjust the gravitational constant.

What gravitational force is

Gravity is the mutual attraction between any two objects that have mass. It is the most familiar force there is, the one that holds you to the ground, yet it is also the most far-reaching, the force that shapes the orbits of planets and binds galaxies together. Newton's great insight was that these are the same thing: the pull that drops an apple and the pull that keeps the Moon in its orbit obey one universal rule.

That rule is that the force depends on just two things, how much mass the objects have and how far apart they are. More mass means a stronger pull, and greater distance means a weaker one. The attraction is always there between any pair of masses, and it is always a pull, never a push: gravity only ever draws things together. This calculator puts numbers to that pull for any two masses at any separation.

The equation it uses

Newton's law of universal gravitation gives the force F between two masses, M and m, separated by a distance R:

F = G × M × m ÷ R²

The force grows in direct proportion to each mass, so doubling either one doubles the pull, and it falls off with the square of the distance. The symbol G is the gravitational constant, the number that sets the overall strength of gravity throughout the universe, with a value of about 6.674 × 10⁻¹¹ in SI units. The calculator uses this value by default and lets you change it in advanced mode, then rearranges the same equation to solve for a mass or the distance when those are unknown.

The inverse-square law

The distance enters the formula as a square in the denominator, which gives gravity its characteristic reach. Because of that square, the force weakens fast as objects move apart, but never quite vanishes. Double the distance and the pull drops not to a half but to a quarter; triple it and the pull falls to a ninth. Move ten times farther away and gravity becomes a hundred times weaker.

This inverse-square behaviour appears throughout physics, and gravity shares it with the electrostatic force between charges. It is the reason a spacecraft feels Earth's grip loosen quickly as it climbs, yet still feels a faint tug from the Sun across the entire solar system. The pull never reaches zero at any finite distance, only ever fainter, which is how gravity manages to act across the vast emptiness of space.

Weak up close, dominant at large scale

There is a puzzle hidden in that tiny constant G. Gravity is, force for force, astonishingly feeble. The pull between two everyday objects sitting near each other is so small as to be unnoticeable, utterly swamped by other forces. A small magnet lifts a paperclip against the entire gravitational pull of the planet beneath it. By the measures physicists use, gravity is the weakest of nature's forces by an enormous margin.

Yet gravity rules the cosmos, and the reason is twofold. It is always attractive, never cancelling itself out the way electric forces do when positive and negative charges balance, so every scrap of mass adds to the total. And it has unlimited range. Pile up enough mass, a planet, a star, a galaxy, and those tiny pulls accumulate into something overwhelming. So gravity loses every local contest but wins on the largest stages, holding worlds in orbit and gathering matter into stars. This calculator shows both faces: tiny forces between small masses, immense ones between astronomical bodies.

Units and precision

The calculator works in SI units underneath, taking masses in kilograms and distances in metres and giving the force in newtons, while the menus let you enter and read values in a huge range of units, from grams and electron masses up to the masses of the Earth and Sun, and from nanometres to astronomical units. The default gravitational constant carries its standard measured value. The relationship is exact; in practice the limit on accuracy is how well the masses, the distance, and G itself are known. Results are shown to many decimal places.

A worked example

Take two 1,000 kilogram masses, about the weight of a small car each, placed 10 metres apart.

The gravitational force between them is F = GMm/R² = (6.674 × 10⁻¹¹ × 1000 × 1000) ÷ 10² ≈ 6.7 × 10⁻⁷ newtons. That is less than a millionth of a newton, far too faint to feel, which captures just how weak gravity is between ordinary objects. The same law, applied to the Earth and the Moon, gives a force of around 10²⁰ newtons, because the masses involved are colossal.

Questions people ask

How do you calculate gravitational force?

Multiply the gravitational constant by both masses and divide by the square of the distance between them, F = GMm/R². The constant G is about 6.674 × 10⁻¹¹ in SI units.

What happens to gravity as distance increases?

It weakens with the square of the distance. Doubling the separation cuts the force to a quarter, tripling it to a ninth. The pull fades fast but never reaches zero at any finite distance.

If gravity is so weak, why does it dominate the universe?

Because it is always attractive and never cancels out, so every bit of mass adds to it, and it has unlimited range. Tiny pulls accumulate over planetary and stellar masses into an overwhelming force.

What is the gravitational constant G?

It is the universal number setting the strength of gravity, about 6.674 × 10⁻¹¹ cubic metres per kilogram per second squared. Its smallness is why gravity is so feeble between everyday objects.

References

A quick note on where the physics comes from. Newton's law of universal gravitation and the inverse-square dependence on distance are standard mechanics, set out in OpenStax's University Physics and in Georgia State University's HyperPhysics. The value of the gravitational constant follows the US National Institute of Standards and Technology. The HyperPhysics link is worth a quick click to confirm it lands where you expect.

1. OpenStax, University Physics Volume 1, Section 13.1, Newton's Law of Universal Gravitation. https://openstax.org/books/university-physics-volume-1/pages/13-1-newtons-law-of-universal-gravitation
2. HyperPhysics, Gravity and Newton's Law of Universal Gravitation. http://hyperphysics.phy-astr.gsu.edu/hbase/grav.html
3. National Institute of Standards and Technology (NIST), Fundamental Physical Constants, Newtonian constant of gravitation. https://physics.nist.gov/cgi-bin/cuu/Value?bg