Gravitational Force Calculator

1. Enter any three of force, mass 1, mass 2 and distance.
2. Leave the one you want to find blank.
3. Read the result.
4. See which value was solved for and the formula used.

Here is what each result means:

Gravitational force is the attraction that every mass exerts on every other mass. Newton's law of universal gravitation says the force grows with the product of the two masses and falls with the square of the distance between them. It is the same force that holds you to the ground, keeps the Moon orbiting the Earth and binds galaxies together.

The constant G, the gravitational constant, sets the strength of gravity and equals about 6.674 x 10^-11 newton meters squared per kilogram squared. Because G is so tiny, gravity between everyday objects is far too weak to feel: two 1000 kilogram masses a few meters apart pull on each other with only a few millionths of a newton. Only when one mass is planet-sized does the force become large.

The distance in the formula is measured between the centres of the two objects, not their surfaces. Because the force depends on the square of that distance, moving twice as far apart cuts the force to a quarter, and three times as far cuts it to a ninth. This inverse-square behaviour is the hallmark of gravity and shapes every orbit in the universe.

It rearranges Newton's law to solve for whichever value you leave blank.

1. For force, multiply G by both masses and divide by the distance squared.
2. For a mass, multiply force by the distance squared and divide by G times the other mass.
3. For distance, take the square root of G times both masses divided by the force.

Gravity is one of several force laws; see the force calculator and potential energy calculator.

Two 1000 kilogram masses sit 5 meters apart.

Calculation: F = G x 1000 x 1000 / 25, which is about 2.7 x 10^-6 newtons. Doubling the distance to 10 meters would quarter the force to about 6.7 x 10^-7 newtons.

One law, rearranged for whatever you need to find.

All four come from F equals G m1 m2 over r squared, so any three of the values give the fourth. Solving for distance takes a square root because the distance appears squared in the law, which is why gravity is called an inverse-square force.

Because the force depends on the square of the distance, small changes in separation have a large effect.

This inverse-square fall-off means gravity never quite reaches zero but weakens quickly with distance. It is why a satellite in a high orbit feels much less pull than one skimming the surface, even though both orbit the same planet.

The Masses

A larger mass gives a stronger force, in direct proportion to the product of the two masses.

The Distance

A greater separation weakens the force by the square of the distance. Twice as far is one quarter the force.

The Gravitational Constant

G fixes the overall strength of gravity. It is the same everywhere in the universe.

Physics Homework

Solve for the force, a mass or the distance in a gravitation problem.

Astronomy

Estimate the pull between planets, moons and stars.

Understanding Orbits

See how the force changes as objects move closer or farther apart.

1. Using Radius Not Separation

The distance is between the centres of the two objects, not their surfaces or a single radius.

2. Forgetting to Square the Distance

The distance appears squared. Leaving it unsquared overstates the force badly.

3. Wrong Units

Use kilograms and meters so the force comes out in newtons with G in SI units.

4. Confusing G and G

Big G is the universal constant; little g, about 9.81, is the acceleration due to gravity at the Earth's surface.

5. Expecting a Large Force

Gravity between everyday objects is minute. A tiny result is usually correct.

The relation is exact; only the displayed decimals are rounded, and very large or small results are shown in scientific notation.

It is the attraction between any two masses. Newton's law says it equals G times the two masses divided by the distance squared. Two 1000 kilogram masses 5 meters apart attract with about 2.7 x 10^-6 newtons.

Multiply the gravitational constant G by both masses, then divide by the square of the distance between their centres. G is about 6.674 x 10^-11 in SI units.

G is a universal constant equal to about 6.674 x 10^-11 newton meters squared per kilogram squared. It sets the strength of gravity and is the same throughout the universe.

Big G is the universal gravitational constant. Little g, about 9.81 meters per second squared, is the acceleration due to gravity at the Earth's surface, which depends on the Earth's mass and radius.

Because G is extremely small. Gravity only becomes strong when at least one mass is very large, like a planet, so the attraction between ordinary objects is far too weak to feel.

The force falls with the square of the distance. Doubling the separation cuts the force to a quarter, and tripling it cuts the force to a ninth.

Use the distance between the centres of the two objects, in meters. For planets and moons this is the centre-to-centre separation, not the gap between their surfaces.

Kilograms for mass, meters for distance and newtons for force, with G in SI units. Keep the units consistent for a correct result.

No. The calculation runs in your browser and nothing you enter is stored or sent anywhere, unless you choose Save, which keeps the result only on this device.

• Newton's law of universal gravitation (Wikipedia).
• Gravitational constant (Wikipedia).
• Gravity explained (Maths Is Fun).