Gravitational Force Calculator
Enter two masses and the distance between their centres to find the gravitational attraction between them using Newton's law of universal gravitation.
How to use the gravitational force calculator
- Enter the first mass in kilograms.
- Enter the second mass in kilograms.
- Enter the centre-to-centre distance in metres and read the force in newtons.
Examples
Two 1000 kg masses
m1 = 1000 kg, m2 = 1000 kg, r = 2 m
F = 1.6685e-5 N
Object on Earth's surface
m1 = 5.972e24 kg, m2 = 1 kg, r = 6.371e6 m
F = 9.82 N
Frequently asked questions
What is Newton's law of universal gravitation?
Every pair of masses attracts with a force F = G x m1 x m2 / r^2, where G is the gravitational constant and r is the distance between their centres.
What is the value of the gravitational constant G?
G is about 6.674 x 10^-11 N m^2 / kg^2. This calculator uses that value but you can override it through the API if needed.
What units should I use?
Mass in kilograms, distance in metres and the resulting force in newtons. These SI units keep G at its standard value.
Why must the distance be greater than zero?
The force depends on 1 / r^2, so a zero distance would give an infinite, non-physical force. The calculator rejects a zero or negative distance.
Why is the force between everyday objects so tiny?
Because G is extremely small, gravity is only noticeable when at least one mass is huge, like a planet. Two small objects attract with a negligible force.
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