Gravitational Force Calculator
Calculate the gravitational force between two masses using Newton's law of universal gravitation and the distance between them.
Last reviewed by the Radiatus Cloud team
Calculate the gravitational attraction between two masses.
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Calculate gravitational force
Newton's law of universal gravitation states that every pair of masses attracts each other with a force proportional to the product of their masses and inversely proportional to the square of the distance between their centres. This calculator applies the law using the gravitational constant, about 6.674 times ten to the minus eleven. The default values model the Earth and the Moon, giving the immense force that holds the Moon in orbit. The inverse-square relationship means force drops sharply as distance grows.
Because the gravitational constant is so tiny, noticeable gravitational forces require at least one very large mass, such as a planet.
Universal gravitation
This single law describes the fall of an apple and the orbits of planets alike, which was Newton's revolutionary insight. It governs the motion of satellites, moons, planets and stars, and remains accurate for everyday situations, with Einstein's general relativity needed only in extreme conditions. The inverse-square dependence on distance is a recurring pattern in physics.
Distances are measured between the centres of mass of the two objects. The results can be very large or very small, so the calculator uses scientific notation. All calculation happens locally in your browser.
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Frequently Asked Questions
What is Newton\'s law of gravitation?
It states that two masses attract with a force proportional to the product of their masses and inversely proportional to the square of the distance between them.
What is the gravitational constant?
It is a fundamental constant, about 6.674 times ten to the minus eleven, that sets the strength of gravity in the equation.
Why do we only notice gravity from big objects?
Because the gravitational constant is tiny, a significant force requires a very large mass, such as a planet, which is why everyday objects barely attract.
How does distance affect the force?
The force follows an inverse-square law, so doubling the distance reduces the force to a quarter of its value.
Which distance do I use?
The distance between the centres of mass of the two objects, not their surfaces, for the calculation to be correct.
Privacy & Security
Everything runs in your browser; nothing is uploaded.
How to Use
Enter the two masses and the distance between their centres.
Disclaimer: This tool is provided "as is" without warranty of any kind. Results are for educational and utility purposes.