Gravitational force calculator
Attraction between two bodies from the law of universal gravitation.
Fill in the fields and the result will appear here automatically.
Find the magnitude of Newtonian attraction between two positive masses and the acceleration of the first body. The formula directly describes point masses; for non-overlapping spherically symmetric bodies outside their volumes, use centre-to-centre distance. Both forces have equal magnitude and opposite directions, while accelerations depend inversely on mass: Earth also accelerates towards a falling object.
How it works
Formula and logic
F = G × m₁ × m₂ ÷ r², with G = 6.674·10⁻¹¹ N·m²/kg². The acceleration of the first body is that force divided by its own mass, which reduces to G × m₂ ÷ r².
Example
Two point masses of 50,000 tonnes each at a distance of 100 m give 16.685 N. Treating ships this way is an idealisation: real ships are extended and nonspherical.
Fields and units
- First mass — kg
- Second mass — kg
- Distance between centres — m
How to use
- — Enter the two masses in kilograms.
- — Enter the distance between their centres in metres.
- — For an exterior point above a spherical planet, r=radius+altitude. Inside the planet, its whole mass cannot be inserted into this formula. Centre distance alone is insufficient for extended nonspherical bodies.
Method and limitations
- Calculation method
- Formula and logic
- Data or methodology source
- OpenStax: point-mass gravitation
- Limitation
- Newtonian point-mass model or exterior field of spherically symmetric bodies. Uses rounded G=6.674·10⁻¹¹ N·m²/kg²; extended nonspherical shapes and relativistic corrections are not computed.
FAQ
Why is the distance measured between centres?
For an exterior point above a spherical planet, r=radius+altitude. Inside the planet, its whole mass cannot be inserted into this formula. Centre distance alone is insufficient for extended nonspherical bodies.
Why does the force on both bodies come out the same?
Because gravity is mutual and the formula is symmetric in the two masses. What differs is the acceleration, since each body divides the same force by its own mass.
How does the force change with distance?
As the inverse square. Doubling the distance quarters the force, and tripling it leaves a ninth — which is why orbital mechanics is so sensitive to altitude.
Why do I never feel the attraction of nearby objects?
Because G is about 6.674·10⁻¹¹. Two people standing a metre apart attract with roughly 10⁻⁷ newtons, thousands of times weaker than the friction holding their shoes still.