Gravitational Force Calculator
Newton's law of gravitation between any two masses.
About this tool
Enter two masses and the distance between their centres (scientific notation such as 5.972e24 works), or choose a preset such as Earth and Moon. The tool shows the force, each body's gravitational field strength at that distance, and the resulting acceleration.
Newton's law of universal gravitation
Every pair of masses attracts with a force F = G m₁ m₂ ÷ r², where r is the distance between their centres and G = 6.674 × 10⁻¹¹ N·m²/kg². Because G is so small, gravity only matters with huge masses: the Earth and Moon pull on each other with about 1.98 × 10²⁰ N, and the Sun pulls on the Earth with about 3.5 × 10²² N, but two 70 kg people a metre apart attract with only about 3.3 × 10⁻⁷ N. The force follows an inverse-square law, so doubling the distance quarters it. Dividing by one mass gives the gravitational field strength g = G M ÷ r² of the other: about 9.82 m/s² at Earth's mean radius, which is why a 70 kg person weighs about 687 N. Honest limits: distances must be centre to centre, so add the planet's radius for heights above the surface; measured g on Earth varies from about 9.78 to 9.83 m/s² because of latitude, rotation and local geology. The weight on other planets calculator and the force calculator are related.
Frequently asked questions
What is the formula for gravitational force?
F = G × m1 × m2 ÷ r², with G = 6.674 × 10⁻¹¹ N·m²/kg² and r the distance between centres.
What is the gravitational force between the Earth and Moon?
About 1.98 × 10²⁰ newtons.
Why don't people attract each other noticeably?
G is tiny, so two 70 kg people a metre apart attract with only about 0.0000003 N.
How does gravity change with distance?
It follows an inverse-square law: double the distance and the force falls to a quarter.
Is my data sent anywhere?
No. Everything is calculated in your browser, and nothing is stored or sent.