Newton's law of gravitation calculator
Enter both masses in kilograms and the center-to-center distance in meters. The acceleration of the second body toward the first is shown too.
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Processing and privacy: The result is calculated inside your browser and your data is not sent to any server.
How to use it
- Enter first mass, second mass and distance between centers.
- The result appears straight away and updates as you edit.
- Copy the result, or copy a link that keeps the same values to share it.
How it is calculated
F = G × m₁ × m₂ ÷ r², where G = 6.67430 × 10⁻¹¹ N·m²/kg² (CODATA). Acceleration a₂ = F ÷ m₂.
Example
Inputs: First mass = 70 kg, Second mass = 80 kg, Distance between centers = 1 m. Result: Gravitational force: 0.000000373761 N; Acceleration of the second body: 0.00000000467201 m/s².
Limits and caveats
- G is measured, with a relative uncertainty of about 2.2 × 10⁻⁵.
- Treats both bodies as points or uniform spheres; not valid for distances inside a body.
Questions about this tool
Why do we not feel the pull of people around us?
G is tiny. Two people of 70 and 80 kg one meter apart attract with about 0.00000037 N.
What happens to the force if the distance doubles?
It drops to a quarter, because the force is inversely proportional to the distance squared.
Where do I measure the distance from?
Between the two centers of mass. For gravity at Earth's surface use Earth's radius, about 6371 km.