Gravitational Force Calculator
Enter two masses and the distance between their centres to get the gravitational force, or enter a force to find the distance. G = 6.67430 × 10⁻¹¹ N m²/kg².
Updated
Report a problem
Formula
Newton's law of universal gravitation:
F = G × m1 × m2 ÷ r² and, solved for distance, r = √(G × m1 × m2 ÷ F)
G = 6.67430 × 10⁻¹¹ m³ kg⁻¹ s⁻² (CODATA 2018). Unit conversions are exact: 1 lb = 0.45359237 kg, 1 t = 1000 kg, 1 km = 1000 m, 1 mi = 1609.344 m, 1 ft = 0.3048 m.
Worked example
1000 kg and 2000 kg at 10 m: F = 6.6743e-11 × 1000 × 2000 ÷ 10² = 1.33486e-6 N.
Distance for two 100 kg masses to attract with 1e-6 N: r = √(6.6743e-11 × 100 × 100 ÷ 1e-6) = 0.8170 m.
Earth and Moon (5.972e24 kg, 7.342e22 kg, 3.844e8 m): F ≈ 1.98e20 N.
Frequently asked questions
What is Newton's law of gravitation?
Every mass attracts every other mass with a force F = G × m1 × m2 ÷ r², where r is the distance between their centres and G = 6.67430 × 10⁻¹¹ N m²/kg². Two masses of 1000 kg and 2000 kg, 10 m apart, attract each other with 6.6743 × 10⁻¹¹ × 2,000,000 ÷ 100 = 1.335 × 10⁻⁶ N.
What happens to the force when the distance doubles?
It falls to a quarter, because the force follows the inverse square of the distance. The 1000 kg and 2000 kg pair at 20 m feel 3.337 × 10⁻⁷ N instead of 1.335 × 10⁻⁶ N.
How strong is the pull between the Earth and the Moon?
With Earth at 5.972 × 10²⁴ kg, the Moon at 7.342 × 10²² kg and a distance of 384,400 km (3.844 × 10⁸ m), the force is about 1.98 × 10²⁰ N.
Why do I measure the distance between centres?
The formula treats each body as a point at its centre of mass, which is exact for spheres. For an object on a planet's surface use the planet's radius, not the height above the ground. For irregular or very close objects the result is only an approximation.