🌍 Gravitational Force Calculator (Newton)
Find the gravitational attraction between two masses (F = Gm₁m₂/r²), or solve for a mass or the separation.
Gravitational force F
1.9821e+20 N
Newton’s law of gravitation: F = G·m₁·m₂/r², with G = 6.6743×10⁻¹¹ N·m²/kg². 🔒 Computed in your browser.
How the gravitational force calculator (newton) works
Newton’s law of universal gravitation: every two masses attract with F = G·m₁·m₂/r², where G = 6.6743×10⁻¹¹ N·m²/kg² and r is the distance between their centres. Enter any three of the four and the tool solves for the last. The forces on the two masses are equal and opposite (Newton’s third law), so both bodies feel the same size of pull no matter which one is heavier.
G is a fixed CODATA constant. The inverse-square distance means doubling the separation quarters the force. Defaults show the Earth, Moon attraction.
Frequently asked questions
What is Newton’s law of gravitation?
Two masses attract with a force F = G·m₁·m₂/r², proportional to each mass and inversely proportional to the square of their distance. G is the gravitational constant.
What is the value of G?
The gravitational constant G = 6.6743×10⁻¹¹ N·m²/kg² (CODATA). It’s the same everywhere in the universe.
Why is gravity so weak between everyday objects?
Because G is tiny. Two 1 kg masses 1 m apart attract with only ~6.7×10⁻¹¹ N, imperceptible. Gravity only dominates at astronomical masses.
What does inverse-square mean here?
Force falls off with the square of distance: double the separation and the force drops to a quarter; triple it and it drops to a ninth.
What distance do I use?
The distance between the centres of the two masses (for spheres), not their surfaces.
Worked example: two 1000 kg masses
Two 1000 kg masses 2 m apart attract with F = 6.6743×10⁻¹¹ × 1000 × 1000 / 2² ≈ 1.7×10⁻⁵ N, a tiny force, showing how weak gravity is between ordinary objects.
How is this related to weight?
Your weight is the gravitational force between you and the Earth. Putting Earth’s mass and radius into F = Gm₁m₂/r² reproduces mg, which is why surface gravity g ≈ 9.81 m/s².
What units does the formula use?
SI throughout: masses in kilograms, distance in metres and force in newtons, with G = 6.6743×10⁻¹¹ N·m²/kg². The distance is measured centre-to-centre.
What is the difference between G and g?
G is the universal gravitational constant (6.6743×10⁻¹¹ N·m²/kg²), the same everywhere. Lowercase g is the local gravitational acceleration, about 9.81 m/s² at Earth’s surface, which depends on the planet’s mass and radius.
Does gravity ever become exactly zero?
No. It weakens with distance as 1/r² but only approaches zero, never quite reaching it. Even between galaxies a tiny attraction remains, which is why gravity shapes structure across the whole universe.