Gravitational Force Calculator
Calculate the gravitational force between any two masses using Newton's Law of Universal Gravitation. Find force, distance, or mass.
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How to use this calculator
F = gravitational force (N), G = 6.674×10⁻¹¹ N·m²/kg², m₁ and m₂ = masses (kg), r = distance between centres of mass (m).
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Enter the two masses and the distance between their centres.
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Defaults show Earth's mass, a 70 kg person, and Earth's radius — giving the person's weight force (~686 N ≈ 70 kgf).
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Use scientific notation for very large or small values (e.g., 5.972e24 for Earth's mass).
Frequently asked questions
How does distance affect gravitational force?
Gravity follows an inverse-square law: doubling the distance reduces the force by a factor of 4; tripling it reduces force by a factor of 9. This is why gravity weakens rapidly with distance but never reaches exactly zero.
What is the gravitational constant G?
G = 6.674×10⁻¹¹ N·m²/kg² is a fundamental constant of nature. It was first measured by Henry Cavendish in 1798 using a torsion balance. Despite being known for over 200 years, G is one of the least precisely known fundamental constants.
Why does everything fall at the same rate?
Gravitational force is proportional to mass, but so is inertia (Newton's F = ma). When you solve for acceleration a = F/m = Gm₁/r², the mass of the falling object cancels out. All objects experience the same gravitational acceleration regardless of mass, as Galileo demonstrated.
Gravitational Force Calculator — Newton's Law of Universal Gravitation
Understanding universal gravitation
Newton's Law of Universal Gravitation states that every mass in the universe attracts every other mass with a force proportional to the product of their masses and inversely proportional to the square of the distance. It successfully explained planetary orbits, tidal forces, and the motion of comets centuries before Einstein's general relativity provided a deeper geometric explanation.
Gravitational acceleration on different planets
The surface gravity of a planet is g = GM/R². Earth: 9.81 m/s²; Moon: 1.62 m/s² (about 1/6 of Earth); Mars: 3.72 m/s²; Jupiter: 24.79 m/s² (2.5× Earth). On Jupiter, a 70 kg person would experience a force of about 1,735 N — equivalent to weighing 177 kg on Earth.
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Results are estimates for informational purposes only and do not constitute professional financial, medical, legal, or technical advice. Read full disclaimer →