Gravitational Force Calculator
Calculates the gravitational force between two masses separated by a given distance, using Newton's law of universal gravitation. Ideal for physics students, astronomy enthusiasts, and anyone modelling orbital mechanics.
Last updated: May 2026
About this calculator
Newton's law of universal gravitation states F = G × m₁ × m₂ / r², where G = 6.6743 × 10⁻¹¹ N·m²/kg² is the universal gravitational constant, m₁ and m₂ are the two masses in kg, and r is the distance between their centres in metres. The force is mutual — both bodies feel the same magnitude pulling them toward each other — and it falls off as the inverse square of the separation, so doubling the distance reduces the force to one quarter. The formula assumes point masses (or spherically symmetric bodies, by the shell theorem) and ignores any relativistic corrections, which only become important near very compact masses or extreme velocities. For comparison, the related orbital and escape speeds are v_orb = √(G·M/r) and v_esc = √(2·G·M/r), but those are separate calculations and are not returned by this calculator — it returns the gravitational force in newtons only.
How to use
Consider the Earth (m₁ = 5.972 × 10²⁴ kg) and the Moon (m₂ = 7.342 × 10²² kg) separated by r = 3.844 × 10⁸ m. F = 6.6743 × 10⁻¹¹ × (5.972 × 10²⁴ × 7.342 × 10²²) / (3.844 × 10⁸)² = 6.6743 × 10⁻¹¹ × 4.385 × 10⁴⁷ / 1.4776 × 10¹⁷ ≈ 1.981 × 10²⁰ N. As a sanity check, the Moon's known orbital acceleration toward Earth is a = F / m_Moon ≈ 1.981 × 10²⁰ / 7.342 × 10²² ≈ 2.70 × 10⁻³ m/s², matching the centripetal acceleration v²/r = (1018)² / 3.844 × 10⁸ ≈ 2.70 × 10⁻³ m/s² for the Moon's mean orbital speed of 1.018 km/s — a strong cross-check that the inverse-square law holds in the Earth-Moon system. Try other pairs: Sun-Earth (m₁ = 1.989 × 10³⁰, m₂ = 5.972 × 10²⁴, r = 1.496 × 10¹¹) gives F ≈ 3.54 × 10²² N.
Frequently asked questions
How does distance affect gravitational force between two objects?
Gravitational force follows an inverse-square law: doubling the distance reduces the force to one-quarter of its original value. This means gravity weakens very rapidly with separation — at ten times the distance, the force is only 1/100th as strong. This principle explains why astronauts feel weightless in orbit (they are in free-fall, not truly beyond gravity's reach) and why planets closer to the Sun experience stronger solar gravity than outer planets.
What is the difference between orbital velocity and escape velocity?
Orbital velocity is the speed needed for a circular orbit at a given altitude: v_orb = √(GM/r). Escape velocity is the minimum speed to break free from a body's gravity well entirely: v_esc = √(2GM/r). Escape velocity is always exactly √2 ≈ 1.414 times greater than circular orbital velocity at the same distance. For Earth at its surface, orbital velocity is about 7.9 km/s and escape velocity is about 11.2 km/s.
Why is the gravitational constant G so small and hard to measure?
G = 6.674 × 10⁻¹¹ N·m²/kg² is intrinsically tiny, meaning gravity is by far the weakest of the four fundamental forces. It is hard to measure precisely because gravitational signals between lab-scale masses are swamped by vibrations and electromagnetic noise. The first measurement by Cavendish in 1798 used a torsion balance, and modern determinations still rely on similar principles. Despite centuries of effort, G remains the least precisely known fundamental constant in physics.