Newton's law of universal gravitation says every pair of masses attracts with a force F = G·m₁·m₂/r² — proportional to both masses and inversely proportional to the square of the distance between them. The constant G is tiny, so the force is negligible for everyday objects and only becomes important when a mass is planet-sized. The same equation that makes two cars attract imperceptibly also holds the Moon in orbit and sets your weight on the ground.
Reviewed: June 20, 2026 · Author: Naveen P N, Founder — AI Calculator · Verified against: Newton's law of universal gravitation, G = 6.674×10⁻¹¹ N·m²/kg².
The gravitation equations
Keep masses in kilograms and the distance in metres so the force lands in newtons. The force grows in direct proportion to either mass but shrinks with the square of the distance, the hallmark inverse-square law. To find a mass from a known force, rearrange to m₁ = Fr²/(Gm₂); to find the separation, take the square root of Gm₁m₂/F. The attraction always acts along the line joining the two centres.
Worked example — two masses, and your weight
Scenario: Two 1000 kg masses sit 2 m apart. What is the attraction? And how does the same law give weight?
The two cars attract with a mere 1.67×10⁻⁵ N — utterly unnoticeable. Halve the distance to 1 m and the force quadruples to 6.67×10⁻⁵ N; stretch it to 5 m and it drops to 2.67×10⁻⁶ N. Yet plug in Earth's huge mass and radius and the same formula gives 9.82 N on a 1 kg object — exactly its weight. That single law spans from imperceptible to everyday simply through the size of the masses involved.
Frequently Asked Questions
F = G·m₁·m₂/r², G = 6.674×10⁻¹¹. Two 1000 kg masses 2 m apart → 1.67×10⁻⁵ N.
The universal gravitational constant, 6.674×10⁻¹¹ N·m²/kg² — the same everywhere.
Gravity spreads over a sphere whose area ∝ r². Double r → ¼ force (inverse-square law).
Weight is gravity from a planet. Earth's mass/radius give ≈ 9.82 N on 1 kg — that's mg.
G is minuscule, so you need a planet-sized mass to feel it. Two cars attract with ~10⁻⁵ N.