Gravitational Force Calculator
Calculate the gravitational attraction between two masses using Newton's law of universal gravitation.
How it works
F = G · m₁ · m₂ / r² · G = 6.674×10⁻¹¹ N·m²/kg²
Newton’s law of universal gravitation says every pair of masses attracts with a force proportional to both masses and inversely proportional to the square of the distance between their centres. The gravitational constant G is tiny, so the force is only noticeable when at least one mass is astronomically large. Halving the distance quadruples the pull.
Worked example
A 70 kg person at Earth’s surface (M = 5.97×10²⁴ kg, r = 6,371 km): F = 6.674e-11 × 5.97e24 × 70 ÷ (6,371,000)² ≈ 687 N — which is simply their weight.
Frequently asked questions
Why don’t I feel gravity toward everyday objects?
Because G is extraordinarily small, the attraction between ordinary masses is minuscule — a fraction of a billionth of a newton. Only planet-sized masses produce a force you can feel.
What does the inverse-square law mean?
The force falls off with the square of distance: move twice as far apart and the pull drops to a quarter; three times as far, to a ninth. This rapid weakening shapes orbits and tides.
Is this the same as weight?
Your weight is exactly this gravitational force between you and the Earth. Plugging in Earth’s mass and radius gives about 9.8 N per kilogram, the familiar value of g.
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Educational estimate. Check the formula and units for your exact case.