Gravitational Force Calculator
Newton's gravitational force between two masses (F = G·m₁·m₂/r²).
Result
Force (N)
0.667400
How it works
Newton's law of universal gravitation says every pair of masses attracts: F = G·m₁·m₂/r², where G ≈ 6.674 × 10⁻¹¹ N·m²/kg². The word "universal" is the revolutionary part — the same equation governs an apple falling and the Moon orbiting. G is astonishingly small, which is why gravity is by far the weakest of the fundamental forces. Two 100 kg people one metre apart attract each other with about 10⁻⁷ newtons — utterly imperceptible. Gravity only becomes dominant when at least one mass is planetary, and it wins at cosmic scale simply because it never cancels out: mass only adds. The inverse square is what shapes orbits: double the distance and the force falls to a quarter. Note that r is measured between centres of mass, not between surfaces — which is why your weight is calculated from the Earth's radius, some 6,371 km, and not from the ground beneath your feet.
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Frequently asked questions
Why is the force so small?
The gravitational constant G is tiny, so everyday masses produce minute forces; only planet-scale masses feel strong.
What is G?
The gravitational constant, 6.674 × 10⁻¹¹ N·m²/kg², linking mass and distance to force.
Why doesn't the Moon fall onto the Earth?
It is falling — continuously. But it also moves sideways fast enough that the curve of its fall matches the curve of the Earth, so it keeps missing. That permanent near-miss is exactly what an orbit is.
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