Gravitational Force Calculator
Newton's law of gravitation, with field strength.
Work out Gravitational Force. Newton's law of gravitation, with field strength. Says where the approximation stops holding.
Earth 5.972e24, Moon 7.348e22, Sun 1.989e30. Scientific notation works.
Earth's radius is 6.371e6 m. Centre to centre, not surface to surface.
Gravitational force
687.398 N
Field strength 9.82 m/s² — 1.001× Earth surface gravity
F = Gm₁m₂/r², with G at 6.674 × 10⁻¹¹ — one of the least precisely known constants in physics, because gravity is so weak that measuring it means detecting the pull between laboratory-sized masses. Inverse square in distance, so doubling the separation quarters the force. That is why orbital altitude matters so much and why the Moon, 60 Earth radii away, feels about 1/3600th of surface gravity. Potential energy is negative by convention, with zero set at infinite separation. A bound system therefore always has negative total energy, and reaching zero is exactly the definition of escaping.
How the Gravitational Force Calculator works
Enter two masses and their separation for the gravitational attraction between them, plus the field strength and potential energy. Separation is measured centre to centre, which is where most of the errors in this calculation come from.
Also known as: newton's law of gravitation calculator · gravity between two objects · f = gm1m2/r2 · gravitational field strength calculator
Frequently asked questions
What is the formula for gravitational force?
F = Gm₁m₂/r², with G at 6.674 × 10⁻¹¹ N·m²/kg². Distance is measured between centres of mass, not between surfaces.
Why is G so imprecisely known?
Because gravity is extraordinarily weak. Measuring G means detecting the pull between laboratory-sized masses, and it remains one of the least precisely determined constants in physics.
Why is gravitational potential energy negative?
Because zero is defined at infinite separation. A bound system therefore has negative total energy, and reaching zero is exactly what escaping means.
Why does the Moon not fall into Earth?
It is falling — continuously. Its sideways velocity means it keeps missing, which is what an orbit is. Gravity provides the centripetal force for that circular path.
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