Universal Gravitation Calculator

Newton's Law of Universal Gravitation

Every object with mass attracts every other object with mass — the strength of that attraction depends on how massive both objects are and how far apart they sit.

$$F = \frac{Gm_1m_2}{r^2}$$

Worked Example: A Person Standing on Earth

Using the calculator's own defaults — a 70 kg person and Earth's mass (about 5.972 × 10²⁴ kg), separated by Earth's radius (about 6,371,000 m) — the gravitational force works out to roughly 686 N. That number should look familiar: it's essentially the person's weight, since weight is nothing more than the gravitational force between an object and the planet it's standing on.

The Inverse-Square Law

Because distance is squared in the denominator, gravitational force falls off much faster than distance grows — double the distance between two masses and the force drops to one-quarter of its original value, not half. Triple the distance and the force drops to one-ninth. This inverse-square relationship shows up throughout physics, from gravity to electrostatic force to light intensity, anywhere an effect spreads outward evenly in three dimensions from a source.

Why We Don't Feel Gravity From Nearby Objects

Every object with mass technically attracts every other object — you and this device you're reading on are pulling on each other gravitationally right now — but G is so small (6.674 × 10⁻¹¹) that the force between everyday-sized objects is far too tiny to detect without extremely sensitive laboratory equipment. Gravity only becomes a noticeable force at planetary scales, where one of the masses involved is enormous.

A Brief History of Universal Gravitation

Isaac Newton published the law of universal gravitation in his 1687 work "Philosophiæ Naturalis Principia Mathematica," unifying the force that makes an apple fall to the ground with the same force that keeps the Moon in orbit around Earth — a genuinely radical idea at the time, since earlier natural philosophy generally treated the heavens and the Earth as governed by entirely different physical laws. The gravitational constant G itself wasn't measured experimentally until more than a century later, when English scientist Henry Cavendish carried out an extremely delicate torsion-balance experiment in 1798 to determine its value, incidentally also becoming the first to accurately estimate Earth's overall density and mass.

Common Universal Gravitation Mistakes

Forgetting to square the distance is the most common calculation error, since it's easy to instinctively treat this like a simple inverse relationship rather than an inverse-square one. Confusing mass with weight is another frequent mix-up — mass is an intrinsic property of an object, while weight is the gravitational force acting on it, which is exactly what this calculator computes. Using the distance between the two objects' surfaces instead of their centers of mass is a third common error, especially significant for large bodies like planets where the difference is enormous.

Gravitation Terms You Should Know

Gravitational Constant (G) — a fundamental physical constant setting the overall strength of gravity, measured experimentally rather than derived from other constants.

Inverse-Square Law — a relationship where an effect's strength falls off in proportion to one over the square of the distance from its source.

Center of Mass — the effective point where an object's entire mass can be treated as concentrated for gravitational calculations.

Weight — the gravitational force exerted on an object by another mass (usually a planet), distinct from the object's mass itself.

This calculator assumes point masses (or objects with spherically symmetric mass distribution) and uses a standard value for G. Consult a physics or astronomy reference for precision scientific work.