Weight (W = mg)

Mass and weight are different quantities, and this formula is the exchange rate between them. Mass is how much matter an object contains, measured in kilograms, and it is the same everywhere in the universe. Weight is the gravitational force acting on that mass, measured in newtons, and it changes with where you are standing. The relation $W = mg$ is just Newton's second law with the acceleration set to whatever gravity supplies locally.

A 70 kg person weighs $70 \times 9.80665 \approx 687$ N on Earth. Take the same person to the Moon, where $g = 1.62$ m/s², and they weigh about 113 N — roughly a sixth — while still being made of exactly 70 kg of person. On Mars, $g = 3.72$, the answer is 260 N. Nothing about the body changed; only the field it sits in did.

The $g$ used here, 9.80665 m/s², is standard gravity, a defined constant fixed by the third General Conference on Weights and Measures in 1901 so that engineering calculations would have one agreed number. Real gravity varies: about 9.780 m/s² at the equator and 9.832 at the poles, a 0.5% spread caused by the Earth's rotation and its slightly flattened shape, with smaller local variations from altitude and the density of the rock underfoot. This whole formula is a near-surface shortcut for universal gravitation — put Earth's mass and radius into $g = GM/R^2$ and 9.8 is what comes out.

The everyday confusion is baked into the instruments. A bathroom scale measures force, using a spring or a load cell, then divides by a value of $g$ programmed at the factory and displays the result as kilograms. Take that scale to the Moon and it will confidently report that you have lost five-sixths of your mass. A balance, which compares your weight against known masses, would read correctly anywhere — which is the older and more honest instrument. The same confusion lives in the kilogram-force, a legacy unit equal to 9.80665 N, and in the imperial pound, which does double duty as a mass and a force. One more, because it comes up constantly: astronauts on the space station are not weightless because gravity has run out. At 400 km altitude $g$ is still about 8.7 m/s², nearly 89% of its surface value. They float because they and the station are both in free fall around the Earth together — falling, and missing.