Mass, Inertia and Weight

The three words get used interchangeably, but they are not the same kind of thing. Mass and inertia are two ways of talking about one property of an object; weight is a force — a different unit, and a value that changes when you change where you stand.

Three definitions, side by side

NIST puts the difference most compactly: the mass of a body is a measure of its inertial property — or how much matter it contains; the weight of a body is a measure of the force exerted on it by gravity, or the force needed to support it.

Inertia, as NASA phrases it, is the "tendency to resist changes in a state of motion", and Newton's first law is normally taken as the definition of it: with no net force, an object keeps its velocity.

So inertia is not a separate quantity with a unit of its own. It is a property, and mass is the number that measures it.

Why mass is the measure of inertia

The answer is in the second law. NASA states it this way: the acceleration of an object depends on the mass of the object and the amount of force applied; the general form is that force equals the rate of change of momentum, and for constant m it reduces to F = m·a.

Read it backwards: for the same force, double the mass and the acceleration is halved. Mass sits in the denominator, and that is the entire content of "heavy things are harder to push" — they are not harder to push because they are pulled harder: in orbit, where the scale reads zero, they are exactly as hard to push.

Weight is a force, and forces change with location

The scientific definition of weight, per NIST: the force that gives a body an acceleration equal to the local acceleration of free fall. The SI unit of the quantity understood this way is the newton. NASA writes it as W = m·g, with g at the Earth's surface about 9.8 m/s². NIST gives a worked example: a copper sphere of mass 10 kg on the Earth's surface has a weight of approximately 98 N.

Because weight is proportional to g, it changes with position — even on Earth, NASA notes that an aircraft's weight falls off with altitude. Leave Earth and the change is far larger: gravity at the Moon's surface is one-sixth of Earth's, so the same person has a different weight on every body in the Solar System. The mass does not change at all.

"Weightless" does not mean gravity is gone

At an altitude of about 250 miles (roughly 400 km), NASA reports that Earth's gravitational field is still at 88.8% of its strength at the surface. The gravity is very nearly all still there.

What is gone is the support. Microgravity arises whenever an object is in free fall: the station and the people inside it fall with the same acceleration, so nobody presses on a scale. NASA states the consequence plainly — the object's mass is the same, but the scale reads zero.

The word "weight" in everyday use

This confusion is older than one might think. In 1901 the General Conference on Weights and Measures (CGPM) issued a declaration specifically to end the practice of using the word weight sometimes for mass and sometimes for force: weight denotes a quantity of the same nature as a "force", the product of a body's mass and the acceleration due to gravity. The conference also adopted a conventional value for the standard acceleration due to gravity: 980.665 cm/s², that is gₙ = 9.806 65 m/s² in NIST's notation — a conventional reference, not a value measured everywhere.

More than a century later the habit is intact. NIST acknowledges it: in commercial and everyday use, weight is usually a synonym for mass, the unit is the kilogram, and "to weigh" means "to determine the mass of". NIST's recommendation is not that everyone change how they speak, but that each use of the word make clear which meaning is intended.

The kilogram: from a lump of metal to a constant

Until recently the unit of mass was tied to a real object: a platinum–iridium cylinder cast in 1879 and kept on the outskirts of Paris. The problem, according to NIST, is that the measured mass of each individual standard "drifted" a little over time — when the object that defines the unit changes, there is nothing left to check it against. The revised SI, in force since 20 May 2019, drops the artefact entirely: BIPM defines the kilogram by fixing the Planck constant h = 6.626 070 15 × 10⁻³⁴ expressed in J·s — that is, through the unit of energy and the second.

Two masses, one number

Mass also turns up in two quite different places: in the second law it measures resistance to acceleration (inertial mass), while in gravitation it measures how strongly a body attracts and is attracted (gravitational mass). There is no obvious reason those two numbers have to be equal.

Experiment has so far found no difference. The MICROSCOPE satellite was designed to test exactly that at a precision of 10⁻¹⁵ in terms of the Eötvös ratio η, by comparing the accelerations of two test masses of titanium and platinum alloys orbiting the Earth. The final result, published in 2022: η(Ti, Pt) = [−1.5 ± 2.3 (stat) ± 1.5 (syst)] × 10⁻¹⁵ — that is, no violation found of the weak equivalence principle at the level measured.

Stated at the right strength: that is an upper bound on any difference, not a proof that the two masses are exactly equal. Why they are equal remains an open question — general relativity takes that equality as a postulate rather than explaining it.