What is mass? And why it isn't the same as weight

Mass is the measure of how hard an object is to speed up, slow down or turn, and of how strongly gravity pulls on it. It is measured in kilograms. Loosely, it says how much matter something contains. Weight is different: it is the force gravity exerts on a mass, measured in newtons. Your mass is the same on Earth, on the Moon and in orbit; your weight is not.

In short

• Mass is resistance to a change in motion, called inertia. A bowling ball has more of it than a football, wherever the two are.
• Weight is a force: mass times the local pull of gravity. It shrinks on the Moon and seems to vanish in orbit, while the mass stays put.
• Since 20 May 2019 the kilogram has been defined by a constant of nature, the Planck constant, not by a metal cylinder in a vault.

What does mass actually measure?

Mass measures inertia, an object's resistance to a change in its motion. Push an empty shopping cart and a loaded one with the same force, and the empty one speeds up more. The loaded cart has more mass. Newton's second law makes this exact: the acceleration a force produces is the force divided by the mass, a = F/m. Double the mass and the same push gives half the acceleration.

Mass also sets how strongly gravity pulls on an object, and how strongly the object pulls on everything else. These two roles, inertial mass and gravitational mass, could in principle have been different quantities. Every experiment so far finds them equal to extraordinary precision, which is why a hammer and a feather fall together in a vacuum. Einstein took that equality, the equivalence principle, as the starting point of general relativity, which explains gravity as curved spacetime.

The everyday definition, "the amount of matter in an object", points the right way but isn't the physics. Matter is made of atoms, and an atom's mass isn't simply the sum of its parts, as the section on where mass comes from shows. What counts as matter is a question of its own. Mass is a single number with no direction, unlike a force or a velocity.

How is mass different from weight?

Weight is a force: the pull of gravity on a mass. It is mass times the strength of gravity where the object is, W = m × g, where W is weight in newtons, m is mass in kilograms, and g is the acceleration gravity gives a falling object in meters per second squared. A newton is the force that speeds up 1 kg by 1 meter per second every second.

Mass belongs to the object; weight depends on where the object is. In everyday speech the two words are used as if they meant the same thing, and a bathroom scale adds to the confusion. A scale measures how hard you press down on it, a force, then divides by Earth's gravity to show a number in kilograms or pounds. That works on Earth. Anywhere else, the number it shows is wrong.

A worked example: a 70 kg person on Earth, the Moon and the space station

Take a person with a mass of 70 kg. NASA's Moon fact sheet gives surface gravity as 1.62 m/s² on the Moon against 9.80 m/s² on Earth. At the International Space Station's height of about 400 km, gravity is still about 8.7 m/s², roughly 90% of its strength on the ground.

Where	Mass	Gravity (g)	Weight, W = m × g	What a bathroom scale shows
Earth's surface	70 kg	9.80 m/s²	about 686 N	70 kg
The Moon's surface	70 kg	1.62 m/s²	about 113 N	about 11.6 kg
The space station, in orbit	70 kg	about 8.7 m/s²	about 610 N	0 kg

Step by step on the Moon: 70 kg × 1.62 m/s² = 113.4 N. An Earth scale divides that by 9.80 and shows 11.6 kg, about a sixth of the true mass. The person could jump far higher, because the same leg muscles push against a sixth of the weight.

The space station is the surprising row. Gravity there is still strong: it is what keeps the station in orbit. The scale reads zero because the person and the scale are falling around Earth together, so the person doesn't press on it. Astronauts are weightless in the everyday sense, not massless. Shoving a heavy crate across the cabin still takes a hard push, and stopping it takes another, because its inertia is all there. The station itself is covered in the note on the space station.

How is the kilogram defined?

From 1889 to 2019, the kilogram was the mass of one object: a platinum-iridium cylinder, the International Prototype of the Kilogram, kept in a locked vault at the International Bureau of Weights and Measures in Sèvres, near Paris. Every mass measurement in the world traced back to it through chains of comparison. The trouble, as NIST explains, was that the cylinder and its official copies drifted slightly against each other over the decades, and nobody could say which one was really changing.

In November 2018, member nations voted to tie the kilogram to a constant of nature instead, and the new definition took effect on 20 May 2019. The BIPM's definition fixes the Planck constant, h, at exactly 6.62607015 × 10⁻³⁴ joule-seconds. A joule-second is a kilogram times meters squared per second, and the meter and the second were already fixed by the speed of light and an atomic clock, so fixing h fixes the kilogram. Laboratories realize it with a Kibble balance, which weighs a mass against an electromagnetic force measured in electrical units linked to h. Nothing changed for kitchen scales; what changed is that the kilogram can now be made anywhere, with no vault.

Where does mass come from?

Mass comes from two places, and the smaller one is the more famous. The Higgs field gives the elementary particles their mass. As CERN describes it, particles that interact more strongly with the field are heavier, and photons, which don't interact with it, have no mass. The field's particle, the Higgs boson, was found at CERN in 2012.

But most of the mass of everything around you does not come from the Higgs field directly. Ordinary matter's mass sits almost entirely in atomic nuclei, in protons and neutrons, and each of those is three quarks bound by gluons. The three quarks' own masses add up to only about 1% of a proton's. The other 99% or so is the energy of the quarks moving and the gluon field holding them together, counted as mass through E = mc², from relativity. Electrons, whose mass does come from the Higgs field, add less than 0.06% to any atom's mass.

So most of your mass is bound-up energy, the energy of the strong force inside every proton and neutron. Mass and energy are two faces of one quantity: a hot cup of coffee has very slightly more mass than the same cup cold, though far too little to measure on any scale.

What do people most often get wrong about mass?

Four mix-ups come up again and again.

The first is that astronauts in orbit have no mass, or no gravity on them. They have the same mass as on the ground and feel about 90% of Earth's pull; they are weightless because they are in free fall.

The second is that heavier objects fall faster. A heavier object is pulled harder, but it has more inertia in exact proportion, so with no air in the way everything falls with the same acceleration.

The third is confusing mass with size or density. A kilogram of feathers and a kilogram of lead have the same mass. Lead packs it into far less space: density is mass divided by volume, and it is what makes one feel "heavier" in the hand.

The fourth is that going to the Moon makes a person lighter in every sense. It changes the weight but not the mass, so stopping a Moon buggy moving at a given speed takes exactly the same total push as on Earth, even though its wheels press down far less hard.

Mass is the starting point for much of the rest of physics. Multiply it by velocity and you get momentum; the pull between masses is gravity; and relativity's E = mc² turns it into energy.

Check yourself

• Without looking back: why does a bathroom scale show the wrong number on the Moon, while a balance comparing two masses would still be right?
• Why are astronauts on the space station weightless, even though gravity there is almost as strong as on the ground?
• If the Higgs field gives particles their mass, why does it account for only a small part of your mass?

Sources

• Kilogram: Introduction — National Institute of Standards and Technology
• SI base unit: kilogram — International Bureau of Weights and Measures (BIPM)
• The Higgs boson — CERN
• Moon Fact Sheet — NASA Space Science Data Coordinated Archive
• Proton — Wikipedia
• 2019 revision of the SI — Wikipedia