Mass versus weight

Say "my weight is 40 kilograms" and you have just mixed up two different physical quantities. Mass is how much matter an object is made of — it never changes, wherever the object goes. Weight is the force with which a planet or moon pulls that matter towards itself — and since different worlds pull with different strength, the very same object weighs different amounts in different places. An astronaut carries the same mass to the Moon as they had on Earth, yet they can suddenly leap metres into the air there, because their weight has dropped to a fraction of what it was. This article pins down the distinction, shows how the chapter's rounded weight-per-kilogram table lets you calculate weight anywhere in the solar system, and works through the numbers so the difference stops feeling like wordplay and starts feeling like physics.

The core insight

Mass is the constant amount of matter in an object, while weight is the gravitational force pulling that mass towards a particular body, so weight changes from world to world even though mass never does.

The core idea

Mass is the amount of matter contained in an object. It is measured in kilogram (kg) or gram (g), and it stays exactly the same no matter where the object is taken — Earth, Moon, Mars, anywhere — because moving an object does not add or remove any matter from it.

Weight is the force with which a body such as the Earth, the Moon, or a planet pulls an object towards itself. Because weight is a force, it is measured in newton (N), and it does change with location, since different bodies pull with different strength. A more massive, more compact body like Jupiter pulls harder; a smaller, lighter body like the Moon pulls more weakly. The chapter captures this with a simple rounded table: how many newtons a 1 kg mass weighs on each body.

Body	Weight of 1 kg mass
Earth	10 N
Moon	1.6 N
Mars	3.8 N
Venus	9 N
Jupiter	25.4 N

Read down the "mass" column in your head — it is 1 kg every single row. Only the weight changes, because it is the pull of the body, not the amount of matter, that differs. This table is really a set of five constants, one weight-per-kilogram value for each body, and it lets you scale up to any mass by simple multiplication.

W = m \times k. \qquad (1)

where: $W$ is the weight of the object on a given body, in newton; $m$ is the object's mass, in kilogram, which is the same number everywhere; and $k$ is that body's weight-per-kilogram constant from the table above, in newton per kilogram, which is different for every body. Notice $m$ never changes across a row-to-row comparison — only $k$ does, and that is the entire reason weight varies while mass does not.

Figure

Bar chart comparing the weight in newtons of a fixed one kilogram mass on Earth Moon Mars Venus and Jupiter, with mass shown as an unchanged flat line above every bar

The weight formula: scaling a table into a rule

An object's weight on any body equals its mass times that body's weight-per-kilogram constant — this generalises the chapter's table from "1 kg" to any mass, so the goal below is to turn the fixed table entries into a rule that works for an object of any mass on any body, and then to use it in reverse to check that mass genuinely stays fixed.

Step 1. Fix the constant from the table. Each body has one number, $k$ , telling you how many newtons a single kilogram weighs there. On Earth, $k_{\text{Earth}} = 10\ \text{N/kg}$ ; on the Moon, $k_{\text{Moon}} = 1.6\ \text{N/kg}$ . This $k$ is what actually differs from world to world — it packages "how strongly this body pulls" into one number.

Step 2. Scale by the mass. If 1 kg weighs $k$ newtons, then $m$ kilograms weighs $m$ times as much, because weight adds up in proportion to the amount of matter present: $W = m \times k$ . This is just repeated addition of the same 1 kg pull, done $m$ times.

Step 3. Apply it to a real mass. For a 4 kg object on Earth, $W = 4 \times 10 = 40\ \text{N}$ . For the same 4 kg object on the Moon, $W = 4 \times 1.6 = 6.4\ \text{N}$ . The mass entered both calculations as the same number, 4 kg — it was never allowed to change.

Step 4. Read the formula backwards to see why mass is untouched. Nothing about $W = m \times k$ lets $m$ vary with location; only $k$ carries the location. So however different $W$ turns out to be, the $m$ you started with is exactly the $m$ you still have — mass is location-independent by construction, not by coincidence.

Worked example

Question. A satellite component has a mass of 4 kg. Using the table (1 kg weighs 10 N on Earth and 3.8 N on Mars), find its weight on Earth and on Mars, and state its mass at both locations.

Step 1. Identify the constants: $k_{\text{Earth}} = 10\ \text{N/kg}$ and $k_{\text{Mars}} = 3.8\ \text{N/kg}$ , with mass $m = 4\ \text{kg}$ fixed throughout.

Step 2. Weight on Earth: $W = m \times k_{\text{Earth}} = 4 \times 10 = 40\ \text{N}$ .

Step 3. Weight on Mars: $W = m \times k_{\text{Mars}} = 4 \times 3.8 = 15.2\ \text{N}$ .

Step 4. Compare. The weight dropped from 40 N to 15.2 N because Mars pulls less strongly than Earth, but the mass is 4 kg on Earth and 4 kg on Mars — unchanged, since no matter was added or removed by launching the component into space.

Answer: weight is 40 N on Earth and 15.2 N on Mars; mass is 4 kg at both locations.

Competitive stretch

If the same component were placed on Jupiter instead, $W = 4 \times 25.4 = 101.6\ \text{N}$ — more than ten times its Moon weight of $4 \times 1.6 = 6.4\ \text{N}$ , purely because $k$ jumped from 1.6 to 25.4 N/kg. The mass, once again, stays exactly 4 kg on Jupiter too.

Common traps

Saying "my weight is 40 kg" — kilogram is a mass unit; weight, being a force, must be quoted in newton.
Assuming a lighter-feeling object on the Moon has actually lost mass — only its weight has dropped; the matter it is made of is unchanged.
Assuming a bigger, heavier planet always gives a smaller weight — Jupiter, more massive than Earth, actually gives a larger weight for the same mass because its pull is stronger.
Forgetting that the mass column in the table is always 1 kg — it is easy to misread the table as if mass itself were changing row to row, when only the weight column moves.

Ask the tutor: Want to work out your own approximate weight on Mars or Jupiter using your mass on Earth and the table above?

If mass never changes, why do astronauts train for months to move around on the Moon?

Because their weight changes even though their mass does not. On the Moon an astronaut's weight drops to roughly a sixth of their Earth weight, using the same $W = m \times k$ rule with a much smaller $k$ . Their muscles are still pushing against the same mass — the same inertia, the same resistance to being shoved — but the ground is pulling them down far more weakly, so a normal push now sends them bounding metres into the air. Training is about relearning how much force is needed against unchanged mass but drastically changed weight.

Is there a proper formula like W equals m g for this, or just the table

At this stage the chapter deliberately sticks to the rounded table rather than the full formula with $g = 9.8\ \text{m/s}^2$ , so that you can focus on the mass-versus-weight idea without extra decimal-heavy arithmetic. The relation you use here, $W = m \times k$ with $k$ read off the table, is the same idea in a simpler form — $k$ is just each body's version of "how strongly it pulls per kilogram," playing the same role that $g$ plays in the fuller formula you will meet in higher classes.

Does an object have weight in empty space, far from every planet?

Essentially no, because weight is defined as the pull of a nearby body, and far from any planet or moon there is nothing pulling with meaningful strength — so weight becomes vanishingly small, which is why astronauts appear to float in that situation. Mass, however, is completely unaffected: the object still contains exactly the same amount of matter it always did, so pushing it still takes exactly as much effort as it would on Earth, even though it no longer presses down with any weight.