Space · Contrast
Mass vs weight
Two quantities, two units, one word used for both in ordinary speech. Sorting them out is worth more marks than any other single idea in this unit.
Start here
You take a hammer to the Moon.
The same hammer you use on Earth, taken to the lunar surface, where the gravitational field is about a sixth as strong.
What is different about using it?
Easier to lift, and every bit as hard to swing. Lifting works against weight, and on the Moon the hammer is pulled with about a sixth of the force. Swinging works against mass — the hammer’s reluctance to start moving and to stop again — and the mass is exactly what it was on Earth. Apollo astronauts described precisely this: everything felt light in the hand and behaved like its full Earth self the moment they tried to move it sideways or stop it.
Mass is a count of matter, measured in kilograms. It is the same on Earth, on the Moon, in orbit and in deep space, and it is also a measure of how reluctant an object is to change how it is moving — how hard it is to start, stop or turn.
Weight is the force gravity pulls on that matter with, measured in newtons. It is mass × gravitational field strength, so it changes with where the object is, and it never disappears entirely anywhere — but far from any large body it falls to almost nothing.
The two are easy to confuse because on Earth they are locked together: multiply any mass in kilograms by ten and you have its weight in newtons. Everyday English makes it worse by using “weight” for both. The moment a question leaves the Earth’s surface — or asks about free fall, or about pushing something sideways — the two come apart, and the answer depends on knowing which one is being asked about.
At the bench · one object, four places, two columns
One column never moves. The other changes everywhere.
Change a control to begin
Pick an object and move it around the solar system. The left-hand figure is its mass and the right-hand figure is its weight — and only one of them is a property of the object.
Commit first. Which of these could you measure with a spring balance and get a different answer for on the Moon?
The object
the Moon
The same object, weighed in four places
Mass
—
—
Field strength
—
—
Weight
—
—
Measured with
—
—
Writing it down · the shape of this relationship
Weight = mass × gravitational field strength
The triangle
Cover the one you want
W = m × g
m = W ÷ g
g = W ÷ m
Two things side by side means multiply. One thing over another means divide.
W · weight, a force, measured with a spring balance · N
m · mass, a count of matter, measured with a pan balance · kg
g · gravitational field strength where the object is · N/kg
The mass goes in as kilograms, because the field strength is quoted in newtons for each kilogram.
Worked example · one step at a time
A spring balance on the Moon reads 32 N. Field strength there is 1.6 N/kg. What is the mass?
Step 0 of 5
Convert
32 N stays 32 N · 1.6 N/kg stays 1.6 N/kg
The weight is already in newtons and the field strength already in newtons per kilogram, so there is nothing to convert.
Formula
m = W ÷ g
Cover m on the triangle: W sits over g, so you divide.
Insert
m = 32 N ÷ 1.6 N/kg
Use the Moon’s field strength, because that is where the reading was taken.
Fine-tune
32 ÷ 1.6 = 20
Newtons divided by newtons per kilogram leaves kilograms.
Answer
m = 20 kg
And that 20 kg is the same on Earth, on Mars and anywhere else.
Worked example · one step at a time
What is the weight on Earth of a 750 g tin of paint?
Step 0 of 5
Convert
750 g ÷ 1000 = 0.750 kg
The field strength is in newtons per kilogram, so the mass has to be in kilograms first.
Formula
W = m × g
Cover W on the triangle: m sits beside g, so you multiply.
Insert
W = 0.750 kg × 10 N/kg
The converted mass goes in. The 750 never does.
Fine-tune
0.750 × 10 = 7.5
Kilograms times newtons per kilogram leaves newtons.
Answer
W = 7.5 N
Insert 750 instead of 0.750 and the tin comes out weighing 7500 N — three quarters of a tonne of paint.
Your turn · the same five steps
Your object: a bag of sugar of 1 kg, on the Moon, where g is 1.6 N/kg.
Write each line out yourself — starting by deciding whether anything needs converting. Then check your working and tick the lines you had.
The five lines · tick what you had
Convert
1 kg stays 1 kg · 1.6 N/kg stays 1.6 N/kg
The mass is already in kilograms and the field strength already in newtons per kilogram, so there is nothing to convert.
Formula
W = m × g
Cover W on the triangle: m sits beside g, so you multiply.
Insert
W = 1 kg × 1.6 N/kg
The field strength is the one for the Moon.
Fine-tune
1 × 1.6 = 1.6
Kilograms times newtons per kilogram leaves newtons.
Answer
W = 1.6 N
The mass in the first line is unchanged, and always will be.
The five lines give the weight on the Moon. Move the slider and only the last four change.
A 900 g rock sample is brought back from Mars, where g is 3.7 N/kg. What did it weigh on Mars?
Write each line out yourself — starting by deciding whether anything needs converting. Then check your working and tick the lines you had.
The five lines · tick what you had
Convert
900 g ÷ 1000 = 0.900 kg
The field strength is in newtons per kilogram, so the mass has to be in kilograms first.
Formula
W = m × g
Cover W on the triangle: m sits beside g, so you multiply.
Insert
W = 0.900 kg × 3.7 N/kg
The converted mass goes in, with the Martian field strength.
Fine-tune
0.900 × 3.7 = 3.33
Kilograms times newtons per kilogram leaves newtons.
Answer
W = 3.33 N
Insert 900 instead of 0.900 and the sample comes out weighing 3330 N.
The five lines give 3.33 N on Mars. Back on Earth the same rock weighs 9.00 N — and is still 900 g.
Key fact
Mass is matter in kilograms and never changes. Weight is a force in newtons and equals mass × field strength. On Earth g is about 10 N/kg; on the Moon 1.6; on Jupiter 24.8. A pan balance measures mass anywhere, a spring balance measures weight.
Think again
“In orbit things are weightless, so they have no mass.”
Mass has nothing to do with gravity. An astronaut on the space station who wants to move a 200 kg equipment rack has to push exactly as hard as they would in a laboratory on the ground, and has to push exactly as hard again to stop it. Nothing is holding it down, and it is every bit as reluctant to be shifted. This is why astronauts train for handling large objects in orbit, and why a loose one is dangerous.
“Weight and mass are the same thing measured in different units, like metres and feet.”
Metres and feet measure the same quantity. Kilograms and newtons do not: one counts matter and the other measures a force. The clue is that the conversion between them is not a fixed number — it is 10 on Earth, 1.6 on the Moon and 24.8 on Jupiter, because it is not a conversion at all. It is a multiplication by a physical property of the place you happen to be standing.
Mastery ladder
Not started yet.
Rungs 3 and 4 you mark yourself.
Rung 1 · Calculate
A spring balance on Earth reads 45 N. What is the mass of the object hanging from it?
Rung 2 · The one that catches people
A hammer is used on the Moon. Which of these is true?
Rung 3 · Explain
Explain the difference between a balance and a spring balance, and say which one would still work correctly on Mars.
Rung 4 · Take it somewhere new
A shipping company charges by mass. Explain why a scale at an airport gives an honest answer, why the same scale on a spacecraft in orbit would read zero, and what the cargo would still do to the crew if it broke loose.
Key note
Mass is the amount of matter in an object, measured in kilograms, unchanged by location, and it is also what makes an object hard to start or stop moving. Weight is the force of gravity on that mass, measured in newtons, and given by W = m × g. On Earth every kilogram weighs about 10 N, which is why the two are so easily confused. A pan balance measures mass anywhere; a spring balance measures weight and only reads a correct mass in the field strength it was calibrated for.
Going further
The link runs deeper than it looks. The mass in W = m × g — how strongly gravity pulls on a thing — and the mass in F = m × a — how strongly a thing resists being accelerated — did not have to be the same number, and for three hundred years nobody could say why they were. Experiments have since shown them equal to within about one part in 10^15. Einstein took that equality as the starting point of general relativity, and it is the reason all objects fall at the same rate.
That equality is what Galileo is said to have tested from the leaning tower of Pisa and what David Scott actually did test, on television, on the Apollo 15 mission: a hammer and a falcon feather, released together on the airless lunar surface, hit the ground at the same instant. The heavier object is pulled harder and is proportionally harder to accelerate, and the two effects cancel exactly.
Before this lesson
Connects to
At GCSE this becomes
- Weight, mass and gravitational field strength as a required relationship, inertial and gravitational mass, and resultant force = mass × acceleration.
Where to next
Ask Mr Badmus AI
Not sure whether a question is asking about mass or about weight?
The bench is a teaching model. Field strengths are surface values rounded to one decimal place: Earth 10.0, the Moon 1.6, Mars 3.7, Jupiter 24.8 N/kg, with Jupiter quoted at the cloud tops since it has no solid surface. Object masses are nominal round figures. Weights are calculated from those two and rounded for display.
Lesson content © MrBadmusAI.