Skip to content

Mass and capacity

Measurement · level 3, lesson 2 of 6

A question to start

A carton of milk holds 1 litre. Put a 1-litre carton of water on a kitchen scale and it shows about 1 kilogram. A small 250 mL glass of water weighs about 250 grams.

Is that a lucky coincidence? No. The people who invented the metric system planned it that way, and by the end of this lesson you will know how. It gives you a handy trick: for water, the number of millilitres and the number of grams are the same.

The idea

Two different questions

This lesson is about two different questions you can ask about a thing.

  • How heavy is it? That is its mass: how much stuff it is made of. We measure mass in grams and kilograms.
  • How much does it hold? That is its capacity: how much liquid (or rice, or sand) a container can take. We measure capacity in millilitres and litres.

A big empty jug has a large capacity but a small mass. A small stone has a large mass for its size and holds nothing at all. Two questions, two kinds of unit.

In everyday talk people say "weight" when they mean mass, as in "my weight is 32 kg". That is fine at home. But scientists keep the two words apart, and Mars shows why. Mars pulls on things less strongly than Earth, a bit less than two fifths as strongly. A 30 kg backpack would feel as light on Mars as an 11 kg backpack feels on Earth, yet it would still hold exactly the same stuff: its mass would still be 30 kg. Mass is how much stuff; weight is how hard a planet pulls on it.

The same prefixes again

In the last lesson the prefixes kilo-, centi- and milli- built the length units out of the metre. Mass and capacity use the very same prefixes.

Kind Small unit Main unit Link
Mass gram (g) kilogram (kg) 1000 g = 1 kg
Capacity millilitre (mL) litre (L) 1000 mL = 1 L

"Kilo" still means a thousand: a kilogram is a thousand grams. "Milli" still means a thousandth: a millilitre is a thousandth of a litre. You already know how to convert: to the smaller unit, multiply by 1000; to the bigger unit, divide by 1000.

For very heavy things there is also the tonne (t): 1 t = 1000 kg. A small car has a mass of about 1 tonne, and an elephant about 4 to 6 tonnes.

Benchmarks to carry in your head

Thing About
a paper clip 1 g
a Canadian nickel 4 g
an apple 150 to 200 g
a litre of water 1 kg
a bag of flour 2.5 kg
a teaspoon of medicine 5 mL
a can of pop 355 mL
a big bottle of juice 2 L
a bathtub, filled for a bath 100 to 150 L

When you meet a new measurement, compare it with one of these. A 500 g bag of pasta is like half a carton of milk. A 2 L bottle is like two cartons.

Why a litre of water is a kilogram

Picture a hollow cube that is 10 cm long, 10 cm wide and 10 cm tall. The metric inventors defined the litre as the space inside that cube. Then they chose the mass unit so that water fits it: the water filling a tiny cube 1 cm on each side has a mass of 1 gram.

How many tiny 1 cm cubes fit in the big 10 cm cube? A bottom layer of 10 rows of 10 is 100 cubes, and there are 10 layers, so \(100 \times 10 = 1000\) small cubes. So:

  • the litre cube holds 1000 tiny cubes of water, each 1 gram: 1000 g = 1 kg;
  • each tiny cube is a thousandth of a litre: 1 millilitre.

That is why 1 mL of water has a mass of 1 g and 1 L of water has a mass of 1 kg. (Real water is a tiny bit lighter or heavier depending on how warm it is, but for everyday measuring the match is perfect.) You will build cubes like this again in level 4, when you measure volume.

Careful: the trick is for water. A litre of cooking oil has a mass of only about 900 g, because oil is lighter than water (that is why oil floats). A litre of honey is about 1.4 kg.

Reading a scale

A kitchen scale, a bathroom scale and a measuring jug all have a scale: a line of marks with only some of them numbered. To read one, first find out what each small step is worth.

  1. Pick two numbered marks next to each other.
  2. Count the spaces (not the lines) between them.
  3. Divide the difference by the number of spaces.
01 kg2 kg ? 123

Here the numbered marks 1 kg and 2 kg have 4 spaces between them. One kilogram is 1000 g, and \(1000 \div 4 = 250\), so each space is worth 250 g. The pointer is 3 spaces past 1 kg: \(1000 + 3 \times 250 = 1750\) g, which is 1.75 kg.

Choosing a sensible unit

As with length, pick the unit that gives an easy number. A strawberry: grams. A dog: kilograms. A truck: tonnes. Medicine: millilitres. A swimming pool: litres (a lot of them, often hundreds of thousands).

Worked examples

1. Kilograms to grams. A bag of flour is 2.5 kg. How many grams?

Grams are smaller, so multiply by 1000: \(2.5 \times 1000 = 2500\) g.

2. Millilitres to litres. A water bottle holds 750 mL. How many litres?

Litres are bigger, so divide by 1000: \(750 \div 1000 = 0.75\) L. That is three quarters of a litre.

3. Enough flour? A bread recipe needs 1.2 kg of flour. You have three bags of 500 g. Is that enough?

Use one unit. 1.2 kg is \(1.2 \times 1000 = 1200\) g. You have \(3 \times 500 = 1500\) g. Yes, it is enough, with \(1500 - 1200 = 300\) g left over.

4. Filling glasses. A 1.5 L jug of lemonade is poured into 250 mL glasses. How many glasses?

1.5 L is \(1.5 \times 1000 = 1500\) mL. Then \(1500 \div 250 = 6\) glasses.

5. Mass of water. A fish bowl holds 3 L of water. About how heavy is the water?

Each litre of water is about 1 kg, so 3 L of water is about 3 kg, as heavy as a big bag of potatoes. (The bowl itself adds more.)

6. Reading a jug. A measuring jug has numbered marks at 0, 200, 400, 600 mL, with 4 spaces between each pair. The water is 1 space above the 400 mark. How much water?

Each gap of 200 mL has 4 spaces, so each space is \(200 \div 4 = 50\) mL. The water is at \(400 + 50 = 450\) mL.

Try it

  1. Change to grams: (a) 3 kg; (b) 0.5 kg; (c) 1.25 kg.
  2. Change to litres: (a) 4000 mL; (b) 250 mL; (c) 1750 mL.
  3. Which unit would you use (g, kg, mL or L): the mass of a pencil; the water in a sink; the mass of a bicycle; a spoon of syrup?
  4. A scale has numbered marks at 0, 500 g and 1 kg, with 5 spaces between each pair. What is each space worth? Where does 700 g sit?
  5. A 2 L bottle fills how many 200 mL cups?
  6. A box holds 24 packets of crackers, each 125 g. What is the mass of the crackers in kilograms?
  7. Which is heavier: 1 L of water, or 900 g of rice? By how much?
  8. A full bucket of water has a mass of 11 kg. The empty bucket is 1 kg. About how many litres of water are in it?
Answers
  1. (a) \(3 \times 1000 = 3000\) g. (b) \(0.5 \times 1000 = 500\) g. (c) \(1.25 \times 1000 = 1250\) g.
  2. (a) \(4000 \div 1000 = 4\) L. (b) \(250 \div 1000 = 0.25\) L. (c) \(1750 \div 1000 = 1.75\) L.
  3. Pencil: grams (about 5 g). Sink: litres. Bicycle: kilograms. Spoon of syrup: millilitres.
  4. 500 g split into 5 spaces: \(500 \div 5 = 100\) g each. 700 g is \(700 - 500 = 200\) g past the 500 mark, so it is 2 spaces past 500 g.
  5. 2 L = 2000 mL, and \(2000 \div 200 = 10\) cups.
  6. \(24 \times 125 = 3000\) g, and \(3000 \div 1000 = 3\) kg.
  7. 1 L of water is about 1 kg = 1000 g. That is \(1000 - 900 = 100\) g heavier than the rice.
  8. The water alone is \(11 - 1 = 10\) kg. Each litre of water is about 1 kg, so about 10 L.

Common mistake

Mixing units in one sum. "I have 2 kg of apples and 500 g of grapes, so 502 of fruit" makes no sense. Change to one unit first: \(2000 + 500 = 2500\) g, or 2.5 kg.

Using the water trick for everything. 1 L is 1 kg only for water (and things nearly as heavy as water, like milk). A litre of feathers would be very light, and a litre of sand is about 1.5 kg. Capacity tells you how much room something takes up; mass tells you how much stuff is in it.

Where it leads