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Play: Measuring with your body, and how big is Mars?

Measurement · step 1 of 5

A question to start

How long is your bed? You do not need a ruler to find out. Stretch your hand out wide, put your thumb at one end of the bed, and "walk" your hand along it, span after span, counting as you go.

Now ask a grown-up to measure the same bed with their hand. Did you get the same number? Almost certainly not. The bed did not change, so what went wrong? Nothing went wrong. You have just discovered why people invented rulers.

The idea

Comparing

Before measuring anything, we can compare. Which pencil is longer? Stand them side by side, with their ends lined up, and look. Which bag is heavier? Hold one in each hand. Which jug holds more? Fill one with water and pour it into the other.

Comparing tells you which is bigger. Measuring tells you how much bigger, with a number.

Measuring with your body

For thousands of years, people measured with the rulers they always carried: their own bodies.

  • A hand span: from the tip of your thumb to the tip of your little finger, with your hand stretched wide.
  • A foot: the length of your foot, heel to toe.
  • A pace: one step when you walk normally.
  • A cubit: from your elbow to the tip of your middle finger. The ancient Egyptians used the cubit to plan buildings.

To measure something, choose one unit (one thing to measure with) and count how many fit. Three rules make your count honest:

  1. Start exactly at the beginning. Line up the end of your first unit with the end of the thing.
  2. No gaps. Each unit starts exactly where the last one finished.
  3. No overlaps. Units must not cover each other.
5 clips

If the thing is not an exact number of units long, say "about": "the pencil is about 5 paper clips long", or "between 5 and 6 paper clips".

Why we need the same units for everyone

Your hand span is smaller than a grown-up's, so you need more of them to cover the bed. That is the surprise from the start of the page: a smaller unit gives a bigger number. Both of you measured correctly; you just used different units.

That is fine at home, but no good for buying cloth, building a house or making a part for a spacecraft. Everyone must use the same unit. So people agreed on standard units, like the metre and the centimetre, and made rulers and tape measures that are the same everywhere. A metre is about the length of a big step for a grown-up. A centimetre is about the width of your little fingernail.

Estimating

An estimate is a sensible guess, made with some thinking. If you know your pace is about half a metre, then a hallway that takes 10 paces is about 5 metres long. Estimating is not cheating: scientists and builders estimate all the time, to check whether a careful measurement "looks about right".

How big is Mars?

Measuring gets more exciting the bigger things are. Here are Earth, the Moon and Mars, drawn to the same scale:

EarthMarsMoon
  • Earth is about 12 700 kilometres wide.
  • Mars is about 6 800 kilometres wide: a little more than half as wide as Earth.
  • The Moon is about 3 500 kilometres wide: about half as wide as Mars.

A kilometre is a thousand metres, about a 12-minute walk. To walk all the way round Mars at its middle (its equator) you would walk about 21 000 kilometres. Walking eight hours every day, that would take you about a year and a half, and there is no sea to stop you, because Mars has no oceans.

Time on Mars is measured differently too. A day on Mars, called a sol, is about 40 minutes longer than a day on Earth. And a year on Mars, once around the Sun, lasts 687 Earth days: nearly two of our years. On Mars, you would have a birthday only about every 23 months.

Worked example

Jo measures a rug with her pace and gets 6 paces. Her brother measures it and gets 8 paces. Who has the longer pace?

  1. The rug is the same length for both of them.
  2. Her brother needed more paces to cover it.
  3. More paces to cover the same length means each pace is shorter.
  4. So Jo has the longer pace.

Then: they measure with a metre stick and find the rug is 4 metres long. About how long is Jo's pace?

  1. 6 of Jo's paces cover 4 metres.
  2. 6 paces of 1 metre would be 6 metres: too much. 6 paces of half a metre would be 3 metres: too little.
  3. So each pace is a bit more than half a metre, roughly two thirds of a metre. An estimate is all we need here.

Try it

  1. A table is 7 of your hand spans long and 5 of your teacher's. Whose hand span is bigger?
  2. Would you measure the length of a classroom in hand spans, paces or kilometres? And the trip to another city?
  3. Mars is about half as wide as Earth. About how many Mars could sit side by side across Earth?
  4. You lay 4 pencils end to end, but leave a gap between each. Is "4 pencils long" too big or too small?
  5. Ali is 9 Earth years old. How many Mars years old is he, roughly?
Answers
  1. Your teacher's. The teacher needed fewer spans to cover the same table, so each span must be bigger.
  2. Paces for the classroom (hand spans would take ages, kilometres would be far too big). Kilometres for a trip to another city.
  3. About 2. Two Mars, each about 6 800 km wide, make about 13 600 km, just a bit more than Earth's 12 700 km.
  4. Too small. The gaps are part of the length too, but you did not count them. The real length is more than 4 pencils.
  5. Almost 5. A Mars year is nearly two Earth years, so 9 Earth years is a bit less than 5 Mars years. (Counting carefully, 9 Earth years is 3287 days. 4 Mars years is 2748 days and 5 Mars years is 3435 days, so he has had his 4th Mars birthday and his 5th is a few months away.)

Common mistake

Thinking a bigger number always means a longer thing. "My desk is 10 hand spans and yours is only 6 paces, so mine is longer" is not a fair comparison: the units are different. Before comparing two measurements, make sure they use the same unit. This is exactly why standard units exist.

Where it leads