Metric system – units of length

The metric system uses base ten. Every step from one unit to the next either multiplies or divides by a power of ten — almost always by 10, with one exception.

The five common units

The conversion ladder

Going down (large → small) you multiply. Going up (small → large) you divide.

In numbers:

• $1\text{cm}=10\text{mm}$
• $1\text{dm}=10\text{cm}=100\text{mm}$
• $1\text{m}=10\text{dm}=100\text{cm}=1000\text{mm}$
• $1\text{km}=1000\text{m}=10000\text{dm}=100000\text{cm}=1000000\text{mm}$

Notice the gap between metres and kilometres: it is ×1000, not ×10. There would be a few extra units in between (dam, hm), but they are rarely used in everyday life.

A simple memory trick

Write the units in order from largest to smallest, with two empty places after the metre:

Each box represents one digit place. To convert, just shift the decimal point:

• to a smaller unit → shift right (add zeros)
• to a larger unit → shift left (group digits)

Example: $4\text{km}=?\text{m}$. From km to m is 3 boxes to the right, so add three zeros: $4000\text{m}$.

Examples

1. $7\text{m}=?\text{cm}$ — m to cm is two boxes right → $7\times 100=700\text{cm}$.
2. $25\text{dm}=?\text{cm}$ — dm to cm is one box right → $250\text{cm}$.
3. $5000\text{mm}=?\text{m}$ — mm to m is three boxes left → $5\text{m}$.

Read more

• Length unit conversions – guide
• Imperial units
• Converting larger to smaller
• Converting smaller to larger

Practise

• Convert larger to smaller
• Convert smaller to larger
• Fill in the unit