Conversion of units to other units

This lesson is a reference list of how to convert between common units. For each pair of units it gives the factor you multiply or divide by. Throughout, $\times$ means multiply by and $\div$ means divide by.

Length

Moving to a smaller unit multiplies; moving to a larger unit divides.

$\text{m} \to \text{cm}: \times 100 \qquad \text{cm} \to \text{m}: \div 100$

$\text{cm} \to \text{mm}: \times 10 \qquad \text{mm} \to \text{cm}: \div 10$

$\text{dm} \to \text{cm}: \times 10 \qquad \text{cm} \to \text{dm}: \div 10$

$\text{km} \to \text{m}: \times 1000 \qquad \text{m} \to \text{km}: \div 1000$

Area

Area conversions use the length factor squared, since area has two length dimensions.

$\text{m}^2 \to \text{cm}^2: \times 100 \times 100 \qquad \text{cm}^2 \to \text{m}^2: \div (100 \times 100)$

The hectare is a unit of area equal to $10000\ \text{m}^2$.

$\text{ha} \to \text{m}^2: \times 10000 \qquad \text{m}^2 \to \text{ha}: \div 10000$

Units of area include $\text{mm}^2$, $\text{cm}^2$, $\text{dm}^2$, $\text{m}^2$, and $\text{km}^2$. When a length has no unit attached, an area is written in square units.

Volume

Volume conversions use the length factor cubed, since volume has three length dimensions.

$\text{m}^3 \to \text{cm}^3: \times 100 \times 100 \times 100 \qquad \text{cm}^3 \to \text{m}^3: \div (100 \times 100 \times 100)$

Units of volume include $\text{mm}^3$, $\text{cm}^3$, $\text{dm}^3$, $\text{m}^3$, and $\text{km}^3$, and a volume with no unit is written in cubic units.

Mass and capacity

$\text{kg} \to \text{g}: \times 1000 \qquad \text{g} \to \text{kg}: \div 1000$

$\text{L} \to \text{mL}: \times 1000 \qquad \text{mL} \to \text{L}: \div 1000$

Money and time

$\text{rupees} \to \text{paise}: \times 100 \qquad \text{paise} \to \text{rupees}: \div 100$

$\text{hours} \to \text{minutes}: \times 60 \qquad \text{minutes} \to \text{hours}: \div 60$

$\text{minutes} \to \text{seconds}: \times 60 \qquad \text{seconds} \to \text{minutes}: \div 60$

$\text{hours} \to \text{seconds}: \times 60 \times 60 \qquad \text{seconds} \to \text{hours}: \div (60 \times 60)$

$\text{days} \to \text{hours}: \times 24$

Volume to capacity

$\text{m}^3 \to \text{L}: \times 1000 \qquad \text{L} \to \text{m}^3: \div 1000$

$\text{cm}^3 \to \text{L}: \div 1000 \qquad \text{L} \to \text{cm}^3: \times 1000$

A cubic metre equals a kilolitre, so $\text{m}^3$ and $\text{kL}$ are the same size: convert either way by $\times 1$.

Speed

Speed can be given in kilometres per hour or metres per second.

$\text{km/h} \to \text{m/s}: \times \tfrac{5}{18} \qquad \text{m/s} \to \text{km/h}: \times \tfrac{18}{5}$

Finally, one dozen equals $12$.

Key takeaways

• Converting to a smaller unit multiplies; converting to a larger unit divides.
• Area uses the length factor squared and volume uses it cubed, so $\text{m}^2 \to \text{cm}^2$ is $\times 100 \times 100$ and $\text{m}^3 \to \text{cm}^3$ is $\times 100 \times 100 \times 100$.
• $1\ \text{ha} = 10000\ \text{m}^2$, $1\ \text{m}^3 = 1000\ \text{L} = 1\ \text{kL}$, and a speed in km/h converts to m/s by $\tfrac{5}{18}$.