Metric Unit Conversion

Metric units come in families that step up in powers of ten — ten, a hundred, or a thousand at a time. Because the steps are clean, converting between two units in the same family is always a single multiply or divide.

The rule is short. To swap to a smaller unit you multiply (each new unit is tinier, so you need more of them); to swap to a larger unit you divide (each new unit holds more, so you need fewer). The number to multiply or divide by is just the size of one big unit measured in the small one:

1\ \text{cm} = 10\ \text{mm} \qquad 1\ \text{m} = 100\ \text{cm} \qquad 1\ \text{km} = 1000\ \text{m}

1\ \text{kg} = 1000\ \text{g} \qquad 1\ \text{l} = 1000\ \text{ml}

For example, kilometres are larger than metres, so going from km to m means multiplying:

3\ \text{km} = 3 \times 1000 = 3000\ \text{m}

Going the other way — grams up to kilograms — means dividing, because kilograms are the larger unit:

4500\ \text{g} = 4500 \div 1000 = 4.5\ \text{kg}

Keep these two halves together: pick whether the target unit is smaller or larger, then pick the right power of ten for that family.

To a smaller unit, multiply.
To a larger unit, divide.
Length, small end: \text{mm} \leftrightarrow \text{cm} is \times / \div\, 10.
Length, middle: \text{cm} \leftrightarrow \text{m} is \times / \div\, 100.
Length, large: \text{m} \leftrightarrow \text{km} is \times / \div\, 1000.
Mass: \text{g} \leftrightarrow \text{kg} is \times / \div\, 1000.
Capacity: \text{ml} \leftrightarrow \text{l} is \times / \div\, 1000.