Unit conversion – ratio tables, area, volume and compound units

What it shows

Metric units are linked by powers of ten, so converting means multiplying or dividing by a conversion factor. Writing the factor as a fraction equal to 1, such as 1000 m / 1 km, lets the units cancel (dimensional analysis). Area and volume scale with the square and the cube of length: 1 m = 100 cm gives 1 m² = 10 000 cm² and 1 m³ = 1 000 000 cm³, while 1 L = 1 dm³ = 1000 cm³. Compound units such as km/h or g/cm³ need the numerator and the denominator converted separately. Time is not decimal, and imperial factors are usually rounded.

How to use

On Convert, choose a Quantity, type a Value and pick the two units; follow the highlighted steps on the ladder and the ratio table, then use New question and Check to practise. On Area and volume, choose Square or Cube and a unit pair, change the Side and press Fill to count the small units. On Compound units, convert 72 km/h into m/s and read each step of the ratio table.

Parameters you can change

• Screen Convert, Area and volume, Compound units
• Quantity (Convert) Length, Mass, Time, Capacity, Area, Volume
• Value to convert (Convert) 0–1000000
• Starting unit, e.g. km (Convert)
• Target unit, e.g. m (Convert)
• Show imperial units
• Shape (Area and volume) Square, Cube
• Unit pair (Area and volume) m → dm, dm → cm, cm → mm, m → cm
• Side length in the larger unit 1–5
• Compound quantity Speed, Density, Flow rate, Pressure
• Value (Compound units) 0–100000
• Starting unit, e.g. km/h (Compound units)
• Target unit, e.g. m/s (Compound units)

Questions to explore

1. Why is 1 m² equal to 10 000 cm² and not 100 cm²?
2. How many litres of water fill a cube with 1 m sides?
3. Why do we divide by 3.6 to change km/h into m/s?