ShapesUnits of area and volume, and how to convert them
Most mistakes in mensuration are not in the formula. They are in the units. A length conversion uses the factor once, an area conversion uses it twice, and a volume conversion three times. This page gives the tables and the reasoning.
Why area factors are squared
One metre is 100 centimetres. A square metre is a square 100 cm long and 100 cm wide, so it holds 100 × 100 = 10,000 square centimetres. In the same way a cubic metre is 100 × 100 × 100 = 10,00,000 cubic centimetres.
Length
| 1 cm | 10 mm |
| 1 m | 100 cm |
| 1 km | 1000 m |
| 1 inch | 2.54 cm |
| 1 foot | 12 inches = 30.48 cm |
Area
| 1 cm² | 100 mm² |
| 1 m² | 10,000 cm² |
| 1 are | 100 m² |
| 1 hectare | 10,000 m² (a square 100 m by 100 m) |
| 1 km² | 100 hectares = 10,00,000 m² |
| 1 square foot | 144 square inches = 929.03 cm² |
| 1 m² | about 10.764 square feet |
| 1 acre | 43,560 square feet, about 4046.86 m² |
Land in India is also measured in bigha, kanal, marla, guntha and other local units, whose sizes differ from state to state. Our neighbour site Land Units converts those.
Volume and capacity
| 1 cm³ | 1000 mm³ = 1 millilitre (mL) |
| 1 litre | 1000 mL = 1000 cm³ |
| 1 m³ | 10,00,000 cm³ = 1000 litres = 1 kilolitre |
A handy picture: a cube 10 cm each way holds exactly one litre. A cube 1 m each way holds a thousand litres, and that much water weighs about a tonne.
Worked conversions
- 2.5 m² to cm²: 2.5 × 10,000 = 25,000 cm².
- 45,000 cm² to m²: 45,000 ÷ 10,000 = 4.5 m².
- 3 hectares to m²: 3 × 10,000 = 30,000 m².
- A tank 2 m × 1.5 m × 1 m in litres: volume 3 m³, and 3 × 1000 = 3000 litres.
- A tin of 7 cm radius and 10 cm height in litres: volume about 1539.4 cm³, which is about 1.54 litres.
Rules that prevent mistakes
- Convert the lengths first, then calculate. Changing 2 m 50 cm to 250 cm before multiplying is safer than converting the area afterwards.
- To go to a smaller unit, multiply. To a larger unit, divide. There are more small units in the same amount.
- Write the unit with every answer. "The area is 24" is not an answer. "24 cm²" is.
- Check the size. A classroom floor is tens of square metres, not thousands.
The calculator lets you pick the unit and labels each answer with the right power. Practice sheets: unit conversion worksheets.