Length, area and volume

Everyday units

The simplicity and logic of the metric system has led it to become the universal measurement system for everyday use all over the world. Factors contributing to its success include:

  • It is based on the decimal number system.
  • Only one unit is needed for each quantity such as length.
  • When dealing with small quantities and large quantities, there is no need for different units or difficult-to-learn conversion factors.
  • Large quantities and small quantities are handled simply by shifting the decimal place and adding a corresponding prefix to the unit name or symbol.

All metric measurements scale seemlessly from the very small, to the very large. Using metric units, it is easy to see the relative sizes of things, which in turn enhances our understanding of our surroundings. For instance, it is easy to see that 6 kilometres is ten times as far as 600 metres, whereas it is not immediately apparent how many miles a distance ten times as far as 600 yards would be.

Thinking in metric

When encountering metric units in everyday situations for the first time, those of us that have grown up in one of the few places on Earth that have yet to fully adopt the metric system can have a tendency to want to convert them into non-metric units that may be more familiar. This involves the use of mental arithmetic and conversion factors. Faced with learning a host of new conversion factors, newcomers to everyday metric units can easily be put off metric completely, which is unfortunate because, when used exclusively, the metric system completely removes the need for all conversion factors.

Learning to think in metric is actually much simpler than converting to non-metric units, and is ultimately far more rewarding. In place of conversion factors, the metric system only requires the learning of a handful of prefix names, and the multiples of ten that they represent. The full benefits of the metric system can only really be appreciated after learning to think exclusively in metric.

One can start thinking in metric, by learning the sizes and weights of various familiar objects as reference points:

  • For example, a compact disc has a diameter of 12 cm, and a thickness of 1.2 mm, and one lap of an Olympic athletics track is 400 m.
  • Similarly, a litre-carton of fruit juice has a mass of about 1 kilogram, most new born babies weigh between 2.5 kg and 4 kg, an average man’s weight is about 80 kg, and the mass of a small car is about 1000 kg, or 1 tonne.
  • Investing in a metric-only tape measure, to measure personal height, and the size of familiar rooms, together with using metric scales to measure body weight, are also good ways to start thinking in metric.

Length

The SI unit of length is the metre, symbol m.

Commonly used subunits include the millimetre, symbol mm, centimetre, symbol cm, and kilometre, symbol km.

The metre was originally defined as being equal to one ten-millionth of the distance from the equator to the North Pole.

The modern definition of the metre is more precise. However, for practical purposes, the distance from the equator to the North Pole remains approximately 10 000 000 metres, or 10 000 kilometres.

100 centimetres = 1 metre
1000 millimetres = 1 metre
1000 metres = 1 kilometre

Orders of magnitude

 1000 nm = 1 μm = 0.000 001 m = 10-6 m 
 1000 μm = 1 mm = 0.001 m = 10-3 m 
 1000 mm = 1 m = 1 m = 100 m 
 1000 m = 1 km = 1000 m = 103 m 
 1000 km = 1 Mm = 1 000 000 m = 106 m 

 


Area

The SI unit of area is the square metre, symbol m2.

Commonly used subunits include the square centimetre, symbol cm2, and square kilometre, symbol km2.

The hectare, symbol ha, is the special name for the square hectometre, symbol hm2. 1 hectare is equal to 10 000 square metres. Prefixes must not be used with the hectare.

 10 000 square centimetres = 1 square metre
10 000 square metres = 1 hectare
100 hectares = 1 square kilometre

Orders of magnitude

 100 mm2 = 1 cm2 = 0.0001 m2 = 10-4 m2 
 100 cm2 = 1 dm2 = 0.01 m2 = 10-2 m2 
 100 dm2 = 1 m2 = 1 m2 = 100 m2 
 100 m2 = 1 dam2 = 100 m2 = 102 m2 
 100 dam2 = 1 hm2 = 10 000 m2 = 104 m2 
 100 hm2 = 1 km2 = 1 000 000 m2 = 106 m2 

 


Volume

The SI unit of volume is the cubic metre, symbol m3.

The litre, symbol L or l, is the special name for the cubic decimetre, symbol dm3. 1 litre is equal to one thousandth of a cubic metre. It follows that 1 millilitre, symbol mL or ml, is equal to 1 cubic centimetre.

In everyday use, the millilitre and litre are the most commonly used subunits to measure volume.

1000 millilitres = 1 litre
1000 litres = 1 cubic metre

Orders of magnitude

 1000 mm3 =  1 cm3 =  1000 µL =  1 mL = 10-6 m3 
 1000 cm3 =  1 dm3 =  1000 mL =  1 L = 10-3 m3 
 1000 dm3 =  1 m3 =  1000 L =  1 kL = 100 m3 
 1000 m3 =  1 dam3 =  1000 kL =  1 ML = 103 m3 
 1000 dam3 =  1 hm3 =  1000 ML =  1 GL = 106 m3 
 1000 hm3 =  1 km3 =  1000 GL =  1 TL = 109 m3