## Metric Weight / Mass

Most people are familiar with the word “weight”, some may also know the term “mass”. For most things in everyday usage, they mean pretty much the same. You might come across the term “mass” in reference to body mass or your BMI (body mass index). It is just a case of measuring how heavy something is.

If you have to pick something up, it is good to know how heavy it is, and in the metric system it would be measured in kilograms. Note that the symbol kg is used both for 1 kilogram or several kilograms, e.g. 75 kg means 75 kilograms.

The kilogram is also divided into 1000 parts called grams. It is easy to remember as kilo at the start of a word means thousand, so 1 kilogram = 1000 grams.

The symbol for grams is g, so 1000 g = 1 kg.

Name of unit | Symbol | Equivalent | Typical item measured in this unit |

microgram | µg | 0.000 001 g | medicine |

milligram | mg | 1000 µg | medicine |

gram | g | 1000 milligrams | small amounts of food or jewellery |

kilogram | kg | 1000 g | body mass, weight of household furniture and large objects, bag of rice |

tonne | t | 1000 kg | weights of cars, boats, ships |

megagram | Mg | 1 tonne | rarely used, tonne is preferred |

megatonne | Mt | 1 million tonnes | megatonne is not actually used, although theoretically it could be used as a unit of mass. However the term megaton is used as a unit of energy, equivalent to the amount of energy in an explosion caused by 1 million tonnes of TNT. |

Your weight, also known as body mass, can be measured in kilograms. If you have a set of scales to weigh yourself, you will probably see kilograms or kg marked on the scale. If you have electronic scales, they can usually be set to either kg or stone-age units. Set it to kg, get on the scales and measure your body mass. Average weights for men are around 66 kg (based on height of 173 cm), and for women around 60 kg (based on height of 165 cm). These figures are also based on a BMI of 22. Although the weight of babies vary, the average birth weight of 3.4 kg remains relatively constant.

### BMI (Body Mass Index)

To calculate your BMI, use the following formula: mass divided by height squared. Mass measured in kilograms, and height in metres, so that for a typical man we have 66 kg / (1.73m×1.73m) = 22.0 (remember that 1 metre = 100 cm, see Length page for more info). This is a healthy BMI, as is any figure between 20 and 25. Below 20 means you are underweight, e.g. 60 / (1.75×1.75) = 19.5 which is slightly underweight.

A more extreme case might be such as a man weighing 55 kg but he is 1.80 metres tall, which means his BMI = 55 / (1.8×1.8) = 17.0 — if your BMI is that low you should try to put on some weight.

At the other end of the scale, a BMI of 25 to 30 is overweight, and over 30 is obese.

For example, if a man weighed 90 kg, and his height was 170 cm, then his BMI = 90 / (1.7×1.7) = 31.1, which is obese. And as height decreases, and weight increases, then the BMI will increase.

The chart below can also be used to calculate your BMI, if you know your height (centimetres) and weight (kilograms), then use a straightedge to help locate the point on the chart where your height and weight intersect. Read the number on the dashed line closest to this point. For example, an individual who weighs 69 kg and is 173 cm tall has a BMI of approximately 23.

For other purposes, we can use kilograms in our everyday lives, such as when shopping, and buying food, either pre-packed with a printed weight, such as 1 kg, 2.25 kg, etc. or loose fruit and vegetables, which might be priced as 74 pence per kg, or £1.20 / kg. For loose goods the price you pay will depend on the weight of the goods, and at the checkout these items will be weighed, and the electronic scales should display a weight, e.g. 0.67 kg, and calculate the price, at least that’s how it works in modern supermarkets. So if it was £1 per kilogram and you buy 670 grams of something, the price would be £1 × 0.67 kg = 67 pence. If it was 50 pence per kilogram and you buy 1 kg, the price would be £0.50 × 1 kg = 50 pence.

If you are buying water, the bottles are always marked in litres (see volume page). 1 litre of water weighs 1 kg, so if you are going to buy lots of water, make sure you can carry as many kilograms as there are litres, e.g. if you can carry 5 kg, then you could buy 5 litres. Most other liquids/drinks are heavier than water, so remember that 1 litre of other drinks will be slightly heavier than 1 kg.

To measure larger than kilograms, we use tonnes. 1 tonne = 1000 kg.

To measure weights smaller than 1 gram, we can use milligrams (mg) and micrograms (µg). 1000 mg = 1 g, 1000 µg = 1 mg, 1 000 000 µg = 1 g. These are used in science and medicine, and you may find that pills and tablets for vitamins or medicines have values of contents in mg or µg. Sometimes though µg will be written as mcg, as the prefix µ is a Greek letter and not easy to type on some systems.

### How are the units of weight defined?

Weight is a factor of length. When we start with the length of one metre, which was carefully defined (see page on length) we can divide that into 100 equal parts, called centimetres. We can then calculate volume in cubic centimetres. If we then take 1 cubic centimetre of water, at room temperature (20°C), we can define this as having a mass of 1 gram. We can also say that 1000 cm^{3} of water can be defined as 1 litre in volume, and that same volume at room temperature of 20°C has a mass of 1 kilogram. So you can see, this is how we get the kilogram, and you can see that weight (mass), volume and length are all inter-related, which makes calculations in metric very easy. 1 litre of water weighs 1 kg.