# Systems of Measurement | Weights and Measures

See also: Special Numbers and ConceptsWhen you want to tell someone how big or how far away something is, you need a ‘common system’ for communicating this information.

Despite what you may read in the newspaper, the length of a London bus or an area the size of Wales or Texas are not common units of measurement, and they are not universally understood!

This page explains the two most common systems of measurement: the metric system, used widely in Europe and most of the rest of the world, and the imperial or English system, now chiefly used in the USA.

### English vs Metric Systems

The English system of measurement has been in use for a very long time. It involves units such as pounds and ounces for weight, miles, yards, feet and inches for distance, and pints and gallons for volume.

It’s not a simple or intuitive system. For example, there are 12 inches in a foot, 3 feet in a yard, and 16 ounces in a pound. What’s more, because the units aren’t in nice easy numbers, neither are the parts: to explain how many ounces you need in terms of pounds, you need to use **fractions**.

In the UK, the invention of the metric system is often attributed to Napoleon, but that is probably a myth. Whoever invented it, the metric system was designed to make measuring and comparing easier. All the units are in multiples of 10: there are 10mm in 1cm, 100cm in a metre, 1000m in a kilometre, and so on. It means that all the sums can be done as **decimals**.

### The English or Imperial System of Measurement

#### Length or distance

Lengths and distances are measured in inches, feet, yards and miles:

12 inches = 1 foot

3 feet = 1 yard

1760 yards = 1 mile

#### Fluid volume

Fluids are measured in fluid ounces, cups, pints, quarts and gallons.

The UK and American systems of fluid measurement are slightly different: the UK imperial system does not use cups, and the sizes are slightly different.

In the American system:

8 fluid ounces (sometimes abbreviated to fl oz) = 1 cup

2 cups = 1 pint

2 pints = 1 quart

4 quarts = 1 gallon

In the English imperial system, 20 fluid ounces = 1 pint, and ‘cups’ are not used at all.

You’re only likely to come across this as a problem in recipes, when it’s usually clear whether you have an English or American recipe by the use of cups as a standard measure, and you can therefore amend your other measurements accordingly.

#### Weight

Weight is measured in ounces, pounds and tons:

16 ounces (oz) = 1 pound (lb)

14 pounds = 1 stone (English imperial system only)

2,000 pounds = 1 ton

Two Minor Diversions

- Don’t confuse ounces and fluid ounces. Helpfully, a fluid ounce is not simply the volume of one ounce of liquid!
- What we call weight is actually mass. Weight is a measure of how strongly gravity drags on something, and is measured in Newtons. Weight changes with gravity; mass does not.

## The Metric System

The metric system is much simpler. There are a series of *basic units*, one for each of distance, mass, and volume, and a series of prefixes to tell you what multiple of the basic unit is being used.

Basic Unit | Measuring |

Metre/meter | Distance |

Gram | Mass |

Litre/liter | Volume |

The prefixes and what they mean are:

Prefix | Symbol | Meaning | Number |

Giga- | G | One billion | 1,000,000,000 |

Mega- | M | One million | 1,000,000 |

Kilo- | K | One thousand | 1,000 |

Deca- | D | Ten | 10 |

(none) | One | 1 | |

Deci- | d | One tenth | 0.1 |

Centi- | c | One hundredth | 0.01 |

Milli- | m | One thousandth | 0.001 |

You will most commonly come across kilo-, centi- and milli-, as in millimetres, centimetres, and kilometres.

However, there are certain times when you will come across some of the others, particularly Giga- and Mega- in terms of your broadband bandwidth and computer memory and storage space.

Science often uses much smaller numbers, and scientists may find themselves referring to nanometres, or 10^{-9}m, and even beyond. But for most purposes, you’ll find these prefixes enough.

Tonnes

The tonne, known in the USA as a metric ton, is not to be confused with the English or imperial ton. It is 1,000kg, and therefore a megagram.

Measuring Volume

Volume can be measured in two ways in the metric system, in litres, and in cubic metres, m^{3}. However, because the metric system is designed to be simple, the two are easily translated. 1cm^{3} is equal to 1 millilitre, or ml.

Another useful relationship is that 1 litre of water weighs exactly 1kg.

WARNING!

Because volume is a cubic measurement (it is calculated by multiplying length by width by depth), 1m^{3} is NOT 1 litre. 1m^{3} is 1m x 1m x 1m, whereas a litre is 1000cm^{3} or 10cm x 10cm x 10cm, which is a LOT smaller.

## Converting Between Metric and English/Imperial Systems

You very seldom need to convert *exactly* between English and metric systems, although if you do, you just multiply by the desired ‘conversion factor’.

However, it is often useful to be able to convert *approximately*, for example, to estimate driving distance or maximum speed limit when travelling in another country.

There are a series of useful approximations which you can use. For example:

- 1 yard is approximately 1 metre
- 1 mile is about 1.5 kilometres (km); alternatively, a km is about two thirds of a mile.
- 1 litre is about 1 American quart
- 1 (UK) pint is about 500ml.
- 1 kilogram (kg) is about 2 pounds (lb)

Warning!

Although these approximations are precise enough to estimate whether you’re driving above the speed limit, or roughly how long it will take you to travel somewhere, they are NOT precise enough for recipes.

Always use the same units in a recipe, whether metric or imperial/English, and don’t move between the two.

### Measuring Temperature

There are three scales commonly used for measuring temperature: Fahrenheit, Celsius or Centigrade, and Kelvin.

**Fahrenheit** is the oldest scale and least obvious for those not used to it. The Fahrenheit scale was formerly used across Europe but has now been replaced by the Centigrade scale. It is however still widely used in the USA. This scale is defined by two measurements: the temperature at which water freezes into ice, which is 32^{o}F, and the temperature at which water boils, which is 212^{o}F.

**Celsius / Centigrade** is used across most of the rest of the world apart from the USA and its associated territories. Like the metric system, it is broadly designed around 10s. The freezing temperature of water is 0^{o}C, and the boiling point is 100^{o}C.

The weather is the most common reason for needing to understand the alternative scale. Anything below 10^{o}C or 50^{o}F is cool to cold, 20^{o}C or 68^{o}F is warm, anything above 30^{o}C, 86^{o}F, is hot.

The final scale, **Kelvin**, is the scientific measurement scale, and the SI unit for temperature. It has exactly the same increments as the Celsius / Centigrade scale. The zero point, or 0K, is -273^{o}C, which is absolute zero, the temperature at which all thermal motion ceases. Conversion to Celsius is therefore very easy: you simply add 273 to the Kelvin temperature.

### Conclusion

In general, you will probably survive with detailed knowledge of only one system of weights and measures. However, it can be helpful to know roughly how to convert between different systems of measurement when you’re travelling, doing business abroad or even just for interest.

Continue to:

Estimation, Approximation and Rounding

Real-World Maths