The metric system, the SI, and units of mass, length, area and volume

What we call the metric system is the ordinary system of “weights and measures” used by most people in most countries except the United States of America. Canada uses the metric system, which regularly confuses visitors and tourists from the United States.

The use of the metric system spread across mainland Europe at the end of the eighteenth century because it was introduced by the French Revolutionary Government and enforced by Napoleon's armies during the Napoleonic Wars. It did not reach Britain at that time only because Napoleon never invaded Britain.

The original metric system also abolished all the existing units of time such as the hour and minute, and introduced new units of time based upon ten rather than sixty and twenty four, and a new calendar and year numbering system, although these were not enforced by Napoleon and were therefore not incorporated into the present metric system - this is further discussed in the section on the Calendar

In Britain the metric system of metres, hectares, litres and kilograms is used alongside the older system of yards, acres, gallons and pounds, for example petrol can only be sold in litres whereas draught beer can only be sold in pints. We usually call the older system the Imperial system. Although the system used in the USA is similar to the Imperial system it is not identical - for example a US gallon is about 20% less than an Imperial gallon.

For many years the United States and Britain have in fact used the metric system for almost all units other than those for mass, length, volume and area, for example electric current has always been measured in amperes.

For the units of temperature please see the Page on Temperature Scales and for units of Pressure see the page on them.

There are many different units, some in common use today, some in less common use, some used in the past. There is a list of many of these, and some very useful conversion charts, on the Easy Unit Converter Web Site.

The SI (Système International d'Unités) is the system of units now used by almost all scientists throughout the world, including almost all in Britain and most, but not all, in the United States of America. Please note it is incorrect to refer to the SI system.

The SI was developed from the metric system but is very much more prescriptive, and many metric units such as the litre are not included in the SI.

Two earlier terms may still be encountered in older scientific textbooks: the cgs (centimetre/gram/second) system and the mks (metre/kilogram/second )system.

In the metric system (and SI) for each quantity there is a base unit, and then the units for larger and smaller quantities can be prefixed to show how much bigger or smaller they are than the base unit, for example a kilometre is a thousand metres.

We can write a million million (twelve zeros) as 1000 000 000 000 and a thousand millionth (nine zeros) as 0.000 000 001 but this takes up a lot of space and it is very easy to make a mistake with the number of zeros, so we usually write very big (or very small) numbers as powers of ten. We write a hundred (with two zeros) as 102, a thousand (with three zeros) as 103, and a million (with six zeros) as 106.

 deca- da 101 Almost never used. Sometimes spelt deka hecto- H 102 Usually only used as in hectares (Ha) kilo- k 103 mega- M 106 giga- G 109 tera- T 1012 peta- P 1015 exa- E 1018

For example three thousand million watts (3×109 W) would be three gigawatts (3 GW). You do not need to know what a watt is to know that a thousand million of them make a gigawatt.

Similarly for smaller units. We can write a thousandth as 10-3, and a millionth as 10-6

 deci- d 10-1 Usually only used as in decimetres cubed (dm3) centi- c 10-2 Usually only used as in cm, cm2 and cm3 or centilitres (cl) milli- m 10-3 micro- µ 10-6 µ is the Greek letter mu nano- n 10-9 pico- p 10-12 femto- f 10-15 ato- a 10-18

So sixteen million millionths of a farad (16×10-12 F) would be written 16 pF. You do not need to understand what a farad is to know that a picofarad is a million millionth of one.

The SI and metric systems prefer to use only thousands and thousandths, so hecto-, deci- and centi- are not usually used except for the special purposes given, and deca- is almost never used.

For example

a thousandth of a volt (10-3 V) is a millivolt (mV)
a thousand millionth of a farad (10-9 F) is a nanofarad (nF)
a thousand watts (103 W) is a kilowatt (kW)
a millionth of a second (10-6 s) is a microsecond (µs)
a million coulombs (106 C) is a megacoulomb (MC)

Take care to use only the capital letters H, M, G, T, P and E for the abbreviations for hecto-, mega-, giga-, tera-, peta- and exa-, and only small letters for the other abbreviations. There is a move to use K rather than k for kilo, to bring it into line with the other large units.

Writing quantities

Where the unit for a quantity is named after a person it is written with a small letter (except for Celsius in degrees Celsius), but the symbol (abbreviation) is written with a capital letter, for example ten volts but 10 V (after the Italian scientist Count Alessandro Volta), sixty newtons but 60 N, fifteen amperes but 15 A. Units not named after people are always written with a little letter, for example ten metres and 10 m. Note also that there is no full stop after the symbol, for example 726 µF not 726 µF..

There is a space between the number and the unit, for example 20 A. If you are using a word processor or computer it is best if you use a non-breaking (hard) space between the quantity and its unit so that if your work is reformatted later they still stay together on the same line.

You never use the symbol when you write the quantity in words, for example ten kilometres or 10 km but never ten km. In a story, or something like a history essay which has nothing to do with maths or science, it is usually considered better to write numbers, particularly numbers less than a hundred, in words, for example ten kilometres not 10 kilometres or 10 km. In a story or essay you should always write a number in words if it starts a sentence.

Units of mass

In SI the base unit of mass is the kilogram not the gram, although this fact will only become important to you if you study science beyond GCSE level.

1000 micrograms make a milligram
1000 milligrams make a gram
1000 grams make a kilogram
1000 kilograms make a tonne - note the spelling! A tonne is very slightly less than an Imperial ton.

Some Imperial units of mass are

16 ounces (oz) make one pound (lb, from the Latin libra)
14 pounds make a stone
2 stones make a quarter
4 quarters make a hundredweight (correctly Cwt for a Roman hundred but usually written cwt. A hundredweight is 112 pounds.)
20 hundredweight make a ton

There are also other Imperial units of mass such as grains, scruples, drams, drachms (not the same) and pennyweights, which are not often used today. The approximate conversions between the Imperial and metric systems are

1 ounce is about 28 g
1 pound is about 450 g
1 stone is about 6.3 kg
1 ton is about 1.02 tonnes

Gold, platinum and silver are weighed in Troy ounces and Troy pounds, which are not the same as Imperial (correctly, avoirdupois) ounces and pounds. There are only twelve Troy ounces in a Troy pound. One Troy ounce is about 31 g whereas an avoirdupois ounce is about 28 g, so an ounce of gold really does weigh more than an ounce of feathers!

Diamonds are measured in carats - confusingly not the same carat as used for measuring the purity of gold! A carat is about 200 milligrams. There are 100 points in a carat.

There are more units of mass and the conversion factors between them on the Easy Unit Converter Web Site

Units of length

The unit of length is the metre

10 millimetres make a centimetre
10 centimetres make a decimetre
10 decimetres make a metre
1000 metres make a kilometre

Decimetres are not usually used for measuring length (but dm3 are used for measuring volume - see below), and lengths involving fractions of a centimetre are usually given in millimetres, for example 50 cm but 475 mm not 47.5 cm. The centimetre is not a SI unit.

Some Imperial units of length are

12 inches make one foot
3 feet make one yard
220 yards make a furlong (from the Old English furrow-long)
1760 yards (eight furlongs) make a mile (from the Latin mille pasuum, a thousand paces. A Roman pace was a double pace, which today we would count as two paces.)

There are also other Imperial units of length such as rods and chains which are not often used today. Some approximate conversions between the Imperial and metric systems are

1 inch is about 25 mm
1 foot is about 30 cm
1 yard is about 90 cm
1 mile is about 1.6 km

There are more units of length and the conversion factors between them on the Easy Unit Converter Web Site

Units of area

The units of area are the centimetre, metre and kilometre squared (cm2, m2 and km2).

Farmland and forest etc. are often measures in ares (pronounced airs) and hectares. One are is 100m2 and a hectare (Ha) is one hundred ares or 10 000 m2 (100 m × 100 m)

In the Imperial system

4840 square yards make an acre (220 yards by 22 yards)
640 acres make a square mile

One square yard is about 0.81 m2
One acre is about 0.4 Ha
One square mile is about 2.5 km2

An acre was as much land as an ox could plough between sunrise and sunset, each furrow being 220 yards long - one furrow long!

There are more units of area and the conversion factors between them on the Easy Unit Converter Web Site

Units of volume

The units of volume are the centimetre, decimetre and metre cubed (cm3, dm3, and m3).

1000 cm3 make 1 dm3
1000 dm3 make 1 m3

In the metric system (but not the SI) volumes of liquids and gases are often measured in litres (l) and millilitres (ml, often pronounced mill, for example take a five mill spoonful of cough mixture). One litre is the same as a decimetre cubed (but see next paragraph) and so 1 cm3 is the same as 1 ml. Take care over the use of l (ell) for litres as it can be confused with 1 (one) on some typefaces - it is safest always to write litres in full, or use dm3 if there is any possibility of confusion. If you are handwriting make certain you write a nice loopy l. The capacity of wine bottles is often given in centilitres (cl) - many wines are sold in bottles containing 70 or 75 cl.

British and European food labelling regulations permit the use of capital L for litres: you may see this on milk cartons or bottles of cooking oil.

Theoretically there is a difference between a litre and a decimetre cubed but it is very small indeed. This difference is fully discussed in the Page on density - to link to it please click here

The SI uses only dm3, but the use of litres and millilitres is quite acceptable in Junior and Middle Schools and in the “real” world. For most purposes cm3 and ml, and litres and dm3, are used synonymously.

In the Imperial system

1728 cubic inches inches make 1 cubic foot
9 cubic feet make 1 cubic yard

Liquids are measured in other units

20 fluid ounces make 1 pint
2 pints make a quart
4 quarts make a gallon

A cubic inch is about 16 cm3
A cubic foot is about 27 dm3
A cubic yard is about 0.7 m3

A fluid ounce is about 28 ml
A pint is about 568 ml
A gallon is about 4.5 litres

There are more units of volume and the conversion factors between them on the Easy Unit Converter Web Site