See also: Special Numbers and Concepts
When 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 newspapers, the length of a London bus, the height of the Eiffel Tower, or an area the size of 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 British system, a form of which is now chiefly used in the USA.
British Imperial vs Metric Systems
The Imperial and U.S. Customary systems of measurement both originate from an amalgamation of early British systems of measurement.
The imperial system was originally formalised by the British Weights and Measures Act of 1824 in order to provide a rapidly-developing industrial society with much-needed consistency.
However, this was half a century after American independence, and the system used in the US is based on earlier 18th Century British systems. The two are predominantly the same, but there are some differences, such as the measurement of volumes—something to watch out for in recipes!
The British Imperial System uses units such as pounds and ounces for mass, miles, yards, feet and inches for distance, and pints and gallons for volume.
It’s not a simple or intuitive system and its origins have baffled many scientists over the decades. 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, it can make converting quantities from one unit to another a bit of a challenge, so it really helps if you have a good understanding of fractions.
The metric system was officially adopted as a standardised system of measurement by the French in the late 18th century, although it was ‘invented’ over a century earlier. Believe it or not, the length of a ‘metre’ was derived from measurements of the earth’s circumference, which at the time aroused much curiosity and suspicion! However, it is the simplicity of the system that led to its rapid adoption throughout much of the industrialised world.
All the units in the metric system are in multiples of 10: there are 10mm in 1cm, 100cm in a metre, 1000m in a kilometre, and so on. It means that calculations can be done as decimals, so multiples of units can be calculated by dividing and multiplying by 10 and its powers. This is much easier to work out in your head and is easily adaptable in all sorts of applications, particularly in science and engineering.
Such was its almost universal appeal, the decimal system is now known globally as the SI system of units (International System or Système Internationale, in its original French).
The British Imperial System of Measurement
There are 20 or more ‘base units’ in the imperial system, unlike the metric system, which has fewer than 10. This is a lot to remember. Some of them are no longer in common usage, such as ‘fathom’, which is a unit of length used for measuring the depth of water. Others are used in very specific applications, such as ‘furlong’, which is still the recognised unit of distance in horse racing, and ‘chain’, which is a unit of distance used in the railway industry.
The following are the most commonly used and officially recognised imperial units:
Length or distance
Lengths and distances are measured in inches, feet, yards and miles:
| 12 inches (in) = 1 foot (ft) |
| 3 feet = 1 yard |
| 1760 yards = 1 mile |
When writing lengths in feet and inches it is common to abbreviate. 6 feet and 2 inches can be written as 6'2". Note that the symbols ' and " (a prime and double prime) are not the same as ‘ (an apostrophe) or “ (a quotation mark).
Fluid volume
Fluids are measured in fluid ounces, cups, pints, quarts and gallons.
In the American system:
| 8 fluid ounces (fl oz) = 1 cup |
| 2 cups = 1 pint |
| 2 pints = 1 quart |
| 4 quarts = 1 gallon |
In the British imperial system, 20 fluid ounces = 1 pint, and ‘cups’ are not used at all.
This is only likely to be a problem in recipes. However, 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 quantities accordingly.
Mass
Mass or Weight? Does it even matter?
When we ‘weigh’ something to find its weight, what we are actually measuring is its mass.
The weight of an object is the combination of its mass and the effect of gravity acting on it. Weight can change, depending on the influence of gravity, but mass always stays the same.
So the weight of an apple down here on the surface of the earth is over 6 times greater than its weight on the moon, because there is very little gravity on the moon. However, the mass of the apple on the earth and on the moon is the same. The physical make-up of its skin, flesh and core do not change on its journey from Earth to Moon, it is only the effect of gravity that changes.
In the imperial system, mass 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 |
Note that a ton is not the same as a tonne – see below under Metric Units in Everyday Use.
Did someone mention a slug? You did hear correctly!
Weight is a ‘force’ and in the imperial system, it is measured in pounds-force (lbf or lbf). You might hear this term used together with the term ‘slug’.
A slug has a mass of 32.174049 lb. A pound-force is the amount of force required to accelerate a slug at a rate of 1 ft/s2. Slugs are still used in American commerce, so it’s possible that you will come across them, but are not advised in scientific measurement.
However, pounds-force is still the correct unit of weight when using the imperial system, although it is not often used. This is because most scientific measurements in today’s world are made using SI units. In the SI system, the unit of weight is the ‘Newton’.
An important note, especially for cooks:
Be careful not to confuse ounces and fluid ounces. When we are talking about mass, there are 16oz in 1lb. When we are talking about liquid volume in the US system, there are 16 fluid ounces in 1 pint (or 20 fluid ounces in one English pint). However 1 oz of solid does not always weigh the same as 1 fluid ounce of liquid.
It is true that 1 fluid ounce of water weighs almost the same as an Imperial (US) ounce (in fact it weighs 1.043 oz), so you can assume a roughly 1:1 relationship in this case. However, this will not true for all liquids. This is because the mass and volume are related to density.
The metal mercury is liquid at room temperature. It’s poisonous, so we shouldn’t handle it, but if we were to hold a jar of mercury, it would feel much heavier than a jar of water. This is because the density of mercury is more than 13 times the density of water. So one fluid ounce of mercury is more than 13 times heavier than one fluid ounce of water. On the other hand, vegetable oil is less dense than water, so the same volume of oil would only weigh around 90% of the water.
The Metric (SI) System
The metric system is much simpler than the imperial system. There are a series of base units, one for each of distance, mass, and volume, and a series of prefixes to tell you what multiple of the base unit is being used. These are the most common:
| Basic Unit | Symbol | Measuring |
| Metre/meter | m | Distance |
| Gram | g | Mass |
| Second | s | Time |
| Litre/liter | l | Volume |
| Newton | N | Weight/Force |
Other standard units in the metric system include the Kelvin (K) to measure temperature, ampere (A) to measure electric current, the candela (cd) to measure light intensity, and the mole (mol) to measure the amount of a substance in a scientific (molecular) context. Some of these are only used in scientific applications, so you are unlikely to come across them in day to day usage.
The prefixes and what they mean are:
| Prefix | Symbol | Meaning | Number |
| Tera- | T | One trillion | 1012 |
| 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 |
| Micro- | µ | One millionth | 0.000001 |
| Nano- | n | One trillionth | 10-9 |
Metric Units in Everyday Use
You will most commonly come across kilo-, centi- and milli-, as in millimetres, centimetres, and kilometres.
There are 1000 metres in a kilometre, just as there are 1000 grams in a kilogram.
You will come across some of the other prefixes, particularly giga- and mega - in terms of your broadband bandwidth and computer memory and storage space. For example, higher capacity hard drives are measured in terabytes (Tb).
Kilo- or kilo- with a big K or small k?
In the table above, we have a list of the metric prefixes and the symbol or abbreviation that we use to describe the units we are using. You can see that there is a mixture of upper case and lower case letters, and it is important that these are used correctly. For example, it should always be a lower case ‘c’ for centi-, but an upper case ‘M’ for mega-. We need to be very careful with ‘D’ and ‘d’, so that we don’t confuse deca- with deci-.
However, we often see kilo- written with a lower case k and an upper case K, and you would be right to wonder why. When we are using metric weights and measures, we always use a lower case ‘k’ to denote kilo- (1000). So we would always write ‘kg’ to denote a kilogram, or ‘km’ to denote a kilometre, never Kg or Km. So why do we see an upper case K when we are talking about Kilobytes (Kb)?
K is a standard prefix used only in computing and this is where it gets confusing, because it doesn’t equate exactly to 1000. In fact, K represents the binary value of 2 to the power 10 (1024). Therefore, 8 Kilobytes (Kb) of memory is 8 times 1024, or 8,192 bytes.
Technically the upper case K represents the prefix Kibi, not Kilo, which is an amalgamation of the prefix ‘kilo’ with the term ‘binary’. You may not see it often, but it is useful to be aware of its existence, especially in an IT context.
Computer storage capacity is usually quoted in the metric (base 10) system (1 kilobyte = 1000 bytes; 1 megabyte = 1000 kilobytes; 1 gigabyte = 1000 megabytes; 1 terabyte = 1000 gigabytes).
However, RAM is usually quoted in binary (base 2) (1 kilobyte = 1024 bytes; 1 megabyte = 1024 kilobytes; 1 gigabyte = 1024 megabytes; 1 terabyte = 1024 gigabytes). So a 1GB hard drive has a capacity of 1000000000 bytes, but 1GB of RAM means 1073741824 bytes.
Tonnes or Tons?
The tonne, known in the USA as a metric ton, is not to be confused with the British or imperial ton. A tonne is 1,000kg, which can also be called a megagram. It equals a little over 1.1 US tons.
Measuring Volume
Volume is usually quoted either in litres, l, or in cubic metres, m3.
1cm3 is equal to 1 millilitre (ml). One litre is equivalent to 1000ml, so it follows that one litre is also the same as 1000cm3.
WARNING!
Volume is a cubic measurement. We can calculate the volume of a box (cuboid shape) by multiplying length by width by depth.
1m3 is NOT 1 litre!
1m3 is 1m x 1m x 1m. A litre is 1000cm3, which is the same as 10cm x 10cm x 10cm, which is a LOT smaller. In fact there are 1000 litres in one cubic metre.
Another useful relationship is that 1 litre of water weighs exactly 1kg.
The mass of 1cm3 or 1ml of water is equal to 1g. For everyday purposes, this can be regarded as true all of the time. However, scientifically this is only strictly true for pure water at 4°C. Sea water (and in fact some fresh water) has a slightly different density from pure water and this also varies with temperature. Mass, volume and density are related, so 1 litre of sea water has a slightly bigger mass than 1 litre of pure water.
Converting Between Metric and British Imperial Systems
You very seldom need to convert exactly between imperial and metric systems. If you do, you can 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), and a km is about two thirds of a mile.
- 1 litre is about 1 American quart
- 1 (UK) pint is about 500ml (half a litre)
- 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, 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 familiar with 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 was originally defined by 18th Century German physicist Fahrenheit as 180 equal intervals between the temperature at which water freezes and the temperature at which it boils. The exact measurement of these temperatures has undergone some refinement since then; freezing point is now 32°F and boiling point is 212°F. This is why it is not the most intuitive temperature scale.
Celsius / Centigrade is used across most of the rest of the world apart from the USA and its associated territories. It was developed to provide a simpler and more scientifically exact scale than the original Fahrenheit system. The freezing temperature of water is 0°C, and the boiling point is 100°C. ‘Centigrade’ broadly translates as ‘100 steps’ in Latin. The Celsius scale was named after the Swedish Astronomer Anders Celsius, who created a virtually identical scale with 100 intervals between the two reference temperatures. ‘Celsius’ is the more commonly-used unit, but is interchangeable with Centigrade.
The weather is the most common reason for needing to understand the alternative scale. Anything below 10°C or 50°F is cool to cold, 20°C or 68°F is warm, and anything above 30°C, 86°F, is hot.
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°C, which is absolute zero. Nothing can be colder than absolute zero, because this is the temperature at which all thermal motion of particles ceases and no thermal energy is left in a substance. Conversion to Celsius is therefore very easy: you simply add 273 to the Kelvin temperature.
A Note on Notation
We refer to ‘degrees’ Celsius or ‘degrees’ Fahrenheit, and abbreviate them using the degree ° symbol, °C and °F. However, when using the Kelvin scale, we do NOT refer to ‘degrees Kelvin’, simply ‘Kelvin’, so we abbreviate to K, not °K.
Conclusion
In today’s world, the common usage of both historic and modern measurement systems can cause some confusion, especially when travelling or doing business, or when using resources from the internet, such as recipes, that originate in a different region. It can therefore be helpful to have a basic understanding of the two main systems of measurement and know roughly how to convert between them.
Continue to:
Estimation, Approximation and Rounding Real-World Maths
See also:
Probability an Introduction
Averages (Mean, Median and Mode)
Polygons
