Units of measurement

One of the fundamental requirements of science is the ability not only to define, but also to measure, and it’s even more important in Physics, where precision and reproducibility are essential. Without the ability to measure, it would be difficult for scientists to conduct experiments or form theories.

All physical quantities must be accompanied by their units. When we associate units to a quantity we are in fact comparing it with a certain reference value. This value is unitary and is called unit of measurement. For instance when we measure a distance and say it is 200 metres, we actually mean this distance is two hundred times the definite predetermined length called metre.

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The definition of a good measurement system is something that has concerned human beings for thousands of years. And it is essential not only in the field of science, but also in commerce. The following image shows a deben, a weight unit used in ancient Egypt.

The first systems of units were based on the dimensions of the human body or of everyday objects (rod, foot, rice grains, etc). The problem with these primitive systems is that they were different depending on the people who created them, which hindered the exchange of goods and knowledge between peoples. But with the rise of travels to increasingly distant lands, the need to create a system of standardized units that could be used by an increasing number of people belonging to different cultures and separated by huge distances became evident.

What is now called the International System (SI) began to be defined during the French Revolution and, on June 22, 1799, two platinum standards were deposited in the Archive de la République, one corresponding to the kilogram (unit of mass) and the second to the meter (unit of length). In order to encourage the use of these new measurement units, marble copies of the standard metre were installed on various buildings in Paris.

The International System of Units has been evolving over time, until its current version (built on seven base units) was completed in 1971. These units, except the kilogram, are based on physical phenomena. However, in May 2019 the kilogram will be redefined as the standard (or Grand K) deposited in the International Bureau of Weights and Measures has been losing mass over time and it has become necessary to define it in a more stable way.

The base units of the International System are included in the following table:

Physical quantity Unit name Symbol
Length metre m
Time second s
Mass kilogram kg
Electric current intensity ampere A
Temperature kelvin K
amount of substance mole mol
Luminous intensity candela cd

The symbols of the units are generally written in lowercase, except for those that come from a person’s name; in this case they are capitalized. This rule is valid for both base units (K, A) and derived units: newton (N), tesla (T), etc.

The following figure shows a diagram of the base units of the International System.

You can get more information about the definition of these units from the the International Bureau of Weights and Measures (BIPM) website.

In these pages we will use the units of the International System, introducing units derived from the seven basic ones when necessary.

The International System is decimal, so the multiples and submultiples of each of its units are expressed in powers of 10. The following table shows the names of some of the prefixes of the International System.

10n Prefix Symbol Decimal equivalent
1024 yotta Y 1 000 000 000 000 000 000 000 000
1021 zetta Z 1 000 000 000 000 000 000 000
1018 exa E 1 000 000 000 000 000 000
1015 peta P 1 000 000 000 000 000
1012 tera T 1 000 000 000 000
109 giga G 1 000 000 000
106 mega M 1 000 000
103 kilo k 1 000
102 hecto h 100
101 deca da / D 10
100 ninguno 1
10-1 deci d 0.1
10-2 centi c 0.01
10-3 mili m 0.001
10-6 micro µ 0.000 001
10-9 nano n 0.000 000 001
10-12 pico p 0.000 000 000 001
10-15 femto f 0.000 000 000 000 001
10-18 atto a 0.000 000 000 000 000 001
10-21 zepto z 0.000 000 000 000 000 000 001
10-24 yocto y 0.000 000 000 000 000 000 000 001
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