The Metric System (SI)
A Concise Reference Guide

David Bartlett Copyright © 1998

Contents

  1. Introduction
  2. A brief History of the Metric System (SI)
  3. The Base and Supplementary units
  4. Derived Units
  5. SI Prefixes
  6. Other units used with the SI
  7. Proposals for binary multiples
  8. The Physical basis for some of the units
  9. A guide to correct usage of SI units
  10. Further References

1. Introduction

The Système International d'Unités (SI), the modern form of the metric system, is the most widely used system of units and measures around the world. But despite this there is widespread misuse of the system with incorrect names and symbols used as a matter a course - even by well educated and trained people who should know better. For example how often do we see: mHz, Mhz or mhz written when referring to computer clock rates? The correct form is actually MHz. Note that the capitalisation does matter.

I have put this brief reference guide together to give accurate but concise information to clarify the mysteries of the SI. Hopefully this will be useful for both the layman and the expert. It is not meant to be an exhaustive guide, for this you are referred to some of the excellent official publications on the subject.

The SI comprises units and SI prefixes used to form decimal multiples or submultiples of the units. The units are classified into Base units, Supplementary units and Derived units. The following sections described the different elements.

2. A brief History of the metric system (SI)

As early as 1584 Simon Stevenius had already proposed a decimal system of units and money in his book De Thiende. However, it was not until the French Revolution that the climate was conducive to creating a completely new system of units. In 1790 the French Academy of Science was commissioned by the National Assembly to design a new system of units for use throughout the world. They decided that this system should have the following attributes:

  1. the system should consist of measuring units based on unvariable quantities in nature,
  2. all units other than the base units should be derived from these base units,
  3. multiples and submultiples of the units should be decimal.

These principles still underpin the modern metric system (SI).

France created worldwide interest with this development and it resulted in 15 countries subscribing to the Metre convention in 1875. Through this the Bureau International des Poids et Mesures (BIPM) came into being. The BIPM now functions under the guidance of the Conférence Générale des Poids et Mesures (CGPM) which has delegates from all the countries that have subscribed to the convention.

Over the years the metric system evolved, and in 1960 at the 11th CGPM the system was officially named the Système International d'Unités, or SI for short. The SI is the logical evolution of the metric system through the years and replaces all previous metric systems. It is a living dynamic system which is continually being improved to keep pace with devlopments in science and technology.

3. Base and Supplementary units of the SI

The seven Base units of the SI
Physical quantity Base unit Symbol
length metre m
time second s
mass kilogram kg
electric current ampere A
thermodynamic temperature kelvin K
luminous intensity candela cd
amount of substance mole mol
The two Supplementary units of the SI
Physical quantity Unit Symbol
plane angle radian rad
solid angle steradian sr

4. The Derived units of the metric system (SI)

Derived Units with special names
Physical quantityName of unitSymbolin base unitsin derived units
frequencyhertzHz1/s1/s
force, weightnewtonNm.kg/s2m.kg/s2
work, energy, quantity of heatjouleJm2.kg/s2N.m
pressure, stresspascalPakg/(m.s2)N/m2
powerwattWm2.kg/s3J/s
electric chargecoulombCs.AA.s
electric potential differencevoltVm2.kg/(s3.A)W/A
electric capacitancefaradFs4.A2/(m2.kg)C/V
electric resistance, reactanceohm(Omega)m2.kg/(s3.A2)V/A
electric conductancesiemensSs3.A2/(m2.kg)A/V
magnetic fluxweberWbm2.kg/(s2.A)V.s
magnetic inductionteslaTkg/(s2.A)Wb/m2
inductancehenryHm2.kg/(s2.A2)Wb/A
luminous fluxlumenlmcd.srcd.sr
illuminanceluxlxcd.sr/m2lm/m2
absorbed dosegrayGym2.kg/(s2.kg)J/kg
activitybecquerelBq1/s1/s
dose equivalentsievertSvm2.kg/(s2.kg)J/kg
Celsius temperaturedegree Celsius°CKK
Some SI units with compound names
Physical quantityName of SI unitSymbol
areasquare metrem2
volumecubic metrem3
speed, velocitymetre per secondm/s
accelerationmetre per second squaredm/s2
angular velocityradian per secondrad/s
angular accelerationradian per second squaredrad/s2
densitykilogram per cubic metrekg/m3
moment of forcenewton metreN.m
electric field strengthvolt per metreV/m
permeabilityhenry per metreH/m
permittivityfarad per metreF/m
specific heat capacityjoule per kilogram kelvinJ/(kg.K)
luminancecandela per square metrecd/m2

5. Prefixes in the SI

Prefix multipliers
PrefixSymbolMultiplierExp
yotta-Y1 000 000 000 000 000 000 000 00010+24
zetta-Z1 000 000 000 000 000 000 00010+21
exa-E1 000 000 000 000 000 00010+18
peta-P1 000 000 000 000 00010+15
tera-T1 000 000 000 00010+12
giga-G1 000 000 00010+9
mega-M1 000 00010+6
kilo-k1 00010+3
hecto-h10010+2
deca-da1010+1
deci-d0.110-1
centi-c0.0110-2
milli-m0.00110-3
micro-µ0.000 00110-6
nano-n0.000 000 00110-9
pico-p0.000 000 000 00110-12
femto-f0.000 000 000 000 00110-15
atto-a0.000 000 000 000 000 00110-18
zepto-z0.000 000 000 000 000 000 00110-21
yocto-y0.000 000 000 000 000 000 000 00110-24

6. Units that may be used with the SI

Units that are used with the SI
QuantityNameSymbol
timeminutemin
hourh
dayd
plane angledegree°
massmetric tonnet
volumelitrel or L
energyelectron volteV
speedkilometre per hourkm/h
areahectareha
rotational frequencyrevolution per minuter/min

The following are some non-SI units which should not be used:

7. Proposals for Binary prefixes

It is generally accepted that a single binary measure of information, the bit, is described symbolically by a small "b", and the byte consisting of 8 bits as capital "B". However, confusion reigns over binary multiplier prefixes.

Considerable confusion exists in the computing industry over the use of kilo meaning either 1000 or 1024 times. Similar confusion exists for Mega being 1000000, 1048576 or even 1024000 in some cases. Some members of the computing industry have proposed using capital K as the prefix for 1024 and small k for 1000. This, however, is still confusing: Frequently we see modems described as 28.8 Kbit/s - which is clearly wrong as they are 28.8 kbit/s (28.8 * 1000). Nor does it address the problems with Mega.

The IEEE (Institution of Electrical and Electronics Engineers), IEEE Computer Society, ISO (International Standards Organisation) and IEC (International Electrotechnical Commission) have begun work jointly on defining standards and conventions for prefixes that are multiples of 2 not 10. A current proposal is to use the prefix Ki (kibi) as the kilobinary prefix for the factor 210 (1024), and Mi (mebi) as the prefix for the factor 220=(210)2. The NIST binary page presents a little more information about the proposals. Note that they are only proposals though.

8. The Physical basis for some of the units

metre
The metre is the length of the path travelled by light in a vacuum during a time interval of 1/299 792 458 of a second.
kilogram
The kilogram is the unit of mass. It is equal to the mass of the international prototype of the kilogram preserved in a vault in Sèvres, France. Since its installation in 1889 it has only been brought out 3 times to be cleaned and weighed. Eighty copies exist, of which 6 are "official". The last time the cylinders were removed and cleaned (between 1988 and 1992) there was found to be a variation of 23 µg, due to microscopic surface contamination and abrasion. Now the race is on to find a suitable replacement definition based on fundamental or atomic constants.
second
The second is the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium-133 atom.
ampere
The ampere is that constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross section, and placed one metre apart in a vacuum, would produce between these conductors a force equal to 200 nN per metre of length.
kelvin
The kelvin is the fraction 1/273.16 of the thermodynamic temperature of the triple point of water.
mole
The mole is the amount of substance of a system that contains as many elementary entities as there are atoms in 0.012 kg of carbon-12.
candela
The candela is the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 540 THz and that has a radiant intensity in that direction of 1/683 watts per steradian.
radian
The radian is the plane angle between two radii of a circle that cut off on the circumference an arc equal in length to the radius.
steradian
The steradian is the solid angle that, having its vertex in the centre of a sphere, cuts off an area on the surface of the sphere equal to that of a square with sides of length equal to the radius of the sphere.

9. Notes about and Correct usage of the SI

The following points underline some of the important aspects about using SI units and their symbols, and also mention some of the common errors that are made. The SI differs from some of the older systems in that it has definite rules governing the way the units and symbols are used.

10. Further References

  1. Chris Keenan's excellent UK metrication web site covering UK legislation, EC directives, Trading Standards etc.
  2. ANSII/IEEE Std 268-1992. American National Standard for Metric Practice. Published by the IEEE, October 28, 1992.
  3. BIPM. Le système international d'unités (SI) 6e édition, textes français et anglais. Sèvres, France. Bureau international des poids et mesures.
  4. The NIST Reference on Constants, Units and Uncertainty.
  5. The US Metric Association also maintains a nice web site.
  6. Theodore Wildi. Metric Units and Conversion Charts - A metrication Handbook for Engineers, Technologists and Scientists. IEEE Press, 1995.
Copyright © 1998 David Bartlett, Pyxidium Limited.