# Bartlett's Guide to SI Units

## 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. In spite of 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 is mHz, Mhz or mhz written when referring to CPU clock rates? The correct form is actually MHz. Note that the capitalisation does matter.

This brief reference guide attempts to give accurate but concise information to clarify some of the mysteries of SI units and their conventions. It is not meant to be an exhaustive treatise on the subject, for this please refer to some of the definitive official publications eg National Institute of Standards & Technology (USA).

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

## 2. Base and Supplementary SI units

The seven Base SI units

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

solid angle

sr

## 3. The Derived units of the metric system (SI)

Derived Units with special names

Physical quantity

Name of unit

Symbol

Expressed in base units

frequency

hertz

Hz

`1/s`

force, weight

newton

N

`m.kg/s²`

work, energy, quantity of heat

joule

J

`m².kg/s²`

pressure, stress

pascal

Pa

`kg/m.s²`

power

watt

W

`m².kg/s³`

electric charge

coulomb

C

`s.A`

electric potential difference

volt

V

`m².kg/s³.A`

electric capacitance

F

`s².s².A²/m².kg`

electric resistance, reactance

ohm

(Omega)

`m².kg/s³.A²`

electric conductance

siemans

S

`s³.A²/m².kg`

magnetic flux

weber

Wb

`m².kg/s².A`

magnetic induction

tesla

T

`kg/s².A`

inductance

henry

H

`m².kg/s².A²`

luminous flux

lumen

lm

`cd.sr`

illuminance

lux

lx

`cd.sr/m²`

SI units with compound names

Physical quantity

Name of SI unit

Symbol

area

square metre

`m²`

volume

cubic metre

`m³`

speed, velocity

metre per second

`m/s`

acceleration

metre per second squared

`m/s²`

density

kilogram per cubic metre

`kg/m³`

moment of force

newton metre

`N.m`

electric field strength

volt per metre

`V/m`

specific heat capacity

joule per kilogram kelvin

`J/kg.K`

## 4. SI Prefixes

Prefix multipliers

Prefix

Symbol

Multiplier

exa-

E

1,000,000,000,000,000,000

peta-

P

1,000,000,000,000,000

tera-

T

1,000,000,000,000

giga-

G

1,000,000,000

mega-

M

1,000,000

kilo-

k

1,000

hecto-

h

100

deca-

da

10

deci-

d

0.1

centi-

c

0.01

milli-

m

0.001

micro-

µ

0.000 001

nano-

n

0.000 000 001

pico-

p

0.000 000 000 001

femto-

f

0.000 000 000 000 001

atto-

a

0.000 000 000 000 000 001

## 5. Units that may be used with the SI

Units that are used with the SI

Quantity

Name

Symbol

time

minute

min

time

hour

h

time

day

d

plane angle

degree

°

mass

metric ton

t

volume

litre

l

energy

electron volt

eV

speed

kilometre per hour

km/h

area

hectare

ha

temperature

degree Celsius

°C

rotational frequency

revolution per minute

r/min

## 6. Correct usage of the SI symbols

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

• The name of a unit always starts with a lower case letter, unless it is the first word in a sentence, where normal grammatical rules apply. This is true even if the symbol uses upper case. For example pascal and Pa are correct.
• The case of the letters in a symbol is important. For example m and M mean distinctly different things. MHz is megahertz (millions of cycles per second) while mHz is millihertz (thousandths of cycles per second). Computer clocks are typically MHz. A mHz computer is a very slow one. :))
• The unit of measure is the metre, not meter. The latter is a device used for measurement. (Unless you live in the USA - in which case you will just have to live with the ambiguity.)

## 7. 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 invariable quantities in nature,
2. all units other than the base units should be derived from these base units,
3. multiples and sub-multiples of the units should be decimal.

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

France created world-wide 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 has evolved, and in 1960 at the 11th CGPM the system was officially named the Système International d'Unités, abbreviated as SI . The SI is the logical evolution of the metric system and replaces all previous metric systems. It is a dynamic system which is continually being revised to keep pace with developments in science and technology.