A Dictionary of Units
This provides a summary of most of the units of measurement
to be found in use around the world today (and a few of historical interest),
together with the appropriate conversion factors needed to change them
into a 'standard' unit of the S I.
The units may be found either by looking under the
category in which they are used [such as length,
mass, density, energy etc.], or else by picking one unit from an alphabetically
ordered list of units. There are NO units of currency.
There is an outline of the S I;
a list of its basic defining standards and also
some of its derived units; then another list of
all the S I prefixes and some notes on conventions
of usage.
There is a short historical
note on measures generally; descriptions of the Metric
system, the U K (Imperial) system with a statement
on the implementation of 'metrication' in the U K,
and the U S system.
Finally there is a list of other
sources concerned with the topic of measures and units (including other
Web sites) and also some notes
about this document.
The Systeme International [S I]
Le Systeme international d'Unites officially came
into being in October 1960 and has been adopted by nearly all countries,
though the amount of actual usage varies considerably.
It is based upon 7 principal units, 1 in each
of 7 different categories -
Category Name Abbreviation
Length metre m
Mass kilogram kg
Time second s
Electric current ampere A
Temperature kelvin K
Amount of substance mole mol
Luminous intensity candela cd
Definitions of these basic
units are given.
Each of these units may take a prefix.
From these basic units many other
units are derived and named.
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this document
Definitions of the Seven Basic S I Units
-
metre [m]
-
The metre is the basic unit of length. It is the
distance light travels, in a vacuum, in 1/299792458th
of a second.
-
kilogram [kg]
-
The kilogram is the basic unit of mass. It is the
mass of an international prototype in the form of a platinum-iridium cylinder
kept at Sevres in France. It is now the only basic unit still defined
in terms of a material object, and also the only one with a prefix[kilo]
already in place.
-
second [s]
-
The second is the basic unit of time. It is the length
of time taken for 9192631770 periods of vibration of
the caesium-133 atom to occur.
-
ampere [A]
-
The ampere is the basic unit of electric current.
It is that current which produces a specified force between two parallel
wires which are 1 metre apart in a vacuum.It is named after the French
physicist Andre Ampere (1775-1836).
-
kelvin [K]
-
The kelvin is the basic unit of temperature. It is
1/273.16th of the thermodynamic temperature of the triple point
of water. It is named after the Scottish mathematician and physicist
William Thomson 1st Lord Kelvin (1824-1907).
-
mole [mol]
-
The mole is the basic unit of substance. It is the
amount of substance that contains as many elementary units as there are
atoms in 0.012 kg of carbon-12.
-
candela [cd]
-
The candela is the basic unit of luminous intensity.
It is the intensity of a source of light of a specified frequency, which
gives a specified amount of power in a given direction.
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Derived Units of the S I
From the 7 basic units of the SI many other units
are derived for a variety of purposes. Only some of them are explained
here. The units printed in bold are either basic units or else,
in some cases, are themselves derived.
-
farad [F]
-
The farad is the SI unit of the capacitance of an
electrical system, that is, its capacity to store electricity. It is a
rather large unit as defined and is more often used as a microfarad. It
is named after the English chemist and physicist Michael Faraday (1791-1867).
-
hertz [Hz]
-
The hertz is the SI unit of the frequency of a periodic
phenomenon. One hertz indicates that 1 cycle of the phenomenon occurs every
second. For most work much higher frequencies are needed such as
the kiloherz [kHz] and megaherz [MHz]. It is named after the German
physicist Heinrich Rudolph Herz (1857-94).
-
joule [J]
-
The joule is the SI unit of work or energy. One joule
is the amount of work done when an applied force of 1 newton moves
through a distance of 1 metre in the direction of the force.It
is named after the English physicist James Prescott Joule (1818-89).
-
newton [N]
-
The newton is the SI unit of force. One newton is
the force required to give a mass of 1 kilogram an acceleration
of 1 metre per second per second. It is named after
the English mathematician and physicist Sir Isaac Newton (1642-1727).
-
ohm [*]
-
The ohm is the SI unit of resistance of an electrical
conductor. Its symbol, shown here as [*] is the Greek letter known as 'omega'.
It is named after the German physicist Georg Simon Ohm (1789-1854).
-
pascal [Pa]
-
The pascal is the SI unit of pressure. One pascal
is the pressure generated by a force of 1 newton acting on an area
of 1 square metre. It is a rather small unit as defined and is more
often used as a kilopascal [kPa]. It is named after the French mathematician,
physicist and philosopher Blaise Pascal (1623-62).
-
volt [V]
-
The volt is the SI unit of electric potential. One
volt is the difference of potential between two points of an electical
conductor when a current of 1 ampere flowing between those points
dissipates a power of 1 watt. It is named after the Italian physicist
Count Alessandro Giuseppe Anastasio Volta (1745-1827).
-
watt [W]
-
The watt is used to measure power or the rate of
doing work. One watt is a power of 1 joule per second. It
is named after the Scottish engineer James Watt (1736-1819).
Note that prefixes may be
used in conjunction with any of the above units.
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The Prefixes of the S I
The S I allows the sizes of units to be made bigger
or smaller by the use of appropriate prefixes. For example, the electrical
unit of a watt is not a big unit even in terms of ordinary household use,
so it is generally used in terms of 1000 watts at a time. The prefix for
1000 is kilo so we use kilowatts[kW] as our unit of measurement.
For makers of electricity, or bigger users such as industry, it is common
to use megawatts[MW] or even gigawatts[GW]. The full range of prefixes
with their [symbols or abbreviations] and their multiplying factors which
are also given in other forms is
yotta [Y] 1 000 000 000 000 000 000 000 000 = 10^24
zetta [Z] 1 000 000 000 000 000 000 000 = 10^21
exa [E] 1 000 000 000 000 000 000 = 10^18
peta [P] 1 000 000 000 000 000 = 10^15
tera [T] 1 000 000 000 000 = 10^12
giga [G] 1 000 000 000 (a thousand millions = a billion)
mega [M] 1 000 000 (a million)
kilo [k] 1 000 (a thousand)
hecto [h] 100
deca [da]10
1
deci [d] 0.1
centi [c] 0.01
milli [m] 0.001 (a thousandth)
micro [µ] 0.000 001 (a millionth)
nano [n] 0.000 000 001 (a thousand millionth)
pico [p] 0.000 000 000 001 = 10^-12
femto [f] 0.000 000 000 000 001 = 10^-15
atto [a] 0.000 000 000 000 000 001 = 10^-18
zepto [z] 0.000 000 000 000 000 000 001 = 10^-21
yocto [y] 0.000 000 000 000 000 000 000 001 = 10^-24
[µ] the symbol used for micro is the
Greek letter known as 'mu'
Nearly all of the S I prefixes are multiples
or sub-multiples of 1000. However, these are inconvenient for many purposes
and so hecto, deca, deci, and centi are also
used.
deca also appears as deka [da]
or [dk] in the USA and Contintental Europe. So much for standards!
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Conventions of Usage in the S I
There are various rules laid down for the use of
the SI and its units as well as some observations to be made that will
help in its correct use.
-
Any unit may take only ONE prefix. For example 'millimillimetre'
is incorrect and should be written as 'micrometre'.
-
Most prefixes which make a unit bigger are written
in capital letters (M G T etc.), but when they make a unit smaller then
lower case (m n p etc.) is used. Exceptions to this are the kilo [k] to
avoid any possible confusion with kelvin [K]; hecto [h]; and deca [da]
or [dk]
-
A unit which is named after a person is written all
in lower case (newton, volt, pascal etc.) when named in full, but starting
with a capital letter (N V Pa etc.) when abbreviated. An exception to this
rule is the litre which, if written as a lower case 'l' could be mistaken
for a '1' (one) and so a capital 'L' is allowed as an alternative. It is
intended that a single letter will be decided upon some time in the future
when it becomes clear which letter is being favoured most in use.
-
Units written in abbreviated form are NEVER pluralised.
So 'm' could always be either 'metre' or 'metres'. 'ms' could represent
'metre second' (whatever that is) or, more correctly, 'millisecond'.
-
An abbreviation (such as J N g Pa etc.) is NEVER
followed by a full-stop unless it is the end of a sentence.
-
To make numbers easier to read they may be divided
into groups of 3 separated by spaces (or half-spaces) but NOT commas.
-
The SI preferred way of showing a decimal fraction
is to use a comma (123,456) to separate the whole number from its fractional
part. The practice of using a point, as is common in English-speaking countries,
is acceptable providing only that the point is placed ON the line of the
bottom edge of the numbers (123.456).
-
It will be noted that many units are eponymous, that
is they are named after persons. This is always someone who was prominent
in the early work done within the field in which the unit is used.
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A Brief History of Measurement
One of the earliest types of measurement concerned
that of length. These measurements were usually based on parts of the body.
A well documented example (the first) is the Egyptian cubit which was derived
from the length of the arm from the elbow to the outstretched finger tips.
By 2500 BC this had been standardised in a royal master cubit made of black
marble (about 52 cm). This cubit was divided into 28 digits (roughly a
finger width) which could be further divided into fractional parts, the
smallest of these being only just over a millimetre.
In England units of measurement were not properly
standardised until the 13th century, though variations (and abuses) continued
until long after that. For example, there were three different gallons
(ale, wine and corn) up until 1824 when the gallon was standardised.
In the U S A the system of weights and measured
first adopted was that of the English, though a few differences came in
when decisions were made at the time of standardisation in 1836. For instance,
the wine-gallon of 231 cubic inches was used instead of the English one
(as defined in 1824) of about 277 cubic inches. The U S A also took as
their standard of dry measure the old Winchester bushel of 2150.42 cubic
inches, which gave a dry gallon of nearly 269 cubic inches.
Even as late as the middle of the 20th century
there were some differences in UK and US measures which were nominally
the same. The UK inch measured 2.53998 cm while the US inch was 2.540005
cm. Both were standardised at 2.54 cm in July 1959, though the U S continued
to use 'their' value for several years in land surveying work - this too
is slowly being metricated.
In France the metric system officially started
in June 1799 with the declared intent of being 'For all people, for all
time'. The unit of length was the metre which was defined as being one
ten-millionth part of a quarter of the earth's circumference. The production
of this standard required a very careful survey to be done which took several
years. However, as more accurate instruments became available so the 'exactness'
of the standard was called into question. Later efforts were directed at
finding some absolute standard based on an observable physical phenomenon.
Over two centuries this developed into the S I. So maybe their original
slogan was more correct than anyone could have foreseen then.
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Metric System of Measurements
Length Area
10 millimetres = 1 centimetre 100 sq. mm = 1 sq. cm
10 centimetres = 1 decimeter 10 000 sq. cm = 1 sq. metre
10 decimetres = 1 metre 100 sq. metres = 1 are
10 metres = 1 decametre 100 ares = 1 hectare
10 decametres = 1 hectometre 10 000 sq. metres = 1 hectare
10 hectometres = 1 kilometre 100 hectares = 1 sq. kilometre
1000 metres = 1 kilometre 1 000 000 sq. metres = 1 sq. kilometre
Volume Capacity
1000 cu. mm = 1 cu. cm 10 millilitres = 1 centilitre
1000 cu. cm = 1 cu. decimetre 10 centilitree = 1 decilitre
1000 cu. dm = 1 cu. metre 10 decilitres = 1 litre
1 million cu. cm = 1 cu. metre 1000 litres = 1 cu. metre
Mass
1000 grams = 1 kilogram
1000 kilograms = 1 tonne
The distinction between 'Volume' and 'Capacity' is
artificial and kept here only for historic reasons.
A millitre is a cubic centimetre
and a cubic decimetre is a litre. But see under 'Volume'
for problems with the litre.
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document
The U K (Imperial) System of Measurements
Length Area
12 inches = 1 foot 144 sq. inches = 1 square foot
3 feet = 1 yard 9 sq. feet = 1 square yard
22 yards = 1 chain 4840 sq. yards = 1 acre
10 chains = 1 furlong 640 acres = 1 square mile
8 furlongs = 1 mile
5280 feet = 1 mile
1760 yards = 1 mile Capacity
20 fluid ounces = 1 pint
Volume 4 gills = 1 pint
1728 cu. inches = 1 cubic foot 2 pints = 1 quart
27 cu. feet = 1 cubic yard 4 quarts = 1 gallon (8 pints)
Mass (Avoirdupois)
437.5 grains = 1 ounce Troy Weights
16 ounces = 1 pound (7000 grains) 24 grains = 1 pennyweight
14 pounds = 1 stone 20 pennyweights = 1 ounce (480 grains)
8 stones = 1 hundredweight [cwt] 12 ounces = 1 pound (5760 grains)
20 cwt = 1 ton (2240 pounds)
Apothecaries' Measures Apothecaries' Weights
20 minims = 1 fl.scruple 20 grains = 1 scruple
3 fl.scruples = 1 fl.drachm 3 scruples = 1 drachm
8 fl.drachms = 1 fl.ounce 8 drachms = 1 ounce (480 grains)
20 fl.ounces = 1 pint 12 ounces = 1 pound (5760 grains)
The old Imperial (now UK) system was originally defined
by three standard measures - the yard, the pound and the gallon which were
held in London. They are now defined by reference to the S I measures of
the metre, the kilogram and the litre. These equivalent measures are exact.
1 yard = 0.9144 metres - same as US
1 pound = 0.453 592 37 kilograms - same as US
1 gallon = 4.546 09 litres
Note particularly that the UK gallon is a different
size to the US gallon so that NO liquid measures of the same name are the
same size in the UK and US systems.
Also that the ton(UK) is 2240 pounds while a
ton(US) is 2000 pounds. These are also referred to as a long ton and short
ton respectively.
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Metrication in the U K
There have been three major Weights and Measures
Acts in recent times (1963, 1976 and 1985) all gradually abolishing various
units, as well re-defining the standards. All the Apothecaries' measures
are gone, and of the Troy measures, only the ounce remains. Currently legislation
has decreed that -
From the 1st October 1995, for economic, public
health, public safety and administrative purposes, only metric units are
allowed EXCEPT that -
-
pounds and ounces for weighing of goods sold from
bulk
-
pints and fluid ounces for beer, cider, waters, lemonades
and fruit juices in RETURNABLE containers
-
therms for gas supply
-
fathoms for marine navigation
may be used until 31st December 1999.
The following may continue to be used WITHOUT
time limit -
-
miles, yards, feet and inches for road traffic signs
and related measurements of speed and distance
-
pints for dispensing draught beer and cider, and
for milk in RETURNABLE containers
-
acres for land registration purposes
-
troy ounces for transactions in precious metals.
Sports are exempt from all of this, but most of them
have (voluntarily) changed their relevant regulations into statements of
equivalent metric measures.
That is how the legislation is framed. In common
usage the 'old' units are still very apparent.
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The U S System of Measurements
Most of the US system of measurements is the same
as that for the UK. The biggest differences to be noted are in Capacity
which has both liquid and dry measures as well as being based on a different
standard - the US liquid gallon is smaller than the UK gallon. There is
also a measurement known at the US survey foot. It is gradually being phased
out as the maps and land plans are re-drawn under metrication. (The changeover
is being made by putting 39.37 US survey feet = 12 metres)
Length Area
12 inches = 1 foot 144 sq. inches = 1 square foot
3 feet = 1 yard 9 sq. feet = 1 square yard
220 yards = 1 furlong 4840 sq. yards = 1 acre
8 furlongs = 1 mile 640 acres = 1 square mile
5280 feet = 1 mile 1 sq.mile = 1 section
1760 yards = 1 mile 36 sections = 1 township
Volume
1728 cu. inches = 1 cubic foot
27 cu. feet = 1 cubic yard
Capacity (Dry) Capacity (Liquid)
16 fluid ounces = 1 pint
2 pints = 1 quart 4 gills = 1 pint
8 quarts = 1 peck 2 pints = 1 quart
4 pecks = 1 bushel 4 quarts = 1 gallon (8 pints)
Mass
437.5 grains = 1 ounce Troy Weights
16 ounces = 1 pound (7000 grains) 24 grains = 1 pennyweight
14 pounds = 1 stone 20 pennyweights = 1 ounce (480 grains)
100 pounds = 1 hundredweight [cwt] 12 ounces = 1 pound (5760 grains)
20 cwt = 1 ton (2000 pounds)
Apothecaries' Measures Apothecaries' Weights
60 minims = 1 fl.dram 20 grains = 1 scruple
8 fl.drams = 1 fl.ounce 3 scruples = 1 dram
16 fl.ounces = 1 pint 8 drams = 1 ounce (480 grains)
12 ounces = 1 pound (5760 grains)
As with the UK system these measures were originally
defined by physical standard measures - the yard, the pound, the gallon
and the bushel.They are now all defined by reference to the S I measures
of the metre, the kilogram and the litre. These equivalent measures are
exact.
1 yard = 0.9144 metres - same as UK
1 pound = 0.453 592 37 kilograms - same as UK
1 gallon (liquid) = 3.785 411 784 litres
1 bushel = 35.239 070 166 88 litres
Note particularly that the US gallon is a different
size to the UK gallon so that NO liquid measures of the same name are the
same size in the US and UK systems.
Also that the ton(US) is 2000 pounds while a
ton(UK) is 2240 pounds. These are also referred to as a short ton and long
ton respectively.
Note than in matters concerned with land measurements,
for the most accurate work, it is necessary to establish whether the US
survey measures are being used or not.
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Categories of Units
-
length
-
area
-
volume or capacity
-
mass
-
density, area
-
density, line
-
density, volume
-
energy
-
force
-
fuel consumption
-
line density
-
mass per unit length
-
mass per unit area
-
mass per unit volume
-
power
-
pressure
-
speed
-
spread rate (by mass)
-
spread rate (by volume)
-
stress
-
torque
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List of Units
The units are listed in alphabetical order but scanning
can be speeded up by selecting the initial letter of the unit from these
individual letters or groups
A - B - C
- D - E - F - G
- H - IJ - K - L
- M
N - O - PQ
- R - S - T - UVW
- XYZ
A
acres
angstroms
ares
astronomical units
atmospheres
B
barleycorns
barrels (oil)
bars
British thermal units
Btu/hour etc.
bushels
C
calories
calories per hour etc.
carats, metric
centigrade heat units
centilitres
centimetres
centimetres of mercury or water
centimetres per minute etc.
chains (surveyors')
circular inches
cubic (+ any units)
cubic measures per area
cubits
D
decilitres
denier
drex
dynes
E
ells (UK)
ems (pica)
ergs (energy)
ergs (torque)
F
fathoms
feet
feet of water
feet per hour etc.
fluid ounces
foot pounds-force
foot pounds-force per minute etc.
foot poundals
furlongs
G
gallons
gallons per area
gigajoules
gigawatts
grains
grains per gallon
grams
gram-force centimetres
grams per area
grams per cm
grams per (any volume)
H
hands
hectares
hides
horsepower
horsepower hours
hundredweights
IJ
inches
inches of mercury or water
inches of rain (by mass)
inches of rain (by volume)
inches per minute etc.
joules
joules per hour etc.
K
kilocalories
kilocalories per hour etc.
kilograms-force
kilogram-force metres (energy)
kilogram-force metres (torque)
kilogram-force metres per hour etc.
kilogram-force per area
kilograms
kilograms per area
kilograms per metre
kilograms per volume
kilojoules
kilojoules per hour etc.
kilometres
kilometres per hour etc.
kilometres per litre
kilonewton per square metre
kilonewtons
kilopascals
kilowatts
kilowatt hours
kips (weight)
kips (force)
kips per square inch
knots
L
leagues
light years
links (surveyors')
litres
litres per area
M
Mach number
megajoules
meganewtons
meganewtons per square metre
megawatts
metres
metres of water
metres per second etc.
microns (=micrometres)
miles
miles per gallon
miles per hour etc.
millibars
milligrams per cm
milligrams per (any volume)
millilitres
millimetres of mercury or water
millimetres of rain (by mass)
millimetres of rain (by volume)
N
newton metres (energy)
newton metres (torque)
newtons (per area)
newtons (force)
newtons (weight)
O
ounces
ounces per inch
ounces per area
ounces per volume
PQ
parsecs
pascals
perch (=rods or poles)
picas
pints
points (printers')
poundals
poundals per square foot
pounds
pounds per area
pounds per foot
pounds per volume
pounds-force
pound-force inches
pounds-force per area
quarts
R
roods
S
slugs (or g-pounds)
stones
square (+ any units)
squares (of timber)
sthenes
T
tex
therms
tonnes
ton-force metres
tonnes-force
tonnes-force per area
tonnes per hectare
tonnes per km
tonnes per volume
ton-force feet
tons
tons-force
tons-force per area
tons per acre
tons per mile
tons per volume
townships
troy ounce
UVW
watt second
watt hours
watts
XYZ
yards
yards per hour etc.
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document
Length
The S I unit of length is the metre. To change
any of these other units of length into their equivalent values in metres
use the operation and conversion factor given. Those marked with # are
exact. Other values are given to an appropriate degree of accuracy.
Where some uncertainty is indicated it means that a good idea of the
size of the unit can be given but that a better value would depend upon
knowing the period and/or culture in which the unit was being used.
angstroms divide by 10 000 000 000 #
astronomical units x 149 598 550 000
barleycorns x 0.008 467
centimetres x 0.01 #
chains (surveyors') x 20.1168 #
cubits x (0.45 to 0.5)
ells (UK) x 0.875 (but many variations)
ems (pica) x 0.004 233 3
fathoms x 1.8288 #
feet (UK and US) x 0.3048 #
feet (US survey) x 0.304 800 609 6
furlongs x 201.168 #
hands x 0.106 #
inches x 0.0254 #
kilometres x 1000 #
leagues x (4000 to 5000)
light years x 9 460 500 000 000 000
links (surveyors') x 0.201 168 #
metres [m] 1
microns (=micrometres) x 0.000 001 #
miles (UK and US) x 1609.344 #
miles (nautical) x 1852 #
parsecs x 30 856 770 000 000 000
perch (=rods or poles) x 5.0292 #
picas (computer) x 0.004 233 333
picas (printers') x 0.004 217 518
points (computer) x 0.000 352 777 8
points (printers') x 0.000 351 459 8
yards x 0.9144 #
Note than in matters concerned with land measurements,
for the most accurate work, it is necessary to establish whether the US
survey measures are being used or not.
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Area
The S I unit of area is the square metre.
To change any of these other units of area into their equivalent values
in square metres use the operation and conversion factor given. Those
marked with # are exact. Other values are given to an appropriate
degree of accuracy. Where some uncertainty is indicated it means that
a good idea of the size of the unit can be given but that a better value
would depend upon knowing the period and/or culture in which the unit was
being used.
acres x 4046.856 422 4 #
ares x 100 #
circular inches x 0.000 506 707 479
hectares x 10 000 #
hides x 485 000 (with wide variations)
roods x 1011.714 105 6 #
square centimetres x 0.000 1 #
square feet (UK and US) x 0.092 903 04 #
square feet (US survey) x 0.092 903 411 613
square inches x 0.000 645 16 #
square kilometres x 1 000 000 #
square metres 1
square miles x 2 589 988.110 336 #
square millimetres x 0.000 001 #
squares (of timber) x 9.290 304 #
square rods (or poles) x 25.292 852 64 #
square yards x 0.836 127 36 #
townships x 93 239 571.972
Note than in matters concerned with land measurements,
for the most accurate work, it is necessary to establish whether the US
survey measures are being used or not.
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Volume or Capacity
The S I unit of volume is the cubic metre. However,
this seems to be much less used than the litre (1000 litres = 1
cubic metre).To change any of these other units of volume into their equivalent
values in litres use the operation and conversion factor given. Those
marked with # are exact. Other values are given to an appropriate
degree of accuracy.
The litre. There can be some ambiguity
about the size of the litre. In 1901 it was defined by reference to a kilogram
of pure water under certain particular conditions. (This was similar to
the way the old UK gallon was set.) In 1964 it was re-defined as a common
usage term for a cubic decimetre. They differ very slightly and for really
accurate work, to avoid any possible confusion, it is recommended that
the litre is not used . It is used here as being a cubic decimetre.
barrels (oil) x 158.987 294 928 #
bushels (UK) x 36.368 72 #
bushels (US) x 35.239 070 166 88 #
centilitres x 0.01 #
cubic centimetres x 0.001 #
cubic decimetres 1
cubic decametres x 1 000 000 #
cubic feet x 28.316 846 592 #
cubic inches x 0.016 387 064 #
cubic metres x 1000 #
cubic millimetres x 0.000 001 #
cubic yards x 764.554 857 984 #
decilitres x 0.1 #
fluid ounces (UK) x 0.028 413 062 5 #
fluid ounces (US) x 0.029 573 529 562 5 #
gallons (UK) x 4.546 09 #
gallons, dry (US) x 4.404 883 770 86 #
gallons, liquid (US) x 3.785 411 784 #
litres [l or L] 1
litres (1901 - 1964) x 1.000 028
millitres x 0.001 #
pints (UK) x 0.568 261 25 #
pints, dry (US) x 0.550 610 471 357 5 #
pints, liquid (US) x 0.473 176 473 #
quarts (UK) x 1.136 522 5 #
quarts, dry (US) x 1.101 220 942 715 #
quarts, liquid (US) x 0.946 352 946 #
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Mass (or Weight)
The S I unit of mass is the kilogram. To change
any of these other units of mass into their equivalent values in kilograms
use the operation and conversion factor given. Those marked with # are
exact. Other values are given to an appropriate degree of accuracy.
carats, metric x 0.000 2 #
grains x 0.000 064 798 91 #
grams x 0.001 #
hundredweights, long x 50.802 345 44 #
hundredweights, short x 45.359 237 #
kilograms [kg] 1
ounces, avoirdupois x 0.028 349 523 125 #
ounces, troy x 0.031 103 476 8 #
pounds x 0.453 592 37 #
slugs (or g-pounds) x 14.593 903
stones x 6.350 293 18 #
tons (UK or long) x 1016.046 908 8 #
tons (US or short) x 907.184 74 #
tonnes x 1000 #
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Line density
Line density is a measure of mass per unit length.
The S I compatible unit of line density is kilograms/metre. A major
use of line density is in the textile industry to indicate the coarseness
of a yarn or fibre. For that purpose the SI unit is rather large so the
preferred unit there is the tex. (1 tex = 1 gram/kilometre) To change
any of these other units of line density into their equivalent values
in kilograms/metre use the operation and conversion factor given. Those
marked with # are exact. Other values are given to an appropriate
degree of accuracy.
denier divide by 9 000 000 #
drex divide by 10 000 000 #
grams/centimetre divide by 10 #
grams/kilometre (tex) divide by 1 000 000 #
grams/metre divide by 1000 #
grams/millimetre 1
kilograms/kilometre divide by 1000 #
kilograms/metre 1
milligrams/centimetre divide by 10 000 #
milligrams/millimetre divide by 1000 #
ounces/inch x 1.116 125
ounces/foot x 0.093 01
pounds/inch x 17.858
pounds/foot x 1.488 164
pounds/yard x 0.496 055
pounds/mile x 0.000 281 849
tex divide by 1 000 000 #
tons(UK)/mile x 0.631 342
tons(US)/mile x 0.563 698
tonnes/kilometre 1
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Density
Density is the shortened term generally used in place
of the more accurate description volumetric density.It is a measure
of mass per unit volume. The S I compatible unit of density is kilograms/cubic
metre. However, this a rather large unit for most purposes (iron is
over 7000, wood is about 600 and even cork is over 200). A much more useful
size of unit is kilograms/litre (for which the previous values then
become 7, 0.6 and 0.2 respectively). This unit also has the great advantage
of being numerically unchanged for grams/cubic centimetre and tonnes/cubic
metre (or megagrams/cubic metre). To change any of these other units of
density into their equivalent values in kilograms/litre use the
operation and conversion factor given. Those marked with # are exact.
Other values are given to an appropriate degree of accuracy.
grains/gallon(UK) divide by 70 156
grains/gallon(US) divide by 58 418
grams/cubic centimetre 1
grams/litre divide by 1000 #
grams/millilitre 1
kilograms/cubic metre divide by 1000 #
megagrams/cubic metre 1
milligrams/millitre divide by 1000 #
milligrams/litre divide by 1 000 000 #
kilograms/litre 1
ounces/cubic inch x 1.729 994 044
ounces/gallon(UK) x 0.006 236 023
ounces/gallon(US) x 0.007 489 152
pounds/cubic inch x 27.679 904
pounds/cubic foot x 0.016 018 463
pounds/gallon(UK) x 0.099 776 373
pounds/gallon(US) x 0.119 826 427
tonnes/cubic metre 1
tons(UK)/cubic yard x 1.328 939 184
tons(US)/cubic yard x 1.186 552 843
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Energy or work
There is a lot of room for confusion in some of the
units used here. The calorie can take 5 different values and, while
these do not vary by very much, for accurate work it is necessary to specify
which calorie is being used.
The 5 calories are known as the International
Table calorie - cal(IT); the thermochemical calorie - cal(th); the mean
calorie - cal(mean); the 15 degree C calorie - cal(15C); and the 20 degree
C calorie - cal(20C).
As a further complication, in working with food
and expressing nutritional values, the unit of a Calorie (capital C)
is often used to represent 1000 calories, and again it is necessary to
specify which calorie is being used for that.
The British thermal unit (Btu) can also
take different values and they are named in a similar way to the calorie,
that is Btu (IT), (th), etc. Also note that the therm
is 100 000 Btu so its exact size depends on which Btu is being
used.
The S I unit of energy or work is the joule.
To change any of these other units of energy or work into their equivalent
values in joules use the operation and conversion factor given. Those
marked with # are exact. Other values are given to an appropriate
degree of accuracy.
British thermal units(IT)x 1055.056
Btu (th) x 1054.350
Btu (mean) x 1055.87
calories - cal (IT) x 4.1868 #
- cal (th) x 4.184 #
- cal (mean) x 4.190 02
- cal (15C) x 4.185 80
- cal (20C) x 4.181 90
Calorie (food) x 4186 (approx.)
centigrade heat units x 1900.4
ergs divide by 10 000 000 #
foot pounds-force x 1.355 817
foot poundals x 0.042 140
gigajoules [GJ] x 1000 000 000 #
horsepower hours x 2 684 520 (approx.)
joules [J] 1
kilocalories (IT) x 4186.8 #
kilocalories (th) x 4184 #
kilogram-force metres x 9.806 65 #
kilojoules [kJ] x 1000 #
kilowatt hours [kWh] x 3 600 000 #
megajoules [MJ] x 1 000 000 #
newton metres [Nm] x 1 #
therms x 105 500 000 (approx.)
watt seconds [Ws] 1
watt hours [Wh] x 3600 #
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Force
The S I unit of force is the newton. To change
any of these other units of force into their equivalent values in newtons
use the operation and conversion factor given. Those marked with # are
exact. Other values are given to an appropriate degree of accuracy.
dynes divide by 100 000 #
kilograms force x 9.806 65 #
kilonewtons [kN] x 1000 #
kips x 4448.222
meganewtons [MN] x 1 000 000 #
newtons [N] 1
pounds force x 4.448 222
poundals x 0.138 255
sthenes (=kN) x 1000
tonnes force x 9806.65 #
tons(UK) force x 9964.016
tons(US) force x 8896.443
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Fuel Consumption
Fuel consumption of any means of transport (car,
aeroplane, ship etc.) that uses fuel is a measure giving the relationship
between the distance travelled for an amount of fuel used. The most common
example is the car where it is usually expressed (in English-speaking countries)
in miles per gallon.
It could also be expressed in gallons per mile.
However, for a car the latter method gives a rather small figure: 35 miles
per gallon is about 0.0286 gallons per mile. In that case it would be better
to give a figure for 100 miles, so it would be 2.86 gallons per 100 miles.
That is the metric way of expressing fuel consumption - as litres per
100 kilometres.
From regular enquiries it appears that in real
life people are using all sorts of ways of expressing their fuel consumption,
so this section (unlike all the others) tries to cover as many ways as
possible. All the values are given to an accuracy of 4 significant figures.
To change into
miles per gallon (UK) miles per gallon (US) multiply by 0.833
miles per gallon (UK) miles per litre multiply by 0.22
miles per litre miles per gallon (UK) multiply by 4.546
miles per gallon (UK) kilometres per litre multiply by 0.354
miles per gallon (US) miles per gallon (UK) multiply by 1.2
miles per gallon (US) miles per litre multiply by 0.2642
miles per litre miles per gallon (US) multiply by 3.785
miles per gallon (US) kilometres per litre multiply by 0.4251
X miles per gallon gallons per 100 miles: divide 100 by X
(both gallons must of the same type)
X miles per gallon (UK) litres per 100 km: divide 282.5 by X
X miles per gallon (US) litres per 100 km: divide 235.2 by X
X km per litre litres per 100 km: divide 100 by X
X miles per litre litres per 100 km: divide 62.14 by X
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Power
Since power is a measure of the rate at which work
is done, the underlying units are those of work or energy,
and that section should be looked at for explanations concerning the calorie
and Btu. In this section the (IT) values have been used.
In this section it is the horsepower which
provides confusion. Just like the calorie, it can take 5 different values,
and these are identified as necessary by the addition of (boiler), (electric),
(metric), (UK) and (water). Unlike the calorie (whose 5 values are reasonably
close to each other), the horsepower has 4 which are close and 1 (boiler)
which is considerably different - it is about 13 times bigger than the
others - but it seems to be very little used.
The S I unit of power is the watt. To change
any of these other units of energy or work into their equivalent values
in watts use the operation and conversion factor given. Those marked
with # are exact. Other values are given to an appropriate degree
of accuracy.
Btu/hour x 0.293 071
Btu/minute x 17.584 267
Btu/second x 1055.056
calories/hour x 0.001 639
calories/minute x 0.069 78
calories/second x 4.1868 #
ft lb-force/minute x 0.022 597
ft lb-force/second x 1.355 82
gigawatts [GW] x 1 000 000 000
horsepower (electric) x 746 #
horsepower (metric) x 735.499
watts [W] 1
joules/hour divide by 3600 #
joules/minute divide by 60 #
joules/second 1
kilocalories/hour x 1.163
kilocalories/minute x 69.78
kg-force metres/hour x 0.002 724
kg-force metres/minute x 0.163 444
kilowatts [kW] x 1000 #
megawatts [MW] x 1 000 000 #
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Pressure or Stress
The S I unit of pressure is the pascal. The
units of pressure are defined in the same way as those for stress - force/unit
area. To change any of these other units of pressure (or stress) into their
equivalent values in pascals use the operation and conversion factor
given. Those marked with # are exact. Other values are given to
an appropriate degree of accuracy. Measures based on water assume a density
of 1 kg/litre - a value which rarely matched in the real world, though
the error is small.
atmospheres x 101 325 #
bars x 100 000 #
centimetres of mercury x 1333.22
centimetres of water x 98.066 5 #
feet of water x 2989.066 92 #
hectopascals [hPa] x 100 #
inches of water x 249.088 91 #
inches of mercury x 3386.388
kg-force/sq.centimetre x 98 066.5 #
kg-force/sq.metre x 9.806 65 #
kilonewton/sq.metre x 1000 #
kilopascal [kPa] x 1000 #
kips/sq.inch x 6 894 760
meganewtons/sq.metre x 1 000 000 #
metres of water x 9806.65 #
millibars x 100 #
pascals [Pa] 1
millimetres of mercury x 133.322
millimetres of water x 9.806 65 #
newtons/sq.centimetre x 10 000
newtons/sq.metre 1
newtons/sq.millimetre x 1 000 000 #
pounds-force/sq.foot x 47.880
pounds-force/sq.inch x 6894.757
poundals/sq.foot x 1.448 16
tons(UK)-force/sq.foot x 107 251
tons(UK)-force/sq.inch x 15 444 256
tons(US)-force/sq.foot x 95 760
tons(US)-force/sq.inch x 13 789 500
tonnes-force/sq.cm x 98 066 500 #
tonnes-force/sq.metre x 9806.65 #
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Speed
The S I compatible unit of speed is metres/second.
To change any of these other units of speed into their equivalent values
in metres/second use the operation and conversion factor given. Those
marked with # are exact. Other values are given to an appropriate
degree of accuracy.
centimetres/minute divide by 6000 #
centimetres/second divide by 100 #
feet/hour divide by 11 811
feet/minute x 0.005 08 #
feet/second x 0.3048 #
inches/minute divide by 2362.2
inches/second x 0.0254 #
kilometres/hour divide by 3.6 #
kilometres/second x 1000 #
knots x 0.514 444
Mach number x 331.5
metres/hour divide by 3600 #
metres/minute divide by 60 #
metres/second [m/s] 1
miles/hour x 0.447 04 #
miles/minute x 26.8224 #
miles/second x 1609.344 #
yards/hour divide by 3937
yards/minute x 0.015 24 #
yards/second x 0.9144 #
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Spread Rate (by mass)
The spread rate of a substance is a measure of how
much of it there is covering a unit area. The 'how much' can be measured
by volume or by mass. The S I compatible unit of spread rate by mass is
kilograms/square metre. It is also a measure of area density (mass/unit
area) and is similar to - but not the same as - pressure, which is force/unit
area. For the rainfall conversions a density of 1 kg/litre has been assumed.
To change any of these other units of spread rate into their equivalent
values in kilograms/square metre use the operation and conversion factor
given. Those marked with # are exact. Other values are given to
an appropriate degree of accuracy. The conversion for rainfall assumes
a density of 1 kg/litre which is accurate enough for all practical purposes.
grams/sq.centimetre x 10 #
grams/sq.metre divide by 1000 #
inches of rainfall x 2.54
kilograms/hectare divide by 10 000 #
kilograms/sq.centimetre x 10 000 #
milligrams/sq.metre divide by 1000 #
millimetres of rainfall 1
kilograms/sq.metre 1
ounces/sq.foot x 0.305 152
ounces/sq.inch x 43.942
ounces/sq.yard divide by 49.494
pounds/acre divide by 8921.791
pounds/sq.foot x 4.882 428
pounds/sq.inch x 703.07
pounds/sq.yard x 0.542 492
tonnes/hectare divide by 10 #
tons(UK)/acre divide by 3.982 942
tons(US)/acre divide by 4.460 896
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Spread Rate (by volume)
The spread rate of a substance is a measure of how
much of it there is covering a unit area. The 'how much' can be measured
by volume or by mass. The S I compatible unit of spread rate by volume
is cubic metres/square metre. However, this is a rather large unit
for most purposes and so litres/square metre is often preferred. To change
any of these other units of spread rate into their equivalent values
in litres/square metre use the operation and conversion factor given.
Those marked with # are exact. Other values are given to an appropriate
degree of accuracy.
cubic feet/acre divide by 142.913
cubic inches/sq.yard divide by 51.024
cubic yards/sq.mile divide by 3387.577
cubic metres/hectare divide by 10 #
cubic metres/sq.km divide by 1000 #
cubic metres/sq.metre x 1000 #
fl. ounces(UK)/sq.yard divide by 29.428
litres/square metre 1
gallons(UK)/acre divide by 890.184
gallons(US)/acre divide by 1069.066
gallons(UK)/hectare divide by 2199.692
gallons(US)/hectare divide by 2641.721
inches of rainfall x 25.4 #
litres/hectare divide by 10 000 #
millitres/sq.metre divide by 1000 #
millimetres of rainfall 1
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Torque
The S I compatible unit of torque is the newton
metre. To change any of these other units of torque into their equivalent
values in newton metres use the operation and conversion factor given.
Those marked with # are exact. Other values are given to an appropriate
degree of accuracy.
dyne centimetres divide by 10 000 000 #
gram-force centimetres x 0.000 098 066 5 #
kg-force centimetres x 0.098 066 5 #
kg-force metres x 9.806 65 #
newton centimetres divide by 100 #
newton metres [Nm] 1
ounce-force inches divide by 141.612
pound-force inches x 0.112 984
pound-force feet x 1.355 818
poundal feet x 0.042 140
ton(UK)-force feet x 3 037.032
ton(US)-force feet x 2 711.636
tonne-force metres x 9 806.65 #
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Other Sources in Books
Conversion Tables of Units for Science and Engineering
by Ari L Horvath
Macmillan Reference Books, London, 1986 (147 pages)
ISBN 0 333 40857 8
Probably the most comprehensive set of conversion factors in print,
covering both old and modern units. There are 77 tables covering categories
from Length to Radiation dosage. The Length table alone lists 107 units
together with the conversion factors needed to change each one into metres.
The Dent Dictionary of Measurement
by Darton and Clark
J M Dent, London, 1994 (538 pages)
ISBN 0 460 861379
Very comprehensive coverage of all kinds of units (including currencies),
ordered in conventional dictionary form, and giving several conversion
factors.
The Economist Desk Companion
Random Century, London, 1992 (272 pages)
ISBN 0 7126 9816 7
A handy compendium of units used in Science, Medicine, Engineering,
Industry, Commerce, Finance and many other places, together with all the
necessary conversion factors. There is also much other incidental (but
related) information.
The Encyclopaedia Britannica
The modern E B has many references to units, but extensive use needs
to be made of the index to find them all. It gives a wide selection of
weights and measures from countries around the world and the appropriate
conversion factors.
World Weights and Measures
Statistical Office of the United Nations, New York 1955 (225 pages)
A very comprehensive survey of each country in the world (as it was
then) from Aden to Zanzibar, giving the units used in each for Length,
Area and Capacity with their British and Metric equivalents. There is an
appendix on the measures used for selected commodities. Currencies are
also given. The indexes are very thorough. |
|
The Weights and Measures of England
by R D Connor
H M S O, London, 1987 (422 pages)
ISBN 0 460 86137 9
A scholarly and detailed account of the history of the development
of the British (Imperial) system of weights and measures from the earliest
times.
British Weights and Measures
by R E Zupko
A history from Antiquity to the Seventeenth Century
The University of Wisconsin Press, 1977 [248 pages]
ISBN 0 299 07340 8
The actual history occupies only 100 pages. There is then an extensive
list of the various units used in commerce, tables of many pre-Imperial
units, a long list of pre-metric measures used in Europe together with
their British and metric equivalents, and nearly 40 pages giving other
sources.
The World of Measurements
by H Arthur Klein
Allen and Unwin, London, 1975 (736 pages)
ISBN 0 04 500024 7
A very readable and comprehensive account of the history of units used
in measuring, from the earliest known beginnings and around the world.
Scientific Unit Conversion
by Francois Cardarelli
Springer-Verlag, London, 1997 (456 pages)
ISBN 3-540-76022-9
It claims "This practical manual aims to be the most comprehensive
work on the subject of unit conversion. It contains more than 10 000 precise
conversion factors."
It is certainly a very chunky and compact (= handy-sized) book. Comprehensive
it certainly is but still not complete. However, with its very wide coverage,
both historical and modern, it should certainly satisfy nearly all users. |
Other Sources on the World Wide Web
There are now several sites concerned with this topic.
In the UK
the two organisations concerned with standards are the
British Standards
Institute (BSI) and the National
Physical Laboratory (NPL).
Sadly, the first offers nothing more than advertisements
for its various books of standards and the second, while giving some information
about constants, has nothing on units of measure.
However, they are changing, and it is certainly
worth looking to see if they are yet providing some useful information.
Fortunately the Yahoo!
site (based in the UK) does provide a gateway to many sources of
information.
In the USA
the
National
Institute of Standards and Technology (NIST)
is much more forthcoming, and there is no shortage
of information concerning units and their conversion. There is even an
excellent 86-page book on the subject (SP 811) which can be read on-line
or downloaded and printed out - but note that Adobe Acrobat Reader
is needed.
The US
Metric Association is also a good starting point which provides
a wealth of links to other suitable sites.
The International
Standards Organisation] [I S O] based in Switzerland, is responsible
for the world-wide publication of standards for just about anything for
which standards can be set. Whilst none of the actual data is online, details
of the work of ISO and the publications they produce are. They also give
many references to other organisations concerned with standards.
Another account of metrication and associated
items which has, in addition, some very good pages on historic measures
(Anglo-Saxon, Biblical etc.) is provided by Jack
Proot (in Canada)
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