Definitions of the Seven Basic S I Units

 
Shafqat's Electronics Glossary

Glossary: A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

 

 
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Definitions of the Seven Basic S I Units
meter [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.
Derived Units of the S I
From the 7 basic units of the SI other units are derived for a variety of purposes. Only a few of are explained here as examples, there are many more.
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 kilohertz [kHz] and megahertz [MHz]. It is named after the German physicist Heinrich Rudolph Hertz (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 [Ω ]
The ohm is the SI unit of resistance of an electrical conductor. Its symbol, is the capital Greek letter '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).

 

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                              (a hundred)
deca  [da]10                               (ten)
  1
deci  [d] 0.1                              (a tenth)
centi [c] 0.01                             (a hundredth)
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 (kilo to yotta) or sub-multiples (milli to yocto) 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!

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.

 

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.

 

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.
 

 

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 in US
1 pound = 0.453 592 37 kilograms - same in US
1 gallon = 4.546 09 litres - different in US

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.

 

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 now gone, and of the Troy measures, only the ounce remains. The legislation decreed that -

From the 1st October 1995, for economic, public health, public safety and administrative purposes, only metric units were to be 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

could be used until 31st December 1999.

The following could 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 were exempt from all of this, but most of them have (voluntarily) changed their relevant regulations into statements of equivalent metric measures.

That was how the legislation was framed. In common usage the 'old' units are still very apparent.

 

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.

 

Errors
Whilst every care has been taken in the compilation of this document, and many checks have been carried out, the possibility of an error is always present in a work like this and that must be borne in mind by all users. The author would be glad to be told of any errors detected.
Accuracy
In a general dictionary like this it is impossible to know just what accuracy is needed by any particular user. Where the given value is an exact one then it has been signalled. In most cases other values are accurate to at least the number of significant figures shown. In some cases it might be more than that as trailing zeros have not been included.
Presentation
The conversion factors have mainly been presented as multipliers, but exceptions to that have been made for two reasons. First, it is easier to convey the exact value 'divide by 60' rather than the approximation 'multiply by 0.0166667' and it is more likely to be keyed in without errors if a calculator is being used. Second, most calculators accept only 8 digits, which means that 'multiply by 0.000 084 666' will become '0.000 0846' (3 significant figures) whereas 'divide by 11 811' will give the result to 6 significant figures. The appearance of a '1' needs no operator but shows that the named unit is exactly equivalent to the standard unit.
Inverse usage
In nearly all cases the conversion factors have been given to change 'non-standard' units into standard units of the SI. For those cases where it is necessary to do a conversion the other way it is only a matter of reversing the operation. For example to convert feet into metres you multiply by 0.3048 so, to convert metres into feet you divide by 0.3048. Following on from this it can be seen how conversions can be made between non-standard units, changing first into the standard unit and then back into the required unit.
Author's Note
A guiding principle behind the writing and presentation of this document has been that of clarity for non-specialist readers. To that end I have been guilty of breaking "the rules" in a few places. I am sorry that these transgressions may offend some readers but I have done so in the belief that it will be a little bit easier for many, and also help the flow of a continuous narrative.
This dictionary is not meant to be encyclopaedic in its coverage, and there are many many more units which are not touched upon, but it is hoped that all 'ordinary' needs are covered. The many references to other sources, both in books and on-line should take care of anything beyond that.
Finally, I must thank all of those who wrote with suggestions (and corrections!) after reading the earlier editions.

 

 
 

Glossary: A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

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