A Dictionary of Units
by Frank Tapson
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 SI.
A more extensive (3-part) version of this dictionary will be found at
www.ex.ac.uk/trol/dictunit/
The Systeme International [S I]
Le Systeme international d'Unites officially came into being in October 1960 and has been officially recognised and 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 Abbrev. 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.
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. |
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). |
Note that prefixes may be used in conjunction with any of the above units.
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. |
| 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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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 |
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.
| 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 -
could be used until 31st December 1999. The following could continue to be used WITHOUT time limit -
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. |
| Some other dates of note Thus, all the measures had been metricated even if the public hadn't! |
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 |
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.
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.
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.
| 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 0.1016 # 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 # |
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. 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.
| 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 |
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. When the metric system was introduced in the 1790's the litre was intended to match up with the volume occupied by 1 kilogram of pure water at a specified pressure and temperature. As the ability to measure things got better (by 100 years later) they found that there was a mismatch between the kilogram and the litre. As a result of this they had to redefine the litre (in 1901) as being 1.000028 cubic decimetres. Very handy!
This nonsense was stopped in 1964 when it was ruled that the word "litre" may be employed as a special name for the cubic decimetre, with the additional recommendation that for really accurate work, to avoid any possible confusion, the litre should not be used.
Here the litre is taken 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 millilitres 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 # |
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 # |
There have been five main temperature scales, each one being named after the person who invented it.
G D FAHRENHEIT (1686-1736) a German physicist, in about 1714 proposed the first practical scale. He called the freezing-point of water 32 degrees (so as to avoid negative temperatures) and the boiling-point 212 degrees.
R A F de REAUMUR (1673-1757) A French entomologist, proposed a similar scale in 1730, but set the freezing-point at 0 degrees and the boiling-point at 80 degrees. This was used quite a bit but is now obsolete.
Anders CELSIUS (1701-1744) a Swedish astronomer, proposed the 100-degree scale (from 0 to 100) in 1742. This was widely adopted as the centigrade scale. But since grades and centigrades were also measures of angle, in 1947 it officially became the Celsius scale. Also, the S I system of units gives preference to naming units after people where possible.
William Thomson, 1st Lord KELVIN (1824-1907) a Scottish mathematician and physicist, worked with J P Joule - about 1862 - to produce an absolute scale of temperature based on laws of heat rather than the freezing/boiling-points of water. This work produced the idea of 'absolute zero', a temperature below which it was not possible to go. Its value is -273.15 degrees on the Celsius scale.
William J M RANKINE (1820-1872) a Scottish engineer and scientist, promoted the Kelvin scale in its Fahrenheit form, when the equivalent value of absolute zero is -459.67 degrees Fahrenheit.
Nowadays, while scientists use the KELVIN scale, the CELSIUS scale is the preferred scale in our everyday lives. However, the Fahrenheit scale is still widely used and there frequently is a need to be able to change from one to the other.
| To change temperature given in Fahrenheit (F) to Celsius (C) Start with (F); subtract 32; multiply by 5; divide by 9; the answer is (C) To change temperature given in Celsius (C) to Fahrenheit (F) Start with (C); multiply by 9; divide by 5; add on 32; the answer is (F) |
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 |
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 70 157 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/millilitre 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 27.679 905 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 |
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) |
Unless a clear statement is made saying otherwise, assume the IT calorie is being used.
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 1.355 818 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 # |
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 |
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 |
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 0.001 163 # 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 # |
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 is 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 107 252 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 # |
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 # |
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 |
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 # millilitres/sq.metre divide by 1000 # millimetres of rainfall 1 |
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 # |
| Conversion Tables of Units for Science and Engineering The Dent Dictionary of Measurement The Economist Desk Companion The Encyclopaedia Britannica World Weights and Measures | | The Weights and Measures of England British Weights and Measures The World of Measurements Scientific Unit Conversion |
Other Sources on the World Wide Web
There are now several sites concerned with this topic. (It is popular with those wishing to start up a site.) Almost all the Search Engines will find links to more sites than anyone could really need, and each of those will give more links . . . . .
The problem is simply: which one best suits the purpose?
| The first to be considered must the Official SI Web-site in France. In the UK a very good place to make a start is the Metrication Resource Site run by Chris Keenan. In the USA the National Institute of Standards and Technology (NIST) is excellent, 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. An excellent A to Z of units is available from this site run by Russ Rowlett at the University of North Carolina. 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) 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. |
| 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. |
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