Physical World/Weights and Measures
SI units
The Metre Convention of 1875 mandated the establishment of a permanent International Bureau of Weights and Measures to be located in Sevres, France
The 10th CGPM (General Conference on Weights and Measures) in 1954 decided that an international system should be derived from six base units to provide for the measurement of temperature and optical radiation in addition to mechanical and electromagnetic quantities. The six base units that were recommended are the metre, kilogram, second, ampere, degree Kelvin (later renamed kelvin), and candela. In 1960, the 11th CGPM named the system the International System of Units, abbreviated SI from the French name, Le Système international d'unités. The seventh base unit, the mole, was added in 1971 by the 14th CGPM. The SI was developed in 1960 from the old metre-kilogram-second system, rather than the centimetre-gram-second system
International Bureau of Weights and Measures (BIPM) is one of three international standards organization established to maintain the International System of Units (SI) under the terms of the Metre Convention
The other organizations that maintain the SI system are the General Conference on Weights and Measures (CGPM) and the International Committee for Weights and Measures (CIPM)
In 2019, four of the seven SI base units were redefined in terms of natural physical constants, rather than human artefacts such as the standard kilogram
The names of SI units are always written in lowercase. The unit symbols of units named after persons, however, are always spelled with an initial capital letter
A coherent system of units is a system of units used to measure physical quantities that are defined in such a way that the equations relating the numerical values expressed in the units of the system have exactly the same form, including numerical factors, as the corresponding equations directly relating the quantities
A coherent derived unit is a derived unit that, for a given system of quantities and for a chosen set of base units, is a product of powers of base units, with the proportionality factor being one
SI base units
| metre | length | m |
| kilogram | mass | kg |
| second | time | s |
| ampere | electric current | A |
| kelvin | thermodynamic temperature | K |
| candela | luminous intensity | cd |
| mole | amount of substance | mol |
Metre represents 1/10 millionth of the distance from the North Pole to the equator through Paris. Defined in 1793
Since 1983, a metre has been defined as ‘the length of the path travelled by light in vacuum during a time interval of 1/299,792,458 of a second’
Kilogram was defined as being equal to the mass of the International Prototype Kilogram (IPK), which is almost exactly equal to the mass of one litre of water
Following the 2019 redefinition of units, the kilogram is defined by setting the Planck constant h exactly to 6.62607015×10−34 J⋅s
Second is defined to be: ‘the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom’
Ampere is a measure of the amount of electric charge passing a point in an electric circuit per unit time with 6.241 × 1018 electrons, or one coulomb per second constituting one ampere
Kelvin was defined as the fraction 1⁄273.16 of the thermodynamic temperature of the triple point of water (exactly 0.01 °C)
Following the 2019 redefinition of units, the kelvin is defined by setting the fixed numerical value of the Boltzmann constant k to 1.380649×10−23 J⋅K−1
Absolute zero (0oK) is equivalent to −273.15 °C (−459.67 °F)
Candela is the SU unit of luminous intensity, in a given direction, of a source that emits monochromatic radiation
Following the 2019 redefinition of units, the candela is defined by taking the fixed numerical value of the luminous efficacy of monochromatic radiation of frequency 540 × 1012 Hz, Kcd, to be 683 when expressed in the unit lm W–1
A common candle emits light with a luminous intensity of roughly one candela
Mole is the amount of substance that contains as many elementary entities (e.g., atoms, molecules, ions, electrons) as there are atoms in 0.012 kg of the isotope carbon-12 (12C). Thus, by definition, one mole of pure 12C has a mass of exactly 12 grams
Following the 2019 redefinition of units, the mole is defined as the amount of substance of exactly 6.02214076×1023 elementary entities. This number is the fixed numerical value of the Avogadro constant, NA, when expressed in the unit mol−1
SI derived units
| radian | angle | rad | |
| steradian | solid angle | sr | |
| hertz | frequency | Hz | 1/s |
| newton | force | N | Kg.m/s2 |
| pascal | pressure | Pa | N/m2 |
| joule | energy | J | N.m |
| watt | power | W | J/s |
| coulomb | electric charge | C | A.s |
| volt | potential difference | V | W/A |
| farad | electrical capacitance | F | C/V |
| ohm | electrical resistance | Ω | V/A |
| siemens | electrical conductance | S | A/V |
| weber | magnetic flux | Wb | V.s |
| tesla | magnetic flux density | T | Wb/m2 |
| henry | inductance | H | Wb/A |
| degree Celsius | temperature | oC | K |
| lumen | luminous flux | lm | cd.sr |
| lux | illuminance | lx | lm/m2 |
| becquerel | radioactivity | Bq | 1/s |
| gray | absorbed dose | Gy | J/kg |
| sievert | equivalent dose | Sv | J/kg |
| katal | catalytic activity | kat | mol/s |
Radian and steradian are dimensionless units
Mho is an alternative name of the siemens, the reciprocal of one ohm
Henry is the only SI unit named after an American person
SI prefixes
| Factor | Name | Symbol | Factor | Name | Symbol |
| 101 | deca | da | 10-1 | deci | d |
| 102 | hecto | h | 10-2 | centi | c |
| 103 | kilo | k | 10-3 | milli | m |
| 106 | mega | M | 10-6 | micro | µ |
| 109 | giga | G | 10-9 | nano | n |
| 1012 | tera | T | 10-12 | pico | p |
| 1015 | peta | P | 10-15 | femto | f |
| 1018 | exa | E | 10-18 | atto | a |
| 1021 | zetta | Z | 10-21 | zepto | z |
| 1024 | yotta | Y | 10-24 | yocto | y |
| 1027 | ronna | R | 10-27 | ronto | r |
| 1030 | quetta | Q | 10-30 | quecto | q |
Non-SI units
Nit – unit of luminescence
Erg – a cgs unit of work or energy; the work done by a force of one dyne acting over a distance of one centimetre
Erg – the amount of work done by a force of one dyne exerted for a distance of one centimetre, in the CGS system
Roentgen – a legacy unit of measurement for exposure to ionizing radiation
Electron volt (symbol eV) is a unit of energy equal to approximately 1.602×10−19 J. By definition, it is equal to the amount of kinetic energy gained by a single unbound electron when it accelerates through an electric potential difference of one volt
Decibel – named after Alexander Graham Bell. A tenth part of a bel
Phon – a measure of the apparent loudness level of a sound
Slug – a unit of mass associated with Imperial units
Horsepower = 746 Watts
Quintal – a historical unit of mass in many countries which is usually defined as 100 base units of either pounds or kilograms
Toise – a unit of measure for length, area and volume originating in pre-revolutionary France
Mina – unit of weight in Babylonia equal to 50 shekels. The shekel was about 180 grains
In Rome, the unit known as the passus (or pace) was standardized as two gradūs or five Roman feet (about 1.48 metres). There are 1000 passus in one mille
Sverdrup – a unit of measure of volume transport. It is used almost exclusively in oceanography, to measure the transport of ocean currents
Poise – unit of dynamic viscosity in the CGS system
Weight
Troy weight is a system of units of mass customarily used for precious metals, black powder, and gemstones. Named after Troyes, France, the troy system of weights was known to exist in medieval times
There are 12 troy ounces per troy pound, rather than the 16 ounces per pound found in the more common avoirdupois system
A grain is a unit of measurement of mass that is nominally based upon the mass of a single seed of a cereal. From the Bronze Age into the Renaissance the average masses of wheat and barley grains were part of the legal definition of units of mass
A pennyweight is equal to 24 grains, 1/240 of a troy pound, 1/20 of a troy ounce
1 oz = 437 grains
Weight of pearls is measured in grains
Metric ton (tonne) = 1000 kg (2205 pounds)
8 stone (112 pounds) = 1 hundredweight
20 hundredweight (2240 pounds) = 1 ton
Avoirdupois pound = 7000 grains
Length
According to Vetruvius, a palm is the width of four fingers , a foot is the width of four palms (and is 12 inch), a cubit is the width of six palms (18 inches) , and a man's height is four cubits (and thus 24 palms)
The Egyptian cubit was subdivided into 7 palms of 4 digits each; surviving cubit rods are between 52.3 and 52.9 cm in length
1 inch = 3 barley corns
6’ = 1.83 m
1 chain = 22 yards
10 chains = 1 furlong
1 hand = 4 inches
Under an agreement in 1959 between Australia, Canada, New Zealand, South Africa, the United Kingdom and the United States, the yard (known as the ‘international yard’ in the United States) was legally defined to be exactly 0.9144 metres
Yards were historically defined by the lengths of body parts of various UK rulers
1 nautical league = 3 nautical miles
1 mile = 1609 metres
1 nautical mile = 1852 metres
1 knot = 1.151 mph
1 cable = 1/10 of a nautical mile or 100 fathoms
League – originally referred to the distance a person or a horse could walk in an hour. On land, the league was most commonly defined as three miles
In typography, a point is the smallest unit of measure, being a subdivision of the larger pica. By the end of the 19th Century, it had settled to around 0.35 to 0.38 mm. In the late 1980s, the traditional point was supplanted by the desktop publishing point (also called the PostScript point), which was defined as 72 points to the inch. There are 12 points to the pica
Area
10,000 square metres = a hectare
1 acre = 4840 square yards
Barn is defined as 10−28 m2 and is approximately the cross sectional area of a uranium nucleus
Volume
US liquid gallon = 3.78 litres
UK gallon = 4.55 litres
Oil barrel: 42 US gallons (159 litres or 35 Imperial (UK) gallons)
UK beer barrel: 36 UK gallons (163.7 litres)
UK wine barrel: 26.25 UK gallons (119.3 litres)
US beer barrel: 31 US gallons (117.3 litres)
UK beer measurements. Firkin – 9 gallons, kilderkin – 18 gallons, barrel – 36 gallons, hogshead = 54 gallons
Flagon = 2 pints
A gallon of water weighs 10 pounds
4 pecks = 1 bushel
Cubic metre = 1000 litres
Teaspoon = 5 millilitres
Tablespoon = 3 teaspoons (15 ml)
Fluid oz = 1/20 pint (UK), 1/16 pint (US)
A fluid ounce is equal to about 28.4 ml in the imperial system or about 29.6 ml in the US system
Gill = ¼ of a pint, also known as a noggin
Metric cup = 250 millilitres
UK cup = 0.5 imperial pints
Cran = 37.5 gallons, measure of quantity of herring
Energy
Therm – 100,000 British thermal units (BTU). The therm is equal to 1.054 × 108 joules, 25,200 kilocalories or 29.3 kilowatt-hours
British Thermal Unit – is the amount of energy needed to heat one pound of water by one degree Fahrenheit
Kilowatt hour is a unit of energy equal to 1000 watt-hours or 3.6 megajoules. Used as a billing unit for energy delivered to consumers by electric utilities
Calorie – the energy needed to increase the temperature of one gram of water by one kelvin. 1 calorie = 4.186 Joules
Gas mark 4 – 350 oF, 180 oC
Gas mark 5 – 375 oF, 190 oC
Gas mark 6 – 400 oF, 200 oC
Pressure
The standard atmosphere (symbol: atm) is a unit of pressure equal to 101,325 Pa or 1013.25 millibars or hectopascals. It is equivalent to 760 mmHg (torr)
Standard Temperature and Pressure (STP) corresponds to 273 K (0° Celsius) and 1 atmosphere pressure
Torr – a unit of pressure with the ratio of 760 to 1 standard atmosphere, chosen to be roughly equal to the fluid pressure exerted by a millimetre of mercury
Barye – old unit of pressure
Bar – 100,000 Pascals
Paper sizes
ISO paper sizes are all based on a single aspect ratio of √2
A0 (841 x 1189mm) – A10 (26 x 37mm)
A4 is 210 x 297mm
ISO 216 – international standard for paper sizes (A series). Posters use B series
ISO 269 – international standard for envelopes (C series)
Folio – paper divided into two leaves, i.e. four pages
Quarto – paper divided into four leaves, i.e. eight pages
Clothes and shoes
Women’s clothing sizes in USA are four smaller than in UK. Smallest size is 4 (USA) and 8 (UK)
EN 13402 is a European standard for labeling clothes sizes
Shoe size in the United Kingdom and Ireland is based on the length of the last, measured in barleycorn (1/3 inch)
The traditional system for shoe size in North America is similar to English sizes but start counting at one rather than zero, so equivalent sizes are one greater
The Continental European system for shoe size is the length of the last, expressed in Paris points (2/3 cm)
Denier (or den) – a unit of measure for the linear mass density of fibres. It is defined as the mass in grams per 9000 meters
Gemstones
Gold is graded in carats, a measure of its purity or fineness, measured in parts pure gold out of 24. Lowest grade is 9 carat (37.5% pure)
Carat is a unit of mass equal to 200 mg, and it is used for measuring gemstones and pearls
George Frederick Kunz, a Tiffany’s gemologist, was instrumental in the international adoption of the metric carat as a weight standard for gems, and the Tiffany standard for sterling and platinum have been adopted as U.S. standards
