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 (0^oK) 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, K_cd, 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, N_A, 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