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Weights and Measures

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Overview

Top - Overview
Prefixes - Units
Commentary - References

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Prefixes

Many measurement systems use prefixes to modify basic units of measurement. We generally use them to indicate larger or smaller units. This table has the "standard" International System (Metric) prefixes, which are also sometimes used in the "English" system. The table shows both the decimal and binary prefixes.

Notes:

• micro: Sometimes written "m" instead, particularly on electrical capacitors (condensors).
• pico: Sometimes written "micro micro" instead, abbreviated "µµ" or "mm", particularly on electrical capacitors (condensors).

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Units

These are common, and not so common, units of measurement. Some units occur in more than one place.

The SI Base Units are the basic "metric" units of measure, the standard on which most other measures are based. They are the meter, kilogram, second, ampere, kelvin, mole, and candela. The SI Derived Units are derived form the base units.

Categories of Measurement

Length: Linear Measures

Linear measures measure, well, lengths. The following table is arranged in alphabetic order by the name of the unit.

Name	Symbol	Comments	Origin
arshin or arshine		28 in	(Russian)
astronomical unit	AU	Average distance from Sun to Earth	Astronomy
cable's length		Varies	Nautical
centimeter, centimetre	cm	10 mm, 0.01 m, 1/2.54=0.3937 in
chain (engineer's)		1/52.8 mi, 100 ft, 100 links
chain (surveyor's)		1/80 mi, 66 feet, 100 links	Land
fathom		6 ft	Nautical
foot	ft
furlong		1/8 mi, 40 rods, 220 yd, 660 ft	Land
inch	in
kilometer, kilometre	km	1000 m, 0.621 mi, 3280.8 ft
league (land)		3 statute miles (nominally)
league (marine)		3 nautical miles
light-minute		Distance light travels in one minute in a vacuum
light-second		Distance light travels in one second in a vacuum, almost exactly 300×106 m
light-year	LY	Distance light travels in one year in a vacuum
link (engineer's)		1/100 engineer's chain, 1 ft
link (surveyor's)		1/100 surveyor's chain, about 7.92 in	Land
meter, metre	m	SI Base Unit
metric foot		0.30 m, 30 cm, 11.81 in, 0.98 ft
micron	µm	one micrometre: 10-6 m
mil	mil	0.001 in
mile (nautical)	NM	Distance subtended by one minute of arc at Earth's equator; or by international agreement, 6076.11549 ft	Navigation
mile (statute)	mi	5280 ft, 1760 yd, 8 furlongs
parsec	Pc	About 3.26 LY	Astronomy
rod or pole or perch		16.5 ft	Land
yard	yd	3 ft

Common Linear Measures

mil	millimetre (mm)	centimetre (cm)	inch (in)	foot (ft)	yard (yd)	metre (m)	rod	furlong	kilometre (km)	statute mile (mi)	land league
1	0.0254	0.00254	0.001
	1	0.1				0.001
	10	1	0.3937			0.01
1000		2.54	1	0.0833
			12	1		0.3048
			36	3	1	0.9144
	1000	100				1			0.001
				16.5	5.5	5.029	1
						201.168	40	1
									1
				5280	1760			8	1.6093	1	0.3333
									4.83	3	1

Note: 1 in is precisely 2.54 cm.

Area: Square Measures

Square measures measure areas. The following table is arranged in alphabetic order by the name of the unit. Area can be measured as the square of any linear measure; e.g., a square micron can be abbreviated either "sq. µm" or "µm²." Many square measures are ambiguously named after the unit used to measure a side; e.g., a square yard is often just called a "yard," and the meaning is taken from context.

Name	Symbol	Comments	Origin
acre	ac	1/640 mi2, 10 sq chain, 160 sq rod, 4840 yd2, 43560 ft2	Land
arpent		about 5/6 ac.	Land (French)
hectare			Land
quarter section		1/4 sq mi, 160 acres	Land
section		1 sq mi, 640 acres	Land
square centimetre	cm2	10-4 m2
square chain or chain		1/10 acre	Land
square metre	m2	SI Derived Unit
square mile	sq mi, mi2		Land
square rod or rod			Land
square yard or yard	sq yd, yd2
township		6 mi sq (nominally)	Land

Common Square Measures

square centimetre (cm2)	square inch (sq in)	square foot (sq ft)	square yard (sq yd)	square metre (m2)	square rod	acre (ac)	hectare	square kilometre (km2)	square mile (sq mi)
1
6.452	1
929.03	144	1
		9	1	0.8361
				1
			30.25	25.292	1
		43560	4840		160	1	0.4047
							1
								1
						640	259.00	2.590	1
								2.590

Notes:

• 1 acre is nominally the amount of land a man can plow in a day: it is 1 furrow long (furlong) by 1 chain wide.
• The arpent is an old French unit of land, approximately 5/6 of an acre, still used in parts of Louisiana and Quebec.

Volume: Cubic Measures

Cubic measures measure volumes. The following table is arranged in alphabetic order by the name of the unit. Volume can be measured as the cube of any linear measure; e.g., a cubic micron can be abbreviated either "cu. µm" or "µm³." Many volumetric measures are ambiguously named after the unit used to measure a side; e.g., a cubic yard is often just called a "yard," and the meaning is taken from context.

Name	Symbol	Comments	Origin
bushel		dry measure of 4 pecks, 32 quarts	Agriculture
cord		wood: 128ft3, 8 cord feet
cord foot		wood: 16ft3
cubic centimeter	cc, cm3
cubic foot	cu ft, ft3	1728in3
cubic inch	cu in, ci, in3
cubic meter	m3	SI Derived Unit
cubic yard or yard	cu yd, yd3
cup	C	1/2 pt, 2 gills, 8 oz	Cooking
fluid ounce	fl oz, oz
gallon	gal	4 quarts
gill		1/4 pint, 1/2 cup, 4 oz
hogshead		liquid measure of 63 gallons	Agriculture
liter	l
peck		2 gallons, 8 quarts	Agriculture
pint		1/2 quart, 4 gills
quart	qt	1/4 gallon, 2 pints
tablespoon	T, tbsp	1/16 cup	Cooking
teaspoon	t, tsp		Cooking
ton (displacement)	ton	35 cu ft, volume of approximately 1 long ton of sea water	Shipping
ton (freight, measurement)	ton	usually 40 cu ft	Shipping
ton (register)	ton	100 cu ft	Shipping

Dry Measures

in3	pint	litre (l)	quart (U.S.)	quart (Brit.)	peck	bushel
1	0.0298	0.0164	0.0149		0.00186	0.000465
3.60	1	0.5506	0.5000		0.0625	0.015625
61.02	1.82	1	0.9081		0.1135	0.028378
67.20	2	1.1012	1		0.1250	0.031250
			1.032	1
537.61	16	8.8098	8		1	0.25
2150.42	64	35.2390	32		4	1

Note: U.S. government standards define bushels as weights avoirdupois for specific grains; e.g., one bushel of oats weighs 32lb, and one bushel of wheat weighs 60lb. Some States provide different definitions.

Liquid Measures

in3	fluid ounce (fl oz)	gill	pint	quart (U.S.)	quart (Brit.)	litre (l)	gallon (U.S.)	gallon (Brit.)	barrel (U.S.)	barrel (Brit.)
1
1.8047	1					0.0296
7.219	4	1				0.1183
28.875		4	1			0.4732
57.75			2	1		0.9464
					1
						1
231				4		3.7854	1
277.42					4			1
							31.5		1
								36		1

Note: The British Imperial barrel is 36 British Imperial gallons. The U.S. barrel is usually 31.5 U.S. gallons.

Apothecaries' Fluid Measures

minim	fluid dram	in3	fluid ounce (fl oz)	pint	litre (l)
1		0.0038			0.0000616
60	1	0.2256			0.00036966
		1
	8	1.8047	1		0.00296
		28.875	16	1	0.4732
					1

Ridiculously Large Table

This table will go away when I have it completely broken into smaller tables.

Base Quantity	Name	Symbol	Comments	Origin
Angle	degree	deg, °	1/360 circle
	grad		1/400 circle
	hour	h, hr	1/24 circle
	minute, arc-minute	m, min, '	1/60 degree
	radian	rad	1/2π circle
	second, arc-second	s, sec, ''	1/60 minute
Mass	gram	g
	kilogram	kg	SI Base Unit
	microgram	µg, ug, mcg
	pound mass	lb, lbm		Latin
	slug		(lb force)/(ft/(s2)) = (lb force)(s2)/ft = approx. 32.2 lb mass
	ton (long, shipping)		2240 lb
	ton (metric)		1000 kg
	ton (short)		2000 lb
Weight (Force, not mass.)	carat		200mg	Precious stones and pearls
	ounce avoirdupois	oz	1/16 pound avoirdupois, 7000 grains
	ounce troy	oz	1/12 pound troy, 5760 grains
	pound	lb, #
	stone		14 pounds
	ton (freight, measurement)		1000 kg
	ton (metric)		1000 kg
Force  (force=mass×acceleration) (force=pressure×area)	dyne		(g)(cm)/s2; a cgs unit
	newton	N	(kg)(m)/s2	Isaac Newton
	pound force	lb, lbf
Pressure  (pressure=force/area)	atmosphere	atm
	bar	bar	1e6dyne/cm2 = 1000mb	meteorology
	hectopascal	hPa	100Pa = 1mb
	inch of mercury	in Hg	33.865mb	meteorology
	kilopascal	kPa	1000Pa = 10mb
	millibar	mb	10e-3bar = 1e3dyne/cm2	meteorology
	millimetre of Mercury	mm Hg	1.3332mb	meteorology
	pound per square inch	psi
	Pascal	Pa	N/m2 = (kg)(m3)/s2	Blaise Pascal
Energy  (energy=power×time)	British thermal unit	BTU	Energy to raise 1lb water by 1°F
	calorie	cal
	Calorie or dietetic calorie or kilocalorie	Cal, kcal	The dietetic calorie is properly 1000 calories.
	erg	erg	(dyne)(cm), 2.388e-8 cal; a cgs unit
	joule	J	(J)(s), (kg)(m2)/s2	Joule
	kilowatt-hour	kWh	3.6MJ; standard U.S. measure of electrical energy
Power  (power=energy/time)	calorie/minute	cal/min	0.06973W	meteorology
	horsepower	HP, hp	746W
	ton		12000 BTU/hr
	watt	W	J/s, (kg)(m2)/s3	James Watt
Speed and Velocity  (speed=distance/time)	feet per second	ft/s
	kilometers per hour	kph, KPH
	knots	kt	NM/hr	Navigation
	meters per second	m/s
	miles per hour	MPH
Angular Velocity	revolutions per minute	RPM	Common U.S. measure
Acceleration  (acceleration=velocity/time)	feet per second per second or feet per second squared	ft/s/s, ft/s2
	gravity	g	1 standard Earth gravity: 9.81m/s2 = 32.2ft/s2
	meters per second per second or meters per second squared	m/s2
Time	century		100 years
	day	dy	24 hours
	decade		10 years
	eon		1,000,000,000 (1 billion) years
	fortnight		2 weeks or 14 days
	hour	hr	60 minutes
	millennium		1,000 years
	minute	min	60 seconds
	month	mo	28-31 days
	second	s	SI Base Unit
	week	wk	7 days
	year	yr	365-366 days, or about 365.25 days
Electric Current	ampere	A	SI Base Unit	Ampère
Electromotive Force	volt	V		Voltaire
Electric Resistance	ohm	Ω
Electric Conductivity	mho		Backwards ohm
Electric Capacitance	farad	f, fd		Faraday
Electric Inductance	henry
Electric Charge	coulomb			Coulomb
Luminous Intensity	candela	cd
Thermodynamic Temperature	degree Celsius or degree Centigrade	°C
	degree Fahrenheight	°F
	kelvin	K	SI Base Unit	Lord Kelvin
Purity	karat	kt	1/24: 24kt is pure, 14kt is 14/24 pure
Amount of a Substance	mole	mol	6.02×1023

Systems:

• cgs: centimetre - gram - second: A system of units based on these measures, as well as the dyne.
• mks: metre - kilogram - second: A system of units based on these measures, as well as kilopascals (kPa), joules (J), newtons (N).
• rsf: rod - stone - fortnight: A system of units based on these measures.

Notes:

• cable's length: A nautical measure of varying length.
  • ordinary: 600ft or 100 fathoms
  • U.S. Navy: 720ft or 120 fathoms
  • British Navy: 608ft
• cicero: A typographic measure used for width and depth of a text block, commonly used in Europe. Equivalent to 12 Didot points, 4.52 mm, 0.178 inch.
• degree: There are several different kinds of degree used to measure temperature and angle.
  • angle, °: 1/360 of a circle, 60 arc-minutes, 3600 arc-seconds.
  • Celsius or Centigrade, °C: International standard, with absolute zero at approximately -273.15°C, water freezing at 0°C, and boiling at 100°C.
  • Farenheight, °F: U.S. standard, with absolute zero at approximately -459.67°F, water freezing at 32°F, and boiling at 212°F.
  • Kelvin, K or °K: Scientific standard, with absolute zero at precisely 0K, water freezing at approximately 273.15K, and boiling at 373.15K.
• dry vs. liquid:
  • dry: 1 bushel = 4 pecks = 32 quarts = 64 pints. The US dry pint is 33.6in³. US government standards specify the weight avoirdupois of various grains, and some States have varying measures. The British dry quart is 1.032 US dry quarts.
  • wet: 1 gallon = 4 quarts = 8 pints = 32 gills = 128 fl oz. The US wet pint is 28.875in³. The British imperial quart is 1.2 US quarts.
• em, en: Typographic measures. Sometimes spoken mutton and nut, given the possibility of verbal confusion.
  • Linear em: The em is the type size; for example, with 12 point type, the em is 12 points. Abbreviated M.
  • Area em: A square with sides one linear em long.
  • Linear en: One half of a linear em.
• hogshead: 63 U.S. gallons (52.5 imperial gallons) is the most common size, but it varies from 63 to 140.
• kilowatt hour: Standard U.S. measure of electrical energy.
• league: The (land) league is nominally 3 miles, but can be longer or shorter.
• parsec: Distance at which an object has an annual parallax of 1 arc-second. In other words, the distance at which a 2 AU line segment subtends 1 arc-second.
• pica: A typographic measure used for width and depth of a text block, commonly used in English speaking countries; equivalent to 12 points.
  • Traditional: 4.22mm or 0.166 inch; slightly smaller than 1/6 inch.
  • PostScript: Precisely 1/6 inch.
• point: A typographic measure used for the size of type and other small features; equivalent to approximately 1/72 inch.
  • Traditional British and American: Equivalent to 1/12 pica, 0.3515 mm, 0.01383 inch; approximately 72 points/inch, 28.5 points/cm.
  • Didot point (Continental Europe): Equivalent to 1/12 cicero, 0.38 mm, 0.01483 inch; approximately 26.5 Didot points/cm, 67.5 Didot points/inch.
  • Modern: Most computer equipment, including PostScript, TrueType, phototypesetting equipment, etc., defines the point as precisely 1/72 inch.
• tons and tonnes: There are multiple kinds of ton, usually referred to as just ton or tonne, with the precise definition determined by context.
  • ton: 12000 BTU/hr. Used for cooling capacity (of an air conditioner).
  • displacement ton: 35 cu ft, approximately the volume of 1 long ton of sea water. Used for displacement of ships.
  • freight ton or measurement ton: Usually 40 cu ft. Used for carrying capacity of ships.
  • long ton or shipping ton: 2240 lb weight. Commonly used in Great Britain.
  • metric ton: 1000 kg weight.
  • register ton: 100 cu ft. Used for the internal capacity of ships.
  • short ton: 2000 lb weight. Commonly used in the U.S. and Canada.
• weight: A measure of force, not mass. Standing on the surface of the earth, your mass and weight are equal (or close enough). In orbit, your mass would remain unchanged, but your weight would be zero. On the moon, your mass would remain unchanged, but your weight would be approximately one sixth.

To Be Documented:

• candle power, frequency (Hz), IU, dram, grain, hundredweight, metric hundredweight, amp-hour (milliamp-hour), peck, pennyweight (dwt, pwt), becquerel, curie, roentgen, sievert(?), scruple
• Energy: eV, BTU, therm, cubic foot (of natural gas)
• Angular Velocity: RPS, deg/s
• Time: lunar vs solar months, solar vs siderial day/month/year, week
• Length: cubit, length (horse racing), hand (horse height)
  • link
  • chain: 100 links
• Torque: ft-lb (lb-ft), N-m (newton-meter)
• Volume: Imperial vs U.S. gallons, fifth (as for liquor bottles), barrels, drums
• avoirdupois vs troy units vs apothecaries' weight
• US vs British Imperal units
• specific impulse (Isp, I_sp)
• Typography: point (approx 1/72 inch), didot point, pica, em, en, quad, mutton, nut, mutton quad, cicero
• barrels, in terms of carburetors.
• Angle: 1grad=16mil
• rood: English, length varying locally from 5.5 to 8 yards, sometimes 1 rod; English, area, about 1/4 acre, or 40 square rods

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Commentary

The "metric system" makes a lot more sense than the U.S. traditional "English" system. Contrary to popular belief, it's not harder to use. It is, in fact, easier to use. It just seems harder to us Americans (and some Britons) because almost all of us learn the English system as children, and later somebody tries to teach is this weird system they use in other places. I bet half the American elementary school teachers who teach the metric system don't understand it, fear it, and pass this on to their students.

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References

The Elements of Typographical Style, Second Edition, Robert Bringhurst.

Hartley & Marks. Point Roberts, Washington, 1997.

National Institutes of Standards and Technology

U.S. government body formerly called the National Bureau of Standards. Responsible for setting national measurement standards.

The NIST Reference on Constants, Units, and Uncertainty

• Fundamental Physical Constants
• International System of Units (SI)
  • SI Prefixes
  • Prefixes for Binary Multiples
• Uncertainty of Measurement Results

Webster's New World Dictionary, Second College Edition.

Collins+World Publishing Company, Cleveland, 1976.

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Last modified May 2, 2004.
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