In Depth Tutorials and Information

Measurements and Numbers

The International System of Units (SI)

Rapid advances in science and technology in the 19th and 20th centuries fostered the development of several overlapping systems of units of measurements as scientists improvised to meet the practical needs of their disciplines. The General Conference on Weights and Measures was chartered by international convention in 1875 to produce standards of physical measurement based upon an earlier international standard, the meter-kilogram-second (MKS) system. The convention calls for regular General Conference meetings to consider improvements or modifications in standards, an International Committee of Weights and Measures elected by the Conference (meets annually), and several consultative committees. The International Bureau of Weights and Measures (Bureau International des Poids et Mesures) at Sevres, France, serves as a depository for the primary international standards and as a laboratory for certification and intercomparison of national standard copies.

The 1960 International System (universally abbreviated as SI, from systeme international) builds upon the MKS system. Its seven basic units, from which other units are derived, are currently defined as follows: the meter, defined as the distance traveled by light in a vacuum in 1/299,792,458 second; the kilogram (about 2.2 pounds avoirdupois), which equals 1,000 grams as defined by the international prototype kilogram of platinum-iridium in the keeping of the International Bureau of Weights and Measures; the second, the duration of 9,192,631,770 periods of radiation associated with a specified transition of the cesium-133 atom; the ampere, which is the current that, if maintained in two wires placed one meter apart in a vacuum, would produce a force of 2 x 10-7 newton per meter of length; the candela, defined as the intensity in a given direction of a source emitting radiation of frequency 540 x 1012 hertz and that has a radiant intensity in that direction of 1/683 watt per steradian; the mole, defined as containing as many elementary entities of a substance as there are atoms in 0.012 kilogram of carbon-12; and the kelvin, which is 1/273.16 of the thermodynamic temperature of the triple point (equilibrium among the solid, liquid, and gaseous phases) of pure water.

	Elemental and Derived SI Units	and Symbols
Quantity		SI Units
		FORMULA/EXPRESSION
	UNIT	IN BASE UNITS	SYMBOL
elemental units
length	meter	—	m
mass	kilogram	—	kg
time	second	—	s
electric current	ampere	—	A
luminous intensity	candela	—	cd
amount of substance	mole	—	mol
thermodynamic temperature	kelvin	^—	K
derived units
acceleration	meter/second squared	m/s²
area	square meter	m²
capacitance	farad	A ^ s/V	F
charge	coulomb	A * s	C
Celsius temperature	degree Celsius	K	°C
density	kilogram/cubic meter	kg/m³
electric field strength	volt/meter	V/m
electrical potential	volt	W/A	V
energy	joule	N x m	J
force	newton	kg x m/s²	N
frequency	hertz	s^-1	Hz
illumination	lux	lm/m²	lx
inductance	henry	V x s/A	H
kinematic viscosity	square meter/second	m²/s
luminance	candela/square meter	cd/m²
luminous flux	lumen	cd x sr	lm
magnetic field strength	ampere/meter	A/m
magnetic flux	weber	V x s	Wb
magnetic flux density	tesla	Wb/m²	T
plane angle	radian	m x m^-1=1	rad
power	watt	J/s	W
pressure	pascal (newton/square meter	) N/m²	Pa
resistance	ohm	V/A	n
solid angle	steradian	m² x m^-2=1	sr
stress	pascal (newton/square meter	) N/m²	Pa
velocity	meter/second	m/s
viscosity	newton-second/square meter	N x s/m²
volume	cubic meter	m³

Conversion of Metric Weights and Measures

The International System of Units is a decimal system of weights and measures derived from and extending the metric system of units. Adopted by the 11th General Conference on Weights and Measures in 1960, it is abbreviated “SI” in all languages. Below are common equivalents and conversion factors for US customary and SI systems.

approximate 1 inch	common equivalents = 25 millimeters	conversions accurate within inches x 25.4¹	10 parts per million = millimeters
1 foot	= 0.3 meter	feet x 0.3048¹	= meters
1 yard	= 0.9 meter	yards x 0.9144¹	= meters
1 mile	= 1.6 kilometers	miles x 1.60934	= kilometers
1 square inch	= 6.5 sq. centimeters	square inches x 6.4516¹	= square centimeters
1 square foot	= 0.09 square meter	square feet x 0.0929030	= square meters
1 square yard	= 0.8 square meter	square yards x 0.836127	= square meters
1 acre	= 0.4 hectare²	acres x 0.404686	= hectares
1 cubic inch	= 16 cubic centimeters	cubic inches x 16.3871	= cubic centimeters
1 cubic foot	= 0.03 cubic meter	cubic feet x 0.0283168	= cubic meters
1 cubic yard	= 0.8 cubic meter	cubic yards x 0.764555	= cubic meters
1 quart (liq)	= 1 liter²	quarts (liquid) x 0.946353	= liters
1 gallon	= 0.004 cubic meter	gallons x 0.00378541	= cubic meters
1 ounce (avdp)³	= 28 grams	ounces (avdp)³ x 28.3495	= grams
1 pound (avdp)³	= 0.45 kilogram	pounds (avdp)³ x 0.453592	= kilograms
1 horsepower	= 0.75 kilowatt	horsepower x 0.745700	= kilowatts
1 millimeter	= 0.04 inch	millimeters x 0.0393701	= inches
1 meter	= 3.3 feet	meters x 3.28084	= feet

Conversion of Metric Weights and Measures

1 meter	= 1.1 yards	meters x 1.09361	= yards
1 kilometer	= 0.6 mile (statute)	kilometers x 0.621371	= miles (statute)
1 square centimeter	= 0.16 square inch	square centimeters x 0.155000	= square inches
1 square meter	= 11 square feet	square meters x 10.7639	= square feet
1 square meter	= 1.2 square yards	square meters x 1.19599	= square yards
1 hectare²	= 2.5 acres	hectares x 2.47105	= acres
1 cubic centimeter	= 0.06 cubic inch	cubic centimeters x 0.0610237	= cubic inches
1 cubic meter	= 35 cubic feet	cubic meters x 35.3147	= cubic feet
1 cubic meter	= 1.3 cubic yards	cubic meters x 1.30795	= cubic yards
1 liter²	= 1 quart (liq)	liters x 1.05669	= quarts (liq)
1 cubic meter	= 264 gallons	cubic meters x 264.172	= gallons
1 gram	= 0.035 ounce (avdp)³	grams x 0.0352740	= ounces (avdp)³
1 kilogram	= 2.2 pounds (avdp)³	kilograms x 2.20462	= pounds (avdp)³
1 kilowatt	= 1.3 horsepower	kilowatts x 1.34102	= horsepower

Tables of Equivalents: Metric System Units and Prefixes

base unit¹
QUANTITY	NAME OF UNIT	SYMBOL
length	meter	m
area	square meter	square m, or m²
	are (100 square meters)	a
volume	cubic meter	cubic m, or m³
	stere (1 cubic meter)	s
mass	gram	^g
	metric ton (1,000,000 grams)	t
capacity	liter	l
temperature	degree Celsius	°C

prefixes designating multiples and submultiples

PREFIX	SYMBOL	FACTOR BY WHICH UNIT IS MULTIPLIED		EXAMPLES
exa-	E	10¹⁸ =	1,000,000,000,000,000,000
peta-	P	10¹⁵ =	1,000,000,000,000,000
tera-	T	10¹² =	1,000,000,000,000
giga-	G	10⁹ =	1,000,000,000
mega-	M	10⁶ =	1,000,000	megaton (Mt)
kilo-	k	10³ =	1,000	kilometer (km)
hecto-, hect-	h	10² =	100	hectare (ha)
deca- dec-	da	10 =	10	decastere (das)
deci-	d	10-¹ =	1 0.1	decigram (dg)
centi-, cent-	c	10^-2 =	0.01	centimeter (cm)
milli-	m	10^-3 =	0.001	milliliter (ml)
micro-, micr-	M	10^-6 =	0.000001	microgram (Mg)
nano-	n	10-⁹ =	0.00000000
pico-	^p	10^-12 =	0.000000000001
femto-	f	10^-15 =	0.000000000000001
atto-	a	10^-18 =	0.000000000000000001

The US was an independent nation for 13 years before the Constitution was signed in 1789, the same year George Washington was elected the country’s first president. In 1781, American Revolutionary leader John Hanson was elected by the Continental Congress “President of the United States in Congress Assembled.” Hanson is thus referred to by some as the first US president, but he was a congressional presiding officer and had none of the presidential powers that would be granted under the Constitution.

British/US System (foot-pound-second, fps)

length
1 statute mi	= 5,280 ft	= 1,760 yd	= 320 rods	= 8 furlongs
1 nautical mi	= 6,076 ft	= 1.151 mi
1 furlong	= 660 ft	= 220 yd	= 40 rods	= 1/8 mi
1 chain (Gunter’s)	= 66 ft	= 22 yd	= 100 links	= 4 rods
1 rod	= 16.5 ft	= 5.5 yd	= 25 links
1 fathom	= 6 ft	= 72 in
1yd	= 3 ft	= 36 in
1 ft	= 12 in
1 link (Gunter’s)	= 0.66 ft	= 7.92 in
1 hand	= 4 in
1 mil	= 0.001 in

area 1 sq mi 1 acre	= 640 acres = 10 sq chains	= 102,400 sq rods = 160 sq rods	= 3,097,600 = 27,878,400 sq ft sq yd = 4,840 sq yd = 43,560 sq ft
1 sq ft	= 144 sq in
volume 1 cu ft 1 cu in	= 1/27 cu yd = 1/46,656 cu yd	= 12 board ft = 1/1,728 cu ft	= 1,728 cu in
1 acre-ft	= 43,560 cu ft	= 1,613 cu yd
1 board ft	= 144 cu in	= 1/12 cu ft	= 1 super ft (lumber)
1 cord (US)	= 128 cu ft
capacity 1 cu ft	= 7.481 gal (US)	= 6.229 gal (British)

liquid measure (US)
1 barrel, oil	= 42 gal (US)	= 34.97 gal (British)
1 gal	= 0.833 gal (British)	= 4 quarts	= 231.00 cu in	= 128 fl oz
1 quart	= 1/4 gal	= 2 pints	= 57.75 cu in	= 32 fl oz
1 pint	= 1/8 gal	= 1/2 quart	= 28.88 cu in	= 16 fl oz
1 gill	= 1/32 gal	= 1/4 pint	= 7.22 cu in	= 4 fl oz
1 fl oz	= 1/128 gal	= 1/16 pint	= 1.80 cu in
dry measure (US)
1 bushel	= 0.97 bushel (British)	= 4 pecks	= 2,150.4 cu in	= 1.24 cu ft
1 peck	= 1/4 bushel	= 8 quarts	= 537.6 cu in	= 0.31 cu ft
1 quart	= 1/32 bushel	= 2 pints	= 67.2 cu in	= 1/8 peck
1 pint	= 1/64 bushel	= 1/2 quart	= 33.6 cu in

liquid and dry measure (British)
1 bushel	= 1.03 bushels (US)	= 8 gal	= 4 pecks = 2,219.36 cu in	= 1.284 cu ft
1 peck	= 0.25 bushel	= 2 gal	= 8 quarts = 554.84 cu in
1 gal	= 1.20 gal (US)	= 4 quarts	= 277.42 cu in
1 quart	= 0.30 gal	= 2 pints	= 1/8 peck = 69.36 cu in
1 pint	= 4.80 gills (US)	= 4 gills	= 34.68 cu in	= 20 fl oz
1 gill	= 1.20 gills (US)		= 8.67 cu in	= 5 fl oz
1 fl oz	= 0.96 fl oz (US)		= 1.73 cu in
weight
1 short ton (US)	= 0.89 long ton	= 2,000 lbs	= 20 short cwt¹
1 long ton (British)	= 1.12 short tons	= 2,240 lbs	= 22.4 short cwt¹
1 short cwt¹ (US)	= 0.05 short ton	= 100 lbs
1 long cwt¹ (British)	= 0.05 long ton	= 112 lbs
1 stone (person)	= 0.14 short cwt¹	= 14 lbs
1 lb	= 0.07 stone (British)
1 oz avoirdupois	= 437.50 grains	= 1/16 lb	= 0.911 oz troy
1 oz troy	= 480.00 grains	= 1/12 lb	= 1.097 oz
1 grain		= 0.0023 oz	= 0.0021 oz troy

UNIT SYMBOL ATTRIBUTE MEASURED EXPRESSION IN OTHER UNITS (S = SECOND)

Ampere A current C/s or V/Q

the basic electrical unit of the International System of Units (SI), since 1948 defined by the International Bureau of Weights and Measures as the constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross section, and placed one meter apart in a vacuum, would produce between these conductors a force equal to 2 x 10-7 newton per meter of length. One ampere is equal to a flow of one coulomb of electricity per second; or, the flow produced in a conductor with a resistance of one ohm by a potential difference of one volt.

farad F capacitance (ability to hold a charge) A x s/V or C/V

the ability of two parallel, oppositely charged plates (a capacitor) to hold an electric charge equals one farad when one coulomb of electricity changes the potential between the plates by one volt.

coulomb C charge A x s

the quantity of electricity transported in one second by a current of one ampere. Approximately equal to 6.24 x 1018 electrons.

watt W power J/s orVxA

one joule of work performed per second; or, the power dissipated in an electrical conductor carrying one ampere current between points at one volt potential difference.

ohm Q resistance V/A or W/A2

resistance of a circuit in which a potential difference of one volt produces a current of one ampere; or, the resistance in which one watt of power is dissipated when one ampere flows through it.

volt V potential W/A or Ax Q

the difference in potential between two points in a conductor carrying one ampere current when the power dissipated between the points is one watt; or, the difference in potential between two points in a conductor across a resistance of one ohm when one ampere is flowing through it.

Temperature Equivalents

Instructions for converting °F into °C or K1, and °C into °F: Find the figure you wish to convert in the second column. If this figure is in °F, the corresponding temperature in °C and K will be found in the third and fourth columns; if the figure is in °C, the corresponding temperature in °F will be found in the first column. To convert a temperature range between two scales, rather than finding equivalent temperatures, see the temperature conversion instructions, below.

FAHRENHEIT	FIGURE	°CELSIUS	KELVIN	°FAHRENHEIT	FIGURE	°CELSIUS	KELVIN
°F)	TO BE	(°CENTIGRADE)	(K)	(°F)	TO BE	(°CENTIGRADE)	(K)
	CONVERTED	(°C)			CONVERTED	(°C)
	-459.67	-273.15	0	+46.4	+8	-13.33	+259.82
				+48.2	+9	-12.78	+60.37
	-400	-240.00	+33.15
	-300	-184.44	+88.71	+50.0	+ 10	-12.22	+260.93
-459.67	-273.15	-169.53	+103.62	+68.0	+20	-6.67	+266.48
				+86.0	+30	-1.11	+272.04
-328.0	-200	-128.89	+144.26	+89.6	+32	0.00	+273.15
-148.0	-100	-73.33	+199.82	+104.0	+40	+4.44	+277.59
				+122.0	+50	+10.00	+283.15
-130.0	-90	-67.78	+205.37	+140.0	+60	+15.56	+288.71
-112.0	-80	-62.22	+210.93	+158.0	+70	+21.11	+294.26
-94.0	-70	-56.67	+216.48	+176.0	+80	+26.67	+299.82
-76.9	-60	-51.11	+222.04	+194.0	+90	+32.22	+305.37
-58.0	-50	-45.56	+227.59
-40.0	-40	-40.00	+233.15	+212.	+100	+37.78	+310.93
-22.0	-30	-34.44	+238.71	+392.0	+200	+93.33	+366.48
-4.0	-20	-28.89	+244.26	+572.0	+300	+148.89	+422.04
+14.0	-10	-23.33	+249.82	+752.0	+400	+204.44	+477.59
				+932.0	+500	+260.00	+533.15
+32.0		-17.78	+255.37	+1112.0	+600	+315.56	+588.71
+33.8	+1	-17.22	+255.93	+1292.0	+700	+371.11	+644.26
+35.6	+2	-16.67	+256.48	+1472.0	+800	+426.67	+699.82
+37.4	+3	-16.11	+257.04	+1652.0	+900	+482.22	+755.37
+39.2	+4	-15.56	+257.59
+41.0	+5	-15.00	+258.15	+1832.0	+1000	+537.78	+810.93
+42.8	+6	-14.44	+258.71	+3632.0	+2000	+1093.33	+1366.45
+44.6	+7	-13.89	+259.26	+5432.0	+3000	+1648.89	+1922.05

Temperature Equivalents (continued)

All systems of measuring temperature in degrees or units (kelvins) on a scale are based on the interval between the freezing and boiling points of water and differ only in the number of degrees or units into which this interval is divided.

Fahrenheit: interval is divided into 180 degrees (32° to 212°); 0° is at 32° below the freezing point of water.

Rankine: degree is the same as the Fahrenheit degree; 0° is at absolute zero (the theoretical point at which a thermodynamic system has the lowest energy, -459.67 °F). Once common in engineering applications in the US, the Rankine scale is now rarely used.

Celsius: interval is divided into 100 degrees; 0° is at the freezing point of water.

Kelvin: interval is the same as the Celsius degree; 0 K is at absolute zero (the theoretical point at which a thermodynamic system has the lowest energy, -273.15 °C).

Reaumur: interval is divided into 80 degrees; 0° is at the freezing point of water. One of the earliest (1730) temperature scales in widespread use, the Reaumur scale had been supplanted by other scales by the late 19th century.

temperature conversion instructions:2

°Fahrenheit	into	°Celsius	subtract 32, divide by 1.8²
°Celsius	into	°Fahrenheit	multiply by 1.8, add 32²
°Celsius	into	kelvin	add 273.15

1Because a kelvin is itself a unit of measurement, it is incorrect to use “degree” or the ° symbol with it, as is necessary with the units of the Rankine, Fahrenheit, Celsius, and Reaumur scales. One kelvin is equal to one degree Celsius. 2Instructions are for finding equivalent temperatures; to find the equivalent number of degrees in a temperature range (e.g., tomorrow’s temperature will be 11.0 °F, or 6.1 °C, warmer than today’s temperature), omit the step of adding or subtracting 32.

Cooking Measurements

MEASURE	CONVENTIONAL EQUIVALENTS¹	METRIC EQUIVALENT
drop	¹/60 teaspoon	0.08 ml
dash	V8 teaspoon	0.62 ml
teaspoon	8 dashes; V3 tablespoon; Ms fluid ounce	4.93 ml
tablespoon	3 teaspoons; ¹/2 fluid ounce	14.79 ml
ounce (weight)	¹/16 pound	28.35 g
fluid ounce (volume)	2 tablespoons	29.57 ml
cup	8 fluid ounces; 16 tablespoons; V2 pint	236.59 ml
pound	16 ounces	453.6 g
pint	16 fluid ounces; 2 cups; ¹/2 quart	473.18 ml
quart	32 fluid ounces; 4 cups; 2 pints; ¹/4 gallon	946.36 ml
gallon	128 fluid ounces; 16 cups; 8 pints; 4 quarts	3.785 l
peck	2 gallons	7.57 l
bushel	8 gallons; 4 pecks	30.28 l

OVEN TEMPERATURE EQUIVALENTS
		AMERICAN OVEN	FRENCH OVEN TEMPERATURE	BRITISH “GAS MARK”
		TEMPERATURE	TERMS AND THERMOSTAT	OVEN THERMOSTAT
°F	°C	TERMS	SETTINGS	SETTINGS
160	71		#1
170	77
200	93		tres doux; etuve
212	100
221	105		#2
225	107	very slow	doux
230	110		#3
250	121			#¹/4 (241 °F)
275	135			#¹/2 (266 °f)
284	140	slow	moyen; modere	#1(291 °F)
300	149
302	150		#4
320	160			#2 (313 °F)
325	163			#3 (336 °f)
350	177	moderate	assez chaud; bon four

Cooking Measurements

OVEN TEMPERATURE EQUIVALENTS
		AMERICAN OVEN TEMPERATURE	FRENCH OVEN TEMPERATURE TERMS AND THERMOSTAT	BRITISH “GAS MARK” OVEN THERMOSTAT
°F	°C	TERMS	SETTINGS	SETTINGS
356	180			#4 (358 °F)
375	190		#5	#5 (379 °F)
390	200
400	205			#6 (403 °F)
410	210	hot	chaud
425	218		#6	#7 (424 °F)
428	220
437	225
450	232			#8 (446 °F)
475	246	very hot	tres chaud; vif	#9 (469 °F)
500	260		#7
525	274		#8
550	288		#9

Spirits Measure

Many specific volumes have varied over time and from place to place, but the proportional relationships within families of measures have generally remained the same. All ounce measures are in US fluid ounces.

MEASURE	CONVENTIONAL EQUIVALENTS METRIC EQUIVALENT
pony	0.75 oz = 34 shot= ¹/2 jigger	22.17 ml
shot/ounce/finger	1 oz = 1¹/3 ponies = % jigger	29.57 ml
jigger	1.5 oz = 2 ponies = 1V2 shots	44.36 ml
double	2 oz = 2 shots	59.15 ml
triple	3 oz = 3 shots	88.72 ml
noggin/imperial gill/drink (whiskey)	4.8 oz	142.1 ml
pint	16 oz = 58 fifth = ¹/2 quart	473.2 ml
quarter yard	20 oz = 114 pints	591.5 ml
bottle (champagne or other wine)	about 25.5 oz or ¹^ imperial gallon 750 ml (industry standard)
fifth	25.6 oz = ⁴/5 quart = ¹/₅ gallon	757.1 ml
quart	32 oz = ¹/2 magnum = ¹/4 gallon	946.3 ml
half yard	40 oz = 2¹/2 pints	1.182 l
magnum	2 bottles (champagne or other wine)	1.5 l
magnum	64 oz = 2 quarts = ¹/2 gallon	1.893 l
yard	80 oz = 5 pints	2.365 l
jeroboam	4 bottles (champagne or other wine)	3l
gallon/double magnum	128 oz = 4 quarts = 5 fifths = 2 magnums	3.785 l
rehoboam	6 bottles (champagne or other wine)	4l
imperial gallon	1.20 gallons = % barn gallon = V10 anker	4.546 l
ale/beer gallon	1.22 gallons	4.620 l
methuselah	8 bottles (champagne or other wine)	6l
salmanazar	12 bottles (champagne or other wine)	9l
barn gallon	2¹/2 imperial gallons = % anker	11.37 l
balthazar	16 bottles (champagne or other wine)	12 l
half keg	5 gallons (type varies)	varies
nebuchadnezzar	20 bottles (champagne or other wine)	15 l
firkin	9 gallons	34.07 l
keg	10 gallons (type varies)	varies
anker	60 bottles = 10 imperial gallons = 4 barn gallons	45.46 l
runlet/rundlet/rudlet	144 pints = 72 quarts = 18 gallons = 2 firkins	68.14 l
octave	15.75 imperial gallons = V8 butt (wine)	71.60 l
British bottle	126 bottles = 21 imperial gallons	95.47 l
aum	120 quarts = 30 gallons	113.6 l
barrel (wine)	126 quarts = 3112 gallons = ³/4 tierce	119.2 l
barrel (ale/beer)	144 quarts = 36 gallons = ¹/2 puncheon (ale/beer)	136.3 l
tierce	168 quarts = 42 gallons = ¹/2 puncheon (wine)	159.0 l
British hogshead (ale/beer)	54 imperial gallons = ¹/2 butt (ale/beer) = ¹/4 tun (ale/beer)	245.5 l
puncheon (ale/beer)	72 gallons = 2 barrels (ale/beer)	272.5 l
British hogshead (wine)	63 imperial gallons = ¹/2 butt (wine) = ¹/4 tun (wine)	286.4 l
puncheon (wine)	84 gallons = 2 tierces	318.0 l
butt/pipe (ale/beer)	108 imperial gallons = ¹/2 tun (ale/beer)	491.0 l
butt/pipe (wine)	126 imperial gallons = ¹/2tun (wine)	572.8 l
tun (ale/beer)	216 imperial gallons = 4 British hogsheads (ale/beer) =	982.0 l
	2 butts (ale/beer)
tun (wine)	252 imperial gallons = 12 British bottles = 2 butts (wine)	1,146 l

Blackjack
Number of two-card combinations in a 52-card deck (where aces equal 1 or 11 and face cards equal 10) for each number between 13 and 21		Approximate chances of various exceeding 21		hands reaching or
TOTAL WITH	POSSIBLE COMBINATIONS	TOTAL IN HAND	CHANCE OF	CHANCE OF EXCEEDING 21
TWO CARDS	FROM 52 CARDS	BEFORE DEAL	REACHING A		ANY
21	64	(TWO OR MORE	COUNT OF	ONE	NUMBER
20	136	CARDS)	17 TO 21	CARD	OF CARDS
19	80		(%)	(%)	(%)
18	86	16	38	62	62
17	96	15	42	54	58
16	86	14	44	46	56
15	96	13		38	52
14	102
13	118

Poker
Number of ways to no wild cards)	reach and odds of reaching various five-card combinations on a single deal (52-card deck,
	NUMBER OF	ODDS OF RECEIVING
HAND	COMBINATIONS	ON A SINGLE DEAL
royal flush	4	1 in 649,740
straight flush	36	1 in 72,193
four of a kind	624	1 in 4,165
full house	3,744	1 in 694
flush	5,108	1 in 509
straight	10,200	1 in 255
three of a kind	54,912	1 in 47
two pairs	123,552	1 in 21
one pair	1,098,240	1 in 2

Dice
Probabilities of two-die totals
TWO-DIE	NUMBER OF	PROBABILITY	TWO-DIE	NUMBER OF	PROBABILITY
TOTAL	COMBINATIONS	(%)	TOTAL	COMBINATIONS	(%)
2	1	2.78	8	5	13.89
3	2	5.56	9	4	11.11
4	3	8.33	10	3	8.33
5	4	11.11	11	2	5.56
6	5	13.89	12	1	2.78
7	6	16.67	total	36	100¹

Ancient Measures

The standard unit of measure is listed first, with a rough modern equivalent in parentheses. Often, standard units varied over time, so a range is sometimes given. The subdivisions below relate to the standard unit of measure given first.

CULTURE	LENGTH	WEIGHT	LIQUID
Egyptian	cubit (524 mm; 20.62 in)	kite (4.5-29.9 g;	cubic cubit (0.14 cubic m;
		0.16-1.05 oz)	37 gal)¹
	digit (¹/28 of a cubit)	deben (10 kites)	khar
	palm (4 digits)	sep (10 debens)	hekat
	hand (5 digits)		hin
	small span (12 digits, or 3 palms)		ro
	large span (14 digits, or ¹/2 cubit)
	small cubit (24 digits, or 6 palms)
Babylonian	kus² (530 mm; 20.9 in)	mina (640-978 g;	ka (99-102 cubic mm;
		23-34 oz)	3.9-4.0 cubic in)
	foot (23 kus)	shekel	gur(300 ka)
	shusi (¹/30 us)
Hebrew³		sacred mina (60 shekels)	bat⁴
		sacred talent (3,000 shekels, or	hin
		50 sacred minas)	log

CULTURE	LENGTH	WEIGHT	LIQUID
Hebrew³		Talmudic mina (25 shekels)
(continued)		Talmudic talent (1,500 shekels, or 60 Talmudic minas)
Greek	finger (19.3 mm; 0.76 in) foot (16 fingers) Olympic cubit (24 fingers)	talent (25.8 kg; 56.9 lb)	metretes (39.4 l; 10.4 gal)
Roman	foot (subdivided into the uncia [plural unciae]; V12 ft)	libra (327.45 g; 11.55 oz)	sextarius (plural sextarii; 0.53 l; 0.14 gal)
	pace, or double step (5 ft)	uncia (¹/12 lb)	amphora (48 sextarii)
	mille passus (1,000 paces)
Chinese⁵	chih (25 cm; 9.8 in) chang (3 m; 9.8 ft)	shih, or tan (60 kg; 132 lb)

¹Measures given below the cubic cubit run from small to large. ²Also called the Babylonian cubit. ³The Hittites, Assyrians, Phoenicians, and Hebrews derived their systems from the Babylonians and Egyptians. Hebrew standards were based on the relationship between the mina, the talent (the basic unit), and the shekel. ⁴Volumes are not definitely known but are listed from largest to smallest. ⁵The Chinese system of measurement exhibited all the principal characteristics of the Western. It was, however, fundamentally chaotic in that there was no relationship between different types of units, such as those of length and those of volume. It also fluctuated from region to region. The first emperor of China, Shi Huangdi (221-210/09 bc), fixed the basic units given here.

Roman Numerals

Seven numeral-characters compose the Roman numeral system. When a numeral appears with a line above it, it represents the base value multiplied by 1,000. However, because Roman numerals are now seldom utilized for values beyond 4,999, this convention is no longer in use.

ARABIC	ROMAN	ARABIC	ROMAN	ARABIC	ROMAN	ARABIC	ROMAN
1	I	15	XV	170	LXX	1,000	M
12	II	16	XVI	180	LXXX	1,001	MI
3	III	17	XVII	190	XC	1,002	MII
14	IV	18	XVIII	100	C	1,003	MIII
15	V	19	XIX	101	CI	1,900	MCM
16	VI	20	XX	102	CII	2,000	MM
17	VII	21	XXI	200	CC	2,001	MMI
18	VIII	22	XXII	300	CCC	2,002	MMII
19	IX	23	XXIII	400	CD	2,100	MMC
10	X	24	XXIV	500	D	3,000	MMM
11	XI	30	XXX	600	DC	4,000	MMMMor MV
12	XII	40	XL	700	DCC	5,000	V
13	XIII	50	L	800	DCCC
14	XIV	60	LX	900	CM

Mathematical Formulas

The ratio of the circumference of a circle to its diameter is n (3.141592653589793238462643383279.., generally rounded to ²²/7 or 3.1416). It occurs in various mathematical problems involving the lengths of arcs or other curves, the areas of surfaces, and the volumes of many solids.

\	SHAPE	ACTION	FORMULA
circumference	circle	multiply diameter by n
area	circle	multiply radius squared by n
	rectangle	multiply height by length
	sphere surface	multiply radius squared by n by 4
	square	length of one side squared
	trapezoid	parallel side length A + parallel side length
\		B multiplied by height and divided by 2
	triangle	multiply base by height and divide by 2
volume	cone	multiply base radius squared by n by height
		and divide by 3
	cube	length of one edge cubed
	cylinder	multiply base radius squared by n by height
	pyramid	multiply base area by height and divide by 3
	sphere	multiply radius cubed by n by 4 and divide by 3

The American system of numeration for denominations above one million was modeled on a French system, but subsequently the French system changed to correspond to the German and British systems. In recent years, British usage reflects widespread and increasing use of the values of the American system. In the American system each of the denominations above 1,000 millions (the American billion) is 1,000 times the preceding one (one trillion = 1,000 billions; one quadrillion = 1,000 trillions). In the British system the first denomination above 1,000 millions (the British milliard) is 1,000 times the preceding one, but each of the denominations above 1,000 milliards (the British billion) is 1,000,000 times the preceding one (one trillion = 1,000,000 billions; one quadrillion = 1,000,000 trillions).

\	VALUE IN
	POWERS	NUMBER
AMERICAN NAME	OF TEN	OF ZEROS
billion	10⁹	9
trillion	10¹²	12
quadrillion	10¹⁵	15
quintillion	10¹⁸	18
sextillion	10²¹	21
septillion	10²⁴	24
octillion	10²⁷	27
nonillion	10³⁰	30
decillion	10³³	33
undecillion	10³⁶	36
duodecillion	10³⁹	39
tredecillion	1042	42
quattuordecillion	10⁴⁵	45
quindecillion	10⁴⁸	48
sexdecillion	10⁵¹	51
septendecillion	10⁵⁴	54
octodecillion	10⁵⁷	57
novemdecillion	1060	60
vigintillion	10⁶³	63
googol	10¹⁰⁰	100
centillion	10303	303

	VALUE IN
	POWERS	NUMBER
BRITISH NAME	OF TEN	OF ZEROS
milliard	109	9
billion	1012	12
trillion	1018	18
quadrillion	1024	24
quintillion	1030	30
sextillion	1036	36
septillion	1042	42
octillion	1048	48
nonillion	1054	54
decillion	1060	60
undecillion	1066	66
duodecillion	1072	72
tredecillion	1078	78
quattuordecillion	1084	84
quindecillion	1090	90
sexdecillion	1096	96
septendecillion	10102	102
octodecillion	10108	108
novemdecillion	₁₀114	114
vigintillion	10120	120
centillion	₁₀600	600

Decimal Equivalents of Common Fractions


4THS 8THS	16THS	32NDS	DECIMAL	4THS	8THS	16THS	32NDS	DECIMAL
			0.015625			15	30	0.9375
		1	0.03125				31	0.96875
	1	2	0.0625	4	8	16	32	1
		3	0.09375
1	2	4	0.125
\	\	5	0.15625
	3	6	0.1875
		7	0.21875		3RDS	6THS	12THS	DECIMAL
12	4	8	0.25				1	0.833334
		9	0.28125			1	2	0.166667
	5	10	0.3125				3	0.25
		11	0.34375		1	2	4	0.333334
3	6	12	0.375				5	0.416667
		13	0.40625			3	6	0.5
	7	14	0.4375				7	0.583333
		15	0.46875		2	4	8	0.666667
24	8	16	0.5				9	0.75
		17	0.53125			5	10	0.833333
	9	18	0.5625				11	0.916667
		19	0.59375			6	12	1
5	10	20	0.625
		21	0.65625
	11	22	0.6875		5THS	DECIMAL	7THS	DECIMAL
		23	0.71875		1	0.2	1	0.142857
36	12	24	0.75		2	0.4	2	0.285714
		25	0.78125		3	0.6	3	0.428571
	13	26	0.8125		4	0.8	4	0.571428
		27	0.84375		5	1	5	0.714285
7	14	28	0.875				6	0.857142
		29	0.90625				7	1

Next post: Applied Science

Previous post: Time

Measurements and Numbers

The International System of Units (SI)

Conversion of Metric Weights and Measures

Conversion of Metric Weights and Measures

Temperature Equivalents

Temperature Equivalents (continued)

Cooking Measurements

Cooking Measurements

Spirits Measure

Ancient Measures

Roman Numerals

Mathematical Formulas

Decimal Equivalents of Common Fractions

Related Links

:: Search WWH ::