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 meterkilogramsecond (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 platinumiridium 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 cesium133 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 107 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 carbon12; 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/s^{2} 

area 
square meter 
m^{2} 

capacitance 
farad 
A ^ s/V 
F 
charge 
coulomb 
A * s 
C 
Celsius temperature 
degree Celsius 
K 
°C 
density 
kilogram/cubic meter 
kg/m^{3} 

electric field strength 
volt/meter 
V/m 

electrical potential 
volt 
W/A 
V 
energy 
joule 
N x m 
J 
force 
newton 
kg x m/s^{2} 
N 
frequency 
hertz 
s^{1} 
Hz 
illumination 
lux 
lm/m^{2} 
lx 
inductance 
henry 
V x s/A 
H 
kinematic viscosity 
square meter/second 
m^{2}/s 

luminance 
candela/square meter 
cd/m^{2} 

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/m^{2} 
T 
plane angle 
radian 
m x m^{1}=1 
rad 
power 
watt 
J/s 
W 
pressure 
pascal (newton/square meter 
) N/m^{2} 
Pa 
resistance 
ohm 
V/A 
n 
solid angle 
steradian 
m^{2} x m^{2}=1 
sr 
stress 
pascal (newton/square meter 
) N/m^{2} 
Pa 
velocity 
meter/second 
m/s 

viscosity 
newtonsecond/square meter 
N x s/m^{2} 

volume 
cubic meter 
m^{3} 

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 25.4^{1} 
10 parts per million = millimeters 
1 foot 
= 0.3 meter 
feet x 0.3048^{1} 
= meters 
1 yard 
= 0.9 meter 
yards x 0.9144^{1} 
= meters 
1 mile 
= 1.6 kilometers 
miles x 1.60934 
= kilometers 
1 square inch 
= 6.5 sq. centimeters 
square inches x 6.4516^{1} 
= 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 hectare^{2} 
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 liter^{2} 
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 hectare^{2} 
= 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 liter^{2} 
= 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 unit^{1} 


QUANTITY 
NAME OF UNIT 
SYMBOL 
length 
meter 
m 
area 
square meter 
square m, or m^{2} 

are (100 square meters) 
a 
volume 
cubic meter 
cubic m, or m^{3} 

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 
10^{18} = 
1,000,000,000,000,000,000 

peta 
P 
10^{15} = 
1,000,000,000,000,000 

tera 
T 
10^{12} = 
1,000,000,000,000 

giga 
G 
10^{9} = 
1,000,000,000 

mega 
M 
10^{6} = 
1,000,000 
megaton (Mt) 
kilo 
k 
10^{3} = 
1,000 
kilometer (km) 
hecto, hect 
h 
10^{2} = 
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 (footpoundsecond, 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 acreft 
= 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 cwt^{1} 

1 long ton (British) 
= 1.12 short tons 
= 2,240 lbs 
= 22.4 short cwt^{1} 

1 short cwt^{1} (US) 
= 0.05 short ton 
= 100 lbs 


1 long cwt^{1} (British) 
= 0.05 long ton 
= 112 lbs 


1 stone (person) 
= 0.14 short cwt^{1} 
= 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 107 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 1.8^{2} 
°Celsius 
into 
°Fahrenheit 
multiply by 1.8, add 32^{2} 
°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 EQUIVALENTS^{1} 
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 = 1^{1}/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 = 2^{1}/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 
2^{1}/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 twocard combinations in a 52card 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 fivecard combinations on a single deal (52card 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 twodie totals 





TWODIE 
NUMBER OF 
PROBABILITY 
TWODIE 
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 
100^{1} 
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 (4.529.9 g; 
cubic cubit (0.14 cubic m; 


0.161.05 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 
kus^{2} (530 mm; 20.9 in) 
mina (640978 g; 
ka (99102 cubic mm; 


2334 oz) 
3.94.0 cubic in) 

foot (23 kus) 
shekel 
gur(300 ka) 

shusi (^{1}/30 us) 


Hebrew^{3} 

sacred mina (60 shekels) 
bat^{4} 


sacred talent (3,000 shekels, or 
hin 


50 sacred minas) 
log 
CULTURE 
LENGTH 
WEIGHT 
LIQUID 
Hebrew^{3} 

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) 


Chinese^{5} 
chih (25 cm; 9.8 in) chang (3 m; 9.8 ft) 
shih, or tan (60 kg; 132 lb) 

^{1}Measures given below the cubic cubit run from small to large. ^{2}Also called the Babylonian cubit. ^{3}The 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. ^{4}Volumes are not definitely known but are listed from largest to smallest. ^{5}The 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 (221210/09 bc), fixed the basic units given here.
Roman Numerals
Seven numeralcharacters 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.
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 
10^{9} 
9 
trillion 
10^{12} 
12 
quadrillion 
10^{15} 
15 
quintillion 
10^{18} 
18 
sextillion 
10^{21} 
21 
septillion 
10^{24} 
24 
octillion 
10^{27} 
27 
nonillion 
10^{30} 
30 
decillion 
10^{33} 
33 
undecillion 
10^{36} 
36 
duodecillion 
10^{39} 
39 
tredecillion 
1042 
42 
quattuordecillion 
10^{45} 
45 
quindecillion 
10^{48} 
48 
sexdecillion 
10^{51} 
51 
septendecillion 
10^{54} 
54 
octodecillion 
10^{57} 
57 
novemdecillion 
1060 
60 
vigintillion 
10^{63} 
63 
googol 
10^{100} 
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 
_{10}114 
114 
vigintillion 
10120 
120 
centillion 
_{10}600 
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 