Orders of magnitude (numbers)

This list compares various sizes of positive numbers, including counts of things, dimensionless numbers and probabilities.
Smaller than 10^{36}
10^{36}
10^{33}
10^{30}
10^{27}
10^{24}
ISO: yocto  y
10^{21}
ISO: zepto  z
10^{18}
ISO: atto  a
10^{15}
ISO: femto  f
10^{12}
One trillionth (American), One billionth (British)
ISO: pico  p
 Math: Roughly the chances of getting heads 40 times in a row on a fair coin.
10^{9}
(0.000 000 001; short scale: one billionth; long scale: one milliardth)
ISO: nano  n
 Math  Lottery: The odds of winning the Grand Prize (matching all 6 numbers) in the US Powerball Multistate Lottery, with a single ticket, under the rules as at 2003, are 120,526,770 to 1 against, for a probability of 8 × 10^{9}.
 Math  Lottery: The odds of winning the Jackpot (matching the 6 main numbers) in the UK National Lottery, with a single ticket, under the rules as at 2003, are 13,983,816 to 1 against, for a probability of 7 × 10^{8}.
10^{6}
(0.000 001; one millionth)
ISO: micro  prefix Greek letter mu
 Math  Poker: The odds of being dealt a royal flush in poker are 649,739 to 1 against, for a probability of 1.5 × 10^{6}
 Math  Poker: The odds of being dealt a straight flush (other than a royal flush) in poker are 72,192 to 1 against, for a probability of 1.4 × 10^{5}
 Math  Poker: The odds of being dealt a four of a kind in poker are 4,164 to 1 against, for a probability of 2.4 × 10^{4}
10^{3}
(0.001; one thousandth)
ISO: milli  m
 Math  Poker: The odds of being dealt a full house in poker are 693 to 1 against, for a probability of 1.4 × 10^{3}
 Math  Poker: The odds of being dealt a flush in poker are 508 to 1 against, for a probability of 1.9 × 10^{3}
 Math  Poker: The odds of being dealt a straight in poker are 254 to 1 against, for a probability of 4 × 10^{3}
 Phys: α = 0.007 297 352 533(27), the fine structure constant
10^{2}
(0.01; one hundredth)
 BioMed  HIV: About 1.2% of all 1549 yearold humans were infected with HIV at the end of 2001
 Math  Lottery: The odds of winning any prize in the UK National Lottery, with a single ticket, under the rules as at 2003, are 54 to 1 against, for a probability of about 0.018 (1.8%)
 Math  Poker: The odds of being dealt a three of a kind in poker are 46 to 1 against, for a probability of 0.021 (2.1%)
 Math  Lottery: The odds of winning any prize in the US Powerball Multistate Lottery, with a single ticket, under the rules as at 2003, are 36.06 to 1 against, for a probability of 0.028 (2.8%)
 Math  Poker: The odds of being dealt two pair in poker are 20 to 1 against, for a probability of 0.048 (4.8%).
10^{1}
(0.1; one tenth)
ISO: deci  d
 Math  Poker: The odds of being dealt only one pair in poker are about 5 to 2 against (2.37 to 1), for a probability of 0.42 (42%).
 Math  Poker: The odds of being dealt no pair in poker are nearly 1 to 2, for a probability of about 0.5 (50%)
10^{0}
(1; one)
 Math: φ ≈ 1.6180339887, the golden ratio
 Math: e ≈ 2.718281828459, the base of the natural logarithm
 Math: π ≈ 3.14159265358979, the ratio of a circle's diameter to its circumference
 BioMed: 7 ± 2, in cognitive science, George A. Miller's estimate of the number of objects that can be simultaneously thought of by the human mind
 Astro: nine planets in the solar system
10^{1}
(10; ten)
ISO: deca  da
 BioMed: there are 10 fingers on a pair of human hands
 Sport: In Olympic basketball, the roster limit for a team is 12 (and they are limited to wearing numbers 4 through 15).
 Lang: there are 26 letters in the Latin alphabet
 Sport: In NCAA basketball, players are not to wear digits above 5, and they are limited to one or two digits, making 42 distinct combinations (although 01, 02, 03, 04, and 05 typically aren't used). Since the roster limit is typically around 12, this doesn't present that much of a problem.
 Lit: 42, The Answer to Life, the Universe, and Everything.
10^{2}
(100; hundred)
ISO: hecto  h
 Sport: In North American professional sports, players typically wear uniform numbers from 1 to 99. In some sports, 0 and 00 are also allowed, making 101 different combinations.
 Pol: There are 100 Senators in the United States Senate.
 Comp: There are 128 characters in the ASCII character set.
 Geo: There were 191 member states of the United Nations as of 2003.
 Lit: 451 degrees Fahrenheit is the ignition temperature of paper. Therefore, Ray Bradbury titled his dystopian novel about book burnings Fahrenheit 451.
10^{3}
(1 000; thousand)
ISO: kilo  k
 Lang: 20003000 letters on a typical typed page of text
 BioMed: the DNA of the simplest viruses has some 5000 base pairs.
10^{4}
(10 000; ten thousand)
 BioMed: Each neuron in the human brain is estimated to connect to 10,000 others
 Lang: There are 20,000  40,000 distinct Chinese characters, depending on how you count them
 BioMed: Each human being is estimated to have 30,000 to 40,000 genes
 Records: As of July 2004, the largest number of decimal places of π that have been recited from memory  > 42000
10^{5}
(100 000; one hundred thousand)
 BioMed  Hairs on a head: The average human head has about 100,000150,000 hairs
 Lang: 267,000 words in James Joyce's Ulysses
 Geo: 338,200 population of the London Borough of Croydon in 1998
 Lang  English words: The New Oxford Dictionary of English claims to contain 350,000 definitions for English words
 Math: 365,596 solutions to nQueens Problem for n = 14
 Lang: 564,000 words in War and Peace
 Info: As of Juny 2005, there are approximately 600 000 articles in Wikipedia
 Info: The FreeDB database has around 1 750 000 (http://freedb.org/freedb_stats_server.php) entries as of Juny 2005
10^{6}
(1 000 000; 1 million)
ISO: mega  M
 Geo/Comp  Geographic places: The NIMA GEOnet Names Server contains approximately 3.88 million named geographical features outside the United States, with 5.34 million names. The USGS Geographic Names Information System claims to have almost 2 million physical and cultural geographic features within the United States.
 BioMed  Species: The World Resources Institute claims that approximately 1.4 million species have been named, out of an unknown number of total species (estimates range between 2 and 100 million species).
 Math  Chess: There are 2 279 184 solutions to nQueens Problem for n = 15
 Math  Playing cards: There are 2 598 960 different 5card poker hands that can be dealt from a standard 52card deck.
 Info  Web sites: as of July 2003, the Netcraft web survey estimates that there are 42 million distinct web sites
 Info  Books: The British Library claims that it holds over 150 million items. The Library of Congress claims that it holds approximately 119 million items. See Gutenberg galaxy
 Math: 14,772,512 solutions to nQueens Problem for n = 16
 Math: 95,815,104 solutions to nQueens Problem for n = 17
 Geo: approx. 402,000,000 native speakers of English
10^{9}
(1 000 000 000; short scale: 1 billion; long scale: 1 milliard)
ISO: giga  G
 Astro  Cataloged stars: The Guide Star Catalog II has entries on 998,402,801 distinct astronomical objects
 Comp  Computational limit of a 32bit CPU: 2 147 483 647 is equal to 2^{31}1, and as such is the largest number which can fit into a signed (two's complement) 32bit integer on a computer, thus marking the upper computational limit of a 32bit CPU such as Intel's Pentiumclass computer chips.
 BioMed  Base pairs in the genome: approximately 3×10^{9} base pairs in the human genome
 Geo  Living human beings: approximately 6.3×10^{9} human beings living as of mid 2003
 Comp  Web pages: approximately 8 × 10^{9} web pages indexed by Google as of 2004
 Astro  Observable galaxies: between 1×10^{10} and 8×10^{10} galaxies in the observable (as of 2003) Universe
 BioMed  Bacteria in the human body: there are roughly 10^{10} bacteria in the human oral cavity [1] (http://science.nasa.gov/newhome/headlines/ast01sep98_1.htm)
 BioMed  Neurons in the brain: approximately 10^{11} neurons in the human brain
 Astro  Stars in our Galaxy: approximately 4 × 10^{11} stars in the Milky Way galaxy
 Geo  India: 1,065,000,000  Approximate population of India in 2003
 Geo  China: 1,300,000,000  Approximate population of the People's Republic of China in 2004.
 Geo  World population: 6,378,000,000  Estimated total midyear population for the world in 2004.
 Math: 4,294,967,296  smallest number of the form (2^(2^n)) that does not produce a prime number when 1 is added.
 Comp: 4,294,967,296  the number of bytes in 4 gigabytes; in computation, the 32bit computers can directly access 2^{32} pieces of address space, this leads directly to the 4 gigabyte limit on main memory.
 Comp: 4,294,967,296  total number of CMYK colors possible when using 8 bit integers for each color component. However, virtually unlimited colors are possible by using floats from 0 to 1 as color components, so this limit is less important than it might seem.
 Math: 2,147,483,647 is a Mersenne prime and a Zsigmondy number
 Math: 275,305,224 is the number of 5x5 magic squares, not counting rotations and reflections. This result was found in 1973 by Richard Schroeppel. It is the third 91768409gonal number.
10^{12}
(1 000 000 000 000; short scale: 1 trillion; long scale: 1 billion)
ISO: tera  T
 BioMed  Bacteria on the human body: the surface of the human body houses roughly 10^{12} bacteria [2] (http://science.nasa.gov/newhome/headlines/ast01sep98_1.htm)
 BioMed  Cells in the human body: the human body consists of roughly 10^{14} cells
 Math  Known digits of pi: As of 2002, the number of known digits of pi was 1 241 100 000 000
10^{15}
(1 000 000 000 000 000; short scale: 1 quadrillion; long scale: 1 billiard)
ISO: peta  P
 BioMed  Bacteria in the human body: there are roughly 10^{15} bacteria in the human body ([3] (http://science.nasa.gov/newhome/headlines/ast01sep98_1.htm) speaks of 10^{14})
10^{18}
(1 000 000 000 000 000 000; short scale: 1 quintillion; long scale: 1 trillion)
ISO: exa  E
 BioMed  Insects: It has been estimated that the insect population of the Earth comprises roughly 10^{18} insects.
 Math  Rubik's Cube: There are 4.3 × 10^{19} different positions of a Rubik's Cube
10^{21}
(1 000 000 000 000 000 000 000; see names of large numbers for naming of this and larger numbers)
ISO: zetta  Z
 Geo  Grains of sand: all the world's beaches put together hold roughly 10^{23} grains of sand. [4] (http://astronomy.swin.edu.au/staff/gmackie/billions.html)
 Astro  Stars: 70 sextillion, was recently given by Australian astronomers as the number of stars visible from Earth by Telescope. It could also be called 70 million trillion or 70 billion billion.
 Astro  Stars in the observable universe: there are very approximately estimated to be 7 × 10^{22} stars in the observable universe, based on galaxy counts and star estimates: [5] (http://www.rednova.com/news/stories/1/2003/07/22/story004.html)
 Chem: there are roughly 6.022 × 10^{23} molecules in one mole of any substance (Avogadro's number)
10^{24}
ISO: yotta  Y
10^{27}
 BioMed  Atoms in the human body: the average human body contains roughly 7×10^{27} atoms, see [6] (http://education.jlab.org/qa/mathatom_04.html)
10^{30}
10^{33}
10^{36}
Larger than 10^{36}
 Math: The EddingtonDirac number is roughly 10^{40}.
 Geo: About 10^{47} molecules of water on Earth
 Geo: Earth consists of roughly 10^{50} atoms
 Astro  Fundamental particles in the observable universe: various sources estimate the total number of fundamental particles in the observable universe in the range 10^{80} to 10^{85}. However, these estimates are best regarded as guesswork.
 Math: 10^{100}, a googol
 Math  Hist: Asankhyeya is equal to 100^{140} in Ancient India
 Math  Go: 10^{365}, number of possible moves in the game of Go
 Math: 10^{7,816,229}, order of magnitude of largest known prime number, as of February 2005. The exact value of that record prime is 2^{25,964,951}  1. Proving prime numbers with a thousand to several tens of thousands of decimal digits, depending on special form, can be done in minutes on modern computers.
 Math  Hist: 10^{80,000,000,000,000,000}, largest named number in Archimedes' Sand Reckoner
 Math: 10^{googol} (<math>10^{10^{100}}<math>), a googolplex
 Math: <math>10^{\,\!10^{10^{34}}}<math>, order of magnitude of an upper bound that occurred in a proof of Skewes
 Math: <math>10^{\,\!10^{10^{1000}}}<math>, order of magnitude of another upper bound in a proof of Skewes
 Math: Graham's number, probably the largest number seriously used in a mathematical proof, can be written as <math>f^{64}(4)<math>; representation in powers of 10 would be impractical, for the definition of the number see the main article about it
Note: To correctly interpret the last few entries, keep in mind that exponentiation is performed from right to left. For example,
 <math>10^{\,\!10^{100}} \mbox{ means } 10^{\,\!(10^{100})}<math>
See also
External links
 Seth Lloyd's paper Computational capacity of the universe (http://arxiv.org/abs/quantph/0110141) provides a number of interesting dimensionless quantitiesko:수의 비교