Orders of magnitude (numbers)

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Orders of magnitude
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Conversion of units
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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 10^-21 10^-18 10^-15 10^-12 10^-9 10^-6 10^-3 10^-2 10^-1
10⁰ 10¹ 10² 10³ 10⁴ 10⁵ 10⁶ 10⁹ 10¹² 10¹⁵ 10¹⁸ 10²¹ 10²⁴ 10²⁷ 10³⁰ 10³³ 10³⁶
10³⁹ to 10¹⁰⁰ Larger than 10¹⁰⁰ Top of page — See also — External links

Smaller than 10^-36

Comp - IEEE floating-point number 5×10^-324 is approximately equal to the smallest positive non-zero value that can be represented by a double-precision IEEE floating-point value.
Comp - IEEE floating-point number 1.4012985×10^-45 is approximately equal to the smallest positive non-zero value that can be represented by a single-precision IEEE floating-point value.

10^-36

(0.000000000000000000000000000000000001)

10^-33

(0.000000000000000000000000000000001)

10^-30

(0.000000000000000000000000000001)

10^-27

(0.000000000000000000000000001)

10^-24

(0.000000000000000000000001)

ISO: yocto - y

10^-21

(0.000000000000000000001)

ISO: zepto - z

10^-18

(0.000000000000000001)

ISO: atto - a

10^-15

(0.000000000000001)

ISO: femto - f

10^-12

(0.000000000001, short scale: One trillionth, long scale: One billionth)

ISO: pico - p

Mathematics: 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

Mathematics - 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 of 2003, are 120,526,770 to 1 against, for a probability of 8×10^-9.
Mathematics - 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 of 2003, are 13,983,816 to 1 against, for a probability of 7×10^-8.

10^-6

(0.000 001; one millionth)

ISO: micro - μ

Mathematics - 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
Mathematics - 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
Mathematics - 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

Mathematics - Poker: The odds of being dealt a full house in poker are 693 to 1 against, for a probability of 1.4 × 10^-3
Mathematics - Poker: The odds of being dealt a flush in poker are 508 to 1 against, for a probability of 1.9 × 10^-3
Mathematics - 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

Meaning in words: 3 orders of magnitude smaller.

10^-2

(0.01; one hundredth)

ISO: centi - c

BioMed - HIV: About 1.2% of all 15–49 year-old humans were infected with HIV at the end of 2001
Mathematics - Lottery: The odds of winning any prize in the UK National Lottery, with a single ticket, under the rules as of 2003, are 54 to 1 against, for a probability of about 0.018 (1.8%)
Mathematics - 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%)
Mathematics - Lottery: The odds of winning any prize in the US Powerball Multistate Lottery, with a single ticket, under the rules as of 2003, are 36.06 to 1 against, for a probability of 0.028 (2.8%)
Mathematics - Poker: The odds of being dealt two pair in poker are 20 to 1 against, for a probability of 0.048 (4.8%).
Comp - Time: 0.01 seconds is equal to a jiffie.

10^-1

(0.1; one tenth)

ISO: deci - d

Mathematics - 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%).
Mathematics - Poker: The odds of being dealt no pair in poker are nearly 1 to 2, for a probability of about 0.5 (50%)

10⁰

(1; one)

Mathematics: φ ≈ 1.6180339887, the golden ratio
Mathematics: e ≈ 2.718281828459, the base of the natural logarithm
Mathematics: 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 held in working memory
Astro: nine planets in the solar system

10¹

(10; ten)

ISO: deca - da

BioMed: there are 10 fingers on a pair of human hands
Mathematics: 17 the second and last Genocchi prime.
Lang: there are 26 letters in the Latin alphabet in the English language

10²

(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.
Pol: There are 120 members each in the Israeli Parliament (The Knesset) and the New Zealand House of Representatives.
Comp: There are 128 characters in the ASCII character set.
Pol There are 179 members in the Danish Parliament Folketinget.
Sport: A major-league baseball season has 162 games.
Geo: There were 192 member states of the United Nations as of 2006.

10³

(1 000; thousand)

ISO: kilo - k

Lang: 2000–3000 letters on a typical typed page of text
BioMed: the DNA of the simplest viruses has some 5000 base pairs.
Lang: There are about 6500 mutually unintelligible languages and dialects.

Meaning in words: 3 orders of magnitude greater.

10⁴

(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
Mathematics: 65537 is a Fermat prime

10⁵

(100 000; one hundred thousand)

BioMed - Hairs on a head: The average human head has about 100,000–150,000 hairs
Mathematics: 110,000 - The approximate number of entries on The On-Line Encyclopedia of Integer Sequences as of August 2005 [link]
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
Mathematics: 365,596 solutions to n-Queens Problem for n = 14
Lang: 564,000 words in War and Peace
Info: The FreeDB database has around [1 750 000] entries as of June 2005

10⁶

(1 000 000; 1 million)

ISO: mega - M

Info: Currently there are 2439462 articles and registered users in the English Wikipedia
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).
Mathematics - Chess: There are 2 279 184 solutions to n-Queens Problem for n = 15
Mathematics - Playing cards: There are 2 598 960 different 5-card poker hands that can be dealt from a standard 52-card 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
Mathematics: 14,772,512 solutions to n-Queens Problem for n = 16
Mathematics: 95,815,104 solutions to n-Queens Problem for n = 17
Mathematics: 215,000,000 - The approximate number of mathematical constants collected on the Plouffe's Inverter as of August 2005 [link]
Mathematics: 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 91768409-gonal number.
Geo: approx. 402,000,000 native speakers of English
Astro - Cataloged stars: The Guide Star Catalog II has entries on 998,402,801 distinct astronomical objects

10⁹

(1 000 000 000; short scale: 1 billion; long scale: 1 milliard)

ISO: giga - G

Comp - Computational limit of a 32-bit CPU: 2 147 483 647 is equal to 2³¹−1, and as such is the largest number which can fit into a signed (two's complement) 32-bit integer on a computer, thus marking the upper computational limit of a 32-bit CPU such as Intel's Pentium-class computer chips.
BioMed - Base pairs in the genome: approximately 3×10⁹ base pairs in the human genome
Comp - Web pages: approximately 8×10⁹ web pages indexed by Google as of 2004
Astro - Observable galaxies: as of 2003 there are between 1×10¹⁰ and 8×10¹⁰ galaxies in the observable Universe
BioMed - Bacteria in the human body: there are roughly 10¹⁰ bacteria in the human oral cavity [link]
BioMed - Neurons in the brain: approximately 10¹¹ neurons in the human brain
Astro - Stars in our Galaxy: approximately 4×10¹¹ 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 mid-year population for the world in 2004.
Mathematics: 4,294,967,296 - smallest number of the form (2^(2^n)) that does not produce a prime number when 1 is added (n=5).
Comp: 4,294,967,296 - the number of bytes in 4 gibibytes; in computation, the 32-bit computers can directly access 2³² pieces of address space, this leads directly to the 4 gigabyte limit on main memory.
Mathematics: 2,147,483,647 is a Mersenne prime.
Mathematics: 4,294,967,297 is a Fermat number and semiprime.
Mathematics: 27,704,267,971 and 27,704,267,977 are sexy primes.

10¹²

(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 10¹² bacteria [link]
Mathematics: 1.1 * 10¹² - The approximate number of known non-trivial zeros of Riemann zeta function as of August 2005 [link]
BioMed - Cells in the human body: the human body consists of roughly 10¹⁴ cells
Mathematics - Known digits of pi: As of 2002, the number of known digits of pi was 1 241 100 000 000

10¹⁵

(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 10¹⁵ bacteria in the human body ([link] speaks of 10¹⁴), the overwhelming majority in the intestinal tract

10¹⁸

(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 10¹⁸ insects.
Comp - Computational limit of a 64-bit CPU: 9.22×10¹⁸ is equal to 2⁶³-1, and as such is the largest number which can fit into a signed (two's complement) 64-bit integer on a computer.
Mathematics - Rubik's Cube: There are 4.3×10¹⁹ different positions of a Rubik's Cube

10²¹

(1 000 000 000 000 000 000 000; short scale: 1 sextillion; long scale: 1000 trillion)

ISO: zetta - Z

Geo - Grains of sand: all the world's beaches put together hold roughly 10²³ grains of sand. [link]
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. This estimate is based on galaxy counts and star estimates: [link]
Chem: there are roughly 6.022×10²³ molecules in one mole of any substance (Avogadro's number)

10²⁴

(1 000 000 000 000 000 000 000 000; short scale: 1 septillion; long scale: 1 quadrillion)

ISO: yotta - Y

Computing: Yottabyte (YB) is 10²⁴ bytes.
Mathematics: 146,361,946,186,458,562,560,000 (≈1.5×10²⁴) is the fifth unitary perfect number.
Mathematics: 2,833,419,889,721,787,128,217,599 (≈2.8×10²⁵) is a Woodall prime.

10²⁷

(1 000 000 000 000 000 000 000 000 000; short scale: 1 octillion; long scale: 1000 quadrillion)

BioMed - Atoms in the human body: the average human body contains roughly 7×10²⁷ atoms, see [link]
Mathematics - Poker: the number of unique combinations of hands and shared cards in a 10-player game of Texas Hold'em is approximately 2.117×10²⁸, see Poker probability (Texas hold 'em).

10³⁰

(1 000 000 000 000 000 000 000 000 000 000; short scale: 1 nonillion; long scale: 1 quintillion)

10³³

(1 000 000 000 000 000 000 000 000 000 000 000; short scale: 1 decillion; long scale: 1000 quintillion)

Mathematics: 1,298,074,214,633,706,835,075,030,044,377,087 (≈1.3×10³⁴) is a Carol prime

10³⁶

(1 000 000 000 000 000 000 000 000 000 000 000 000; short scale: 1 undecillion; long scale: 1 sextillion)

Comp - Address range of IPv6 (2¹²⁸) is approximately equal to 3.4×10³⁸, and is the theoretical maximum number of internet addresses that can be allocated under the IPv6 addressing system.
Comp - IEEE floating-point number 3.4028235×10³⁸ is approximately equal to the largest value that can be represented by a single-precision IEEE floating-point value.

10³⁹ to 10¹⁰⁰

See names of large numbers for the names of these and larger numbers.

Mathematics: 170,141,183,460,469,231,731,687,303,715,884,105,727 (≈1.7×10³⁹) is a double Mersenne prime
Cosmology: The Eddington-Dirac number is roughly 10⁴⁰.
Physics: [e^2/Gm^2 \,], the ratio of the electrical to the gravitational forces between two protons, is roughly 10⁴⁰.
Mathematics: 53,694,226,297,143,959,644,031,344,050,777,763,036,004,353 (≈5.4×10⁴⁴) is a Pierpont prime
Mathematics: 393,050,634,124,102,232,869,567,034,555,427,371,542,904,833 (≈3.9×10⁴⁵) is a Cullen prime
Geo: About 10⁴⁷ molecules of water on Earth
Geo: Earth consists of roughly 10⁵⁰ atoms
Mathematics: 359,334,085,968,622,831,041,960,188,598,043,661,065,388,726,959,079,837 (≈3.6×10⁵⁴) is a Bell prime
Cosmology: 8×10⁶⁰ is roughly the number of Planck time intervals since the universe is theorized to have been created in the Big Bang 13.7 ± 0.2 billion years ago
Mathematics: 709,601,635,082,267,320,966,424,084,955,776,789,770,864,725,643,996,885,415,676,682,297 (≈7×10⁶⁶) - The largest known prime factor found by ECM factorization as of August 2005 [link]
Mathematics - Cards: 52! = 80,658,175,170,943,878,571,660,636,856,403,766,975,289,505,440,883,277,824,000,000,000,000 (≈8×10⁶⁸) - the number of ways to order the cards in a 52-card deck.
Mathematics: 475,420,437,734,698,220,747,368,027,166,749,382,927,701,417,016,557,193,662,268,716,376,935,476,241 (≈4.8×10⁷²) is a Fibonacci prime
Astro - Fundamental particles in the observable universe: various sources estimate the total number of fundamental particles in the observable universe in the range 10⁸⁰ to 10⁸⁵. However, these estimates are best regarded as guesswork.
Mathematics: 10¹⁰⁰, a googol

Larger than 10¹⁰⁰

Chess: Shannon number, 10¹²⁰, an estimation of the game-tree complexity of chess
Mathematics - Hist: Asankhyeya is equal to 10¹⁴⁰ in Ancient India
Xiangqi: 10¹⁵⁰, an estimation of the game-tree complexity of xiangqi
Physics: 8×10¹²⁰, ratio of the mass-energy in the observable universe to the energy of a photon with a wavelength the size of the observable universe.
Physics: 4×10¹⁸⁵, approximate number of Planck volumes in the observable universe.
Comp - IEEE floating-point number 1.7976931348623157×10³⁰⁸ is approximately equal to the largest value that can be represented by a double-precision IEEE floating-point value.
Mathematics - Go: 10³⁶⁵, number of possible moves in the game of Go
Mathematics: 7068555 · 2¹²¹³⁰¹ − 1 is a Sophie Germain prime
Mathematics: 16869987339975 · 2¹⁷¹⁹⁶⁰ − 1 is a Chen prime
Mathematics: 16869987339975 · 2¹⁷¹⁹⁶⁰ ± 1 are twin primes
Mathematics: 34790!–1 is a factorial prime
Mathematics: 392113#+1 is a primorial prime
Mathematics: 10^9,152,051, order of magnitude of the largest known prime, as of December 2005. The exact value of that record prime is 2^30,402,457−1. 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.
Mathematics - Hist: 10^{80,000,000,000,000,000}, largest named number in Archimedes' Sand Reckoner
Mathematics: 10^googol ([10^}]), a googolplex
Mathematics: [10^}}], order of magnitude of an upper bound that occurred in a proof of Skewes
Mathematics: [10^}}], order of magnitude of another upper bound in a proof of Skewes
Mathematics: Moser's number should appear somewhere in this section, but is difficult to calculate
Mathematics: Graham's number, probably the largest number seriously used in a mathematical proof, can be written as [f^(4)]; 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,

[10^} \mbox 10^)}]

External links

Seth Lloyd's paper [Computational capacity of the universe] provides a number of interesting dimensionless quantities.

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Orders of magnitude (numbers)

Smaller than 10-36

10-36

10-33

10-30

10-27

10-24

10-21

10-18

10-15

10-12

10-9

10-6

10-3

10-2

10-1

100

101

102

103

104

105

106

109

1012

1015

1018

1021

1024

1027

1030

1033

1036

1039 to 10100

Larger than 10100

See also