# Mathematical constants

| Constant | Symbol | Value | Decimal expansion | Year | Year described | Rational | Algebraic | Period | Exponential period |
| --- | --- | ---: | --- | ---: | --- | --- | --- | --- | --- |
| Pi | π | 3.141592653589793 | 3.14159 26535 89793 23846 | -1900 | 1900 to 1600 BCE | false | false | true | true |
| Tau | τ | 6.283185307179586 | 6.28318 53071 79586 47692 | -1900 | 1900 to 1600 BCE | false | false | true | true |
| Square root of 2, Pythagoras constant | √2 | 1.4142135623730951 | 1.41421 35623 73095 04880 | -1800 | 1800 to 1600 BCE | false | true | true | true |
| Square root of 3, Theodorus' constant | √3 | 1.7320508075688772 | 1.73205 08075 68877 29352 | -465 | 465 to 398 BCE | false | true | true | true |
| Zero | 0 | 0 | 0 | -300 | 300 to 100 BCE | true | true | true | true |
| Phi, Golden ratio | φ or ϕ | 1.618033988749895 | 1.61803 39887 49894 84820 | -300 | ~300 BCE | false | true | true | true |
| Silver ratio | σ | 2.414213562373095 | 2.41421 35623 73095 04880 | -300 | ~300 BCE | false | true | true | true |
| Negative one | −1 | -1 | −1 | -300 | 300 to 200 BCE | true | true | true | true |
| Cube root of 2, Delian constant | ³√2 | 1.2599210498948732 | 1.25992 10498 94873 16476 | 46 | 46 to 120 CE | false | true | true | true |
| Imaginary unit | i |  | 0 + 1i | 1501 | 1501 to 1576 | false | true | true | true |
| Connective constant for the hexagonal lattice | μ | 1.8477590650225735 | 1.84775 90650 22573 51225 | 1593 | 1593 | false | true | true | true |
| Kepler–Bouwkamp constant | K^′ | 0.1149420448532962 | 0.11494 20448 53296 20070 | 1596 | 1596 |  |  |  |  |
| Wallis's constant |  | 2.0945514815423265 | 2.09455 14815 42326 59148 | 1616 | 1616 to 1703 | false | true | true | true |
| Euler's number | e | 2.718281828459045 | 2.71828 18284 59045 23536 | 1618 | 1618 | false | false |  | true |
| Natural logarithm of 2 | ln2 | 0.6931471805599453 | 0.69314 71805 59945 30941 | 1619 | 1619 & 1668 | false | false | true | true |
| Sophomore's dream second constant | I₂ | 1.2912859970626636 | 1.29128 59970 62663 54040 | 1697 | 1697 |  |  |  |  |
| Lemniscate constant | ϖ | 2.6220575542921196 | 2.62205 75542 92119 81046 | 1718 | 1718 to 1798 | false | false | true | true |
| Basel's number | ζ(2) | 1.6449340668482264 | 1.64493 40668 48226 43647 | 1734 | 1734 | false | false | true | true |
| Euler's constant | γ | 0.5772156649015329 | 0.57721 56649 01532 86060 | 1735 | 1735 |  |  |  | true |
| Erdős–Borwein constant | E | 1.6066951524152917 | 1.60669 51524 15291 76378 | 1749 | 1749 | false |  |  |  |
| Square super-root of 2 | √2ₛ | 1.5596104694623694 | 1.55961 04694 62369 34997 | 1758 | 1758 & 1783 | false | false |  |  |
| Omega constant | Ω | 0.5671432904097838 | 0.56714 32904 09783 87299 | 1758 | 1758 & 1783 | false | false |  |  |
| Apéry's constant | ζ(3) | 1.2020569031595942 | 1.20205 69031 59594 28539 | 1780 | 1780 | false |  | true | true |
| Laplace limit |  | 0.6627434193491816 | 0.66274 34193 49181 58097 | 1782 | ~1782 | false | false |  |  |
| Soldner constant | μ | 1.451369234883381 | 1.45136 92348 83381 05028 | 1792 | 1792 |  |  |  |  |
| Gauss's constant | G | 0.8346268416740732 | 0.83462 68416 74073 18628 | 1799 | 1799 | false | false |  | true |
| Second Hermite constant | γ₂ | 1.1547005383792515 | 1.15470 05383 79251 52901 | 1822 | 1822 to 1901 | false | true | true | true |
| First continued fraction constant | C₁ | 0.697774657964008 | 0.69777 46579 64007 98201 | 1855 | 1855 | false | false |  |  |
| Ramanujan's constant |  | 262537412640768740 | 262 53741 26407 68743 .99999 99999 99250 073 | 1859 | 1859 | false | false |  |  |
| Glaisher–Kinkelin constant | A | 1.2824271291006226 | 1.28242 71291 00622 63687 | 1860 | 1860 |  |  |  |  |
| Catalan's constant | G | 0.915965594177219 | 0.91596 55941 77219 01505 | 1864 | 1864 |  |  | true | true |
| Dottie number | D | 0.7390851332151607 | 0.73908 51332 15160 64165 | 1865 | 1865 | false | false |  |  |
| Meissel–Mertens constant | M | 0.26149721284764277 | 0.26149 72128 47642 78375 | 1866 | 1866 & 1873 |  |  |  |  |
| Cahen's constant | C | 0.643410546288338 | 0.64341 05462 88338 02618 | 1891 | 1891 | false | false |  |  |
| Gelfond's constant | e^π | 23.14069263277927 | 23.14069 26327 79269 0057 | 1900 | 1900 | false | false |  |  |
| Totient summatory constant |  | 1.3397841535743473 | 1.33978 41535 74347 24659 | 1900 | 1900 |  |  |  |  |
| Second Favard constant | K₂ | 1.2337005501361697 | 1.23370 05501 36169 82735 | 1902 | 1902 to 1965 | false | false | true | true |
| Golden angle | g | 2.3999632297286535 | 2.39996 32297 28653 32223 | 1907 | 1907 | false | false | true | true |
| Sierpiński's constant | K | 2.5849817595792532 | 2.58498 17595 79253 21706 | 1907 | 1907 |  |  |  |  |
| Landau–Ramanujan constant | K | 0.7642236535892206 | 0.76422 36535 89220 66299 | 1908 | 1908 |  |  |  |  |
| First Nielsen–Ramanujan constant | a₁ | 0.8224670334241132 | 0.82246 70334 24113 21823 | 1909 | 1909 | false | false | true | true |
| Gieseking constant | V | 1.0149416064096537 | 1.01494 16064 09653 62502 | 1912 | 1912 |  |  | true | true |
| Bernstein's constant | β | 0.2801694990238691 | 0.28016 94990 23869 13303 | 1913 | 1913 |  |  |  |  |
| Tribonacci constant | ρ | 1.8392867552141612 | 1.83928 67552 14161 13255 | 1914 | 1914 to 1963 | false | true | true | true |
| Kempner series's value |  | 22.92067661926415 | 22.92067 66192 64150 34816 | 1914 | 1914 |  |  |  |  |
| Kempner number | κ | 0.8164215090218931 | 0.81642 15090 21893 14370 | 1916 | 1916 | false | false |  |  |
| Brun's constant | B₂ | 1.902160583104 | ≈ 1.90216 05831 04 | 1919 | 1919 |  |  |  |  |
| Twin primes constant | C₂ | 0.6601618158468696 | 0.66016 18158 46869 57392 | 1922 | 1922 |  |  |  |  |
| Plastic ratio | ρ | 1.324717957244746 | 1.32471 79572 44746 02596 | 1924 | 1924 | false | true | true | true |
| Bloch's constant | B |  | 0.4332≤B≤0.4719 | 1925 | 1925 |  |  |  |  |
| Z score for the 97.5 percentile point | z_.975 | 1.9599639845400543 | 1.95996 39845 40054 23552 | 1925 | 1925 |  |  |  |  |
| Landau's constant | L |  | 0.5<L≤0.54326 | 1929 | 1929 |  |  |  |  |
| Landau's third constant | A |  | 0.5<A≤0.7853 | 1929 | 1929 |  |  |  |  |
| Prouhet–Thue–Morse constant | τ | 0.4124540336401076 | 0.41245 40336 40107 59778 | 1929 | 1929 | false | false |  |  |
| Golomb–Dickman constant | λ | 0.6243299885435508 | 0.62432 99885 43550 87099 | 1930 | 1930 & 1964 |  |  |  |  |
| Constant related to the asymptotic behavior of Lebesgue constants | c | 0.9894312738311469 | 0.98943 12738 31146 95174 | 1930 | 1930 |  |  |  |  |
| Feller–Tornier constant | 𝒞_FT | 0.6613170494696223 | 0.66131 70494 69622 33528 | 1932 | 1932 |  |  |  |  |
| Base 10 Champernowne constant | C₁₀ | 0.12345678910111213 | 0.12345 67891 01112 13141 | 1933 | 1933 | false | false |  |  |
| Salem constant | σ₁₀ | 1.1762808182599176 | 1.17628 08182 59917 50654 | 1933 | 1933 | false | true | true | true |
| Khinchin's constant | K₀ | 2.6854520010653062 | 2.68545 20010 65306 44530 | 1934 | 1934 |  |  |  |  |
| Lévy's constant (1) | β | 1.1865691104156255 | 1.18656 91104 15625 45282 | 1935 | 1935 |  |  |  |  |
| Lévy's constant (2) | e^β | 3.2758229187218113 | 3.27582 29187 21811 15978 | 1936 | 1936 |  |  |  |  |
| Linnik's constant | L |  | L ≤ 3.99 | 1944 | 1944 |  |  |  |  |
| Copeland–Erdős constant | 𝒞_CE | 0.23571113171923294 | 0.23571 11317 19232 93137 | 1946 | 1946 | false |  |  |  |
| Mills' constant | A | 1.3063778838630806 | 1.30637 78838 63080 69046 | 1947 | 1947 | false |  |  |  |
| Third continued fraction constant | C₃ | 1.525135276160981 | 1.52513 52761 60981 20908 | 1948 | 1948 |  |  |  |  |
| de Bruijn–Newman constant | Λ |  | 0≤Λ≤0.2 | 1950 | 1950 |  |  |  |  |
| Porter's constant | C | 1.4670780794339755 | 1.46707 80794 33975 47289 | 1961 | 1961 |  |  |  |  |
| Lochs constant | L | 0.9702701143920339 | 0.97027 01143 92033 92574 | 1964 | 1964 |  |  |  |  |
| Infinite tetration of imaginary unit |  |  | 0.438283 + 0.360592i | 1966 | 1966 | false |  |  |  |
| DeVicci's tesseract constant |  | 1.0074347568842794 | 1.00743 47568 84279 37609 | 1966 | 1966 | false | true | true | true |
| Lieb's square ice constant |  | 1.539600717839002 | 1.53960 07178 39002 03869 | 1967 | 1967 | false | true | true | true |
| Growth rate constant of fixed polyomino (Klarner's constant) | λ₂ |  | 4.00253 < λ2 < 4.5252 | 1967 | 1967 |  |  |  |  |
| Growth rate constant of fixed polycube | λ₃ |  | 6.3795 < λ3 < 9.3835 | 1967 | 1967 |  |  |  |  |
| Niven's constant | C | 1.7052111401053678 | 1.70521 11401 05367 76428 | 1969 | 1969 |  |  |  |  |
| Stephens' constant | C_S | 0.5759599688929454 | 0.57595 99688 92945 43964 | 1969 | 1969 |  |  |  |  |
| Regular paperfolding sequence | P | 0.8507361882018672 | 0.85073 61882 01867 26036 | 1970 | 1970 | false | false |  |  |
| Reciprocal Fibonacci constant | ψ | 3.3598856662431777 | 3.35988 56662 43177 55317 | 1974 | 1974 | false |  |  |  |
| Chvátal–Sankoff constant for the binary alphabet | γ₂ |  | 0.788071≤γ2≤0.826280 | 1975 | 1975 |  |  |  |  |
| Feigenbaum constant δ | δ | 4.66920160910299 | 4.66920 16091 02990 67185 | 1975 | 1975 |  |  |  |  |
| Chaitin's constants | Ω |  | In general they are uncomputables; one such number is 0.00787 49969 97812 3844. | 1975 | 1975 | false | false | false | false |
| Freiman's constant | F | 4.527829566160879 | 4.52782 95661 60879 14088 | 1975 | 1975 | false | true | true | true |
| Robbins constant | Δ(3) | 0.6617071822671763 | 0.66170 71822 67176 23515 | 1977 | 1977 | false | false | true | true |
| Fransén–Robinson constant | F | 2.8077702420285195 | 2.80777 02420 28519 36522 | 1978 | 1978 |  |  |  |  |
| Feigenbaum constant α | α | 2.5029078750958926 | 2.50290 78750 95892 82228 | 1979 | 1979 |  |  |  |  |
| Irrational number from Moser–de Bruijn sequence | α | 3.30033 | 3.30033 00000 00000 33003 | 1982 | 1982 | false | false |  |  |
| Second du Bois-Reymond constant | C₂ | 0.19452804946532512 | 0.19452 80494 65325 11361 | 1983 | 1983 | false | false |  | true |
| Erdős–Tenenbaum–Ford constant | δ | 0.0860713320559342 | 0.08607 13320 55934 20688 | 1984 | 1984 |  |  |  |  |
| Conway's constant | λ | 1.3035772690342964 | 1.30357 72690 34296 39125 | 1987 | 1987 | false | true | true | true |
| Hard hexagon entropy constant | κ(1) | 1.3954859724793027 | 1.39548 59724 79302 73522 | 1988 | 1988 | false | true | true | true |
| Hafner–Sarnak–McCurley constant | σ | 0.353236371854996 | 0.35323 63718 54995 98454 | 1991 | 1991 |  |  |  |  |
| Backhouse's constant | B | 1.4560749485826896 | 1.45607 49485 82689 67139 | 1995 | 1995 |  |  |  |  |
| Viswanath constant | V | 1.1319882487943 | 1.13198 82487 943 | 1997 | 1997 |  |  |  |  |
| Komornik–Loreti constant | q | 1.787231650182966 | 1.78723 16501 82965 93301 | 1998 | 1998 | false | false |  |  |
| Embree–Trefethen constant | β^⋆ | 0.70258 | 0.70258 | 1999 | 1999 |  |  |  |  |
| Heath-Brown–Moroz constant | C | 0.001317641154853178 | 0.00131 76411 54853 17810 | 1999 | 1999 |  |  |  |  |
| MRB constant | S | 0.18785964246206713 | 0.18785 96424 62067 12024 | 1999 | 1999 |  |  |  |  |
| Prime constant | ρ | 0.41468250985111166 | 0.41468 25098 51111 66024 | 1999 | 1999 | false |  |  |  |
| Somos' quadratic recurrence constant | σ | 1.6616879496335941 | 1.66168 79496 33594 12129 | 1999 | 1999 |  |  |  |  |
| Foias constant | α | 1.1874523511265012 | 1.18745 23511 26501 05459 | 2000 | 2000 |  |  |  |  |
| One | 1 | 1 | 1 |  | Prehistory | true | true | true | true |
| Two | 2 | 2 | 2 |  | Prehistory | true | true | true | true |
| One half | 1/2 | 0.5 | 0.5 |  | Prehistory | true | true | true | true |
| Square root of 5 | √5 | 2.23606797749979 | 2.23606 79774 99789 69640 |  |  | false | true | true | true |
| Cube root of 3 | ³√3 | 1.4422495703074083 | 1.44224 95703 07408 38232 |  |  | false | true | true | true |
| Twelfth root of 2 | ¹²√2 | 1.0594630943592953 | 1.05946 30943 59295 26456 |  |  | false | true | true | true |
| Supergolden ratio | ψ | 1.465571231876768 | 1.46557 12318 76768 02665 |  |  | false | true | true | true |
| Liouville's constant | L | 0.110001 | 0.11000 10000 00000 00000 0001 |  | Before 1844 | false | false |  |  |
| Universal parabolic constant | P | 2.295587149392638 | 2.29558 71493 92638 07403 |  | Before 1891 | false | false | true | true |
| Gelfond–Schneider constant | 2^(√2) | 2.665144142690225 | 2.66514 41426 90225 18865 |  | Before 1902 | false | false |  |  |
| Gompertz constant | δ | 0.5963473623231941 | 0.59634 73623 23194 07434 |  | Before 1948 |  |  |  | true |
| Van der Pauw constant | π/ln2 | 4.532360141827194 | 4.53236 01418 27193 80962 |  | Before 1958 | false |  |  |  |
| Magic angle | θₘ | 0.9553166181245093 | 0.95531 66181 245092 78163 |  | Before 1959 | false | false | true | true |
| Artin's constant | C_Artin | 0.37395581361920227 | 0.37395 58136 19202 28805 |  | Before 1961 |  |  |  |  |
| Weierstrass constant |  | 0.47494937998792064 | 0.47494 93799 87920 65033 |  | Before 1978 | false | false |  |  |
| Beam detection constant | L |  | 3.1415926535 ≤ L ≤ 4.7998 |  | Before 1980 |  |  |  |  |
| Natural density constant of abundant numbers | d_A |  | 0.2476171 < dA < 0.2476475 |  | Before 1998 |  |  |  |  |
| Logarithmic capacity of the unit disk |  | 0.5901702995080481 | 0.59017 02995 08048 11302 |  | Before 2003 | false | false |  | true |
| Taniguchi constant | C_T | 0.6782344919173919 | 0.67823 44919 17391 97803 |  | Before 2005 |  |  |  |  |

Source: https://aidb.si/d/mathematical-constants — Table from the Wikipedia article “List of mathematical constants” (CC BY-SA 4.0); decimal expansions there are cited to MathWorld and the OEIS.