List of mathematical constants
A mathematical constant is a number whose value is fixed by an unambiguous definition, often referred to by a symbol or by mathematicians' names to facilitate using it across multiple mathematical problems. For example, the constant π may be defined as the ratio of the length of a circle's circumference to its diameter. The following list includes a decimal expansion and set containing each number, ordered by year of discovery.
Explanations of the symbols in the right hand column can be found by clicking on them.
Antiquity
| Name | Symbol | Decimal Expansion | Formula | Year | Set |
| One | 1 | 1 | None | Prehistory | Natural number| |
| Two | 2 | 2 | Prehistory | Natural number| | |
| One half | 1/2 | 0.5 | Prehistory | Rational number| | |
| Pi | 3.14159 26535 89793 23846 | Ratio of a circle's circumference to its diameter. | 1900 to 1600 BCE | Transcendental number| | |
| Square root of 2, Pythagoras constant. | 1.41421 35623 73095 04880 | Positive root of | Algebraic number| | ||
| Square root of 3, Theodorus' constant | 1.73205 08075 68877 29352 | Positive root of | 465 to 398 BCE | Algebraic number| | |
| Square root of 5 | 2.23606 79774 99789 69640 | Positive root of | Algebraic number| | ||
| Phi, Golden ratio | 1.61803 39887 49894 84820 | Positive root of | ~300 BCE | Algebraic number| | |
| Zero | 0 | 0 | The additive identity: | 300-100 century BCE | Integer| |
| Negative one | -1 | -1 | 300-200 BCE | Integer| | |
| Cube root of 2 Delian Constant | 1.25992 10498 94873 16476 | Real root of | 46 -120 CE | Algebraic number| | |
| Cube root of 3 | 1.44224 95703 07408 38232 | Real root of |
Medieval and Early Modern
19th century
1900–1949
1950–1999
| Name | Symbol | Decimal Expansion | Formula | Year | Set |
| Van der Pauw constant | 4.53236 01418 27193 80962 | Before 1958 | |||
| Lochs constant | 0.97027 01143 92033 92574 | 1964 | |||
| Lieb's square ice constant | 1.53960 07178 39002 03869 | 1967 | Algebraic number| | ||
| Niven's constant | 1.70521 11401 05367 76428 | 1969 | |||
| :ja:ベイカーの定理|Baker constant | 0.83564 88482 64721 05333 | Before 1969 | |||
| Porter's constant | 1.46707 80794 33975 47289 | 1974 | |||
| Feigenbaum constant δ | 4.66920 16091 02990 67185 | 1975 | |||
| Chaitin's constants | In general they are uncomputable numbers. But one such number is 0.00787 49969 97812 3844 |
| 1975 | Transcendental number| | |
| Fransén–Robinson constant | 2.80777 02420 28519 36522 | 1978 | |||
| Robbins constant | 0.66170 71822 67176 23515 | 1978 | |||
| Feigenbaum constant α | 2.50290 78750 95892 82228 | 1979 | Transcendental number|? | ||
| Fractal dimension of the Cantor set | 0.63092 97535 71457 43709 | Before 1979 | Transcendental number| | ||
| Connective constant | 1.84775 90650 22573 51225 | as a root of the polynomial | 1982 | Algebraic number| | |
| Salem number, Lehmer's conjecture | 1.17628 08182 59917 50654 | 1983? | Algebraic number| | ||
| Chebyshev constant | 0.59017 02995 08048 11302 | Before 1987 | |||
| Conway constant | 1.30357 72690 34296 39125 | 1987 | Algebraic number| | ||
| Prévost constant, Reciprocal Fibonacci constant | 3.35988 56662 43177 55317 | Fn: Fibonacci series | Before 1988 | ||
| Brun 2 constant = Σ inverse of Twin primes | 1.90216 05831 04 | 1989 | |||
| Hafner–Sarnak–McCurley constant | 0.35323 63718 54995 98454 | 1993 | |||
| Fractal dimension of the Apollonian packing of circles | 1.30568 6729 ≈ by Thomas & Dhar 1.30568 8 ≈ by McMullen | 1994 1998 | |||
| Backhouse's constant | 1.45607 49485 82689 67139 | 1995 | |||
| Viswanath constant | 1.13198 82487 943 | where an = Fibonacci sequence | 1997 | Transcendental number|? | |
| Time constant | 0.63212 05588 28557 67840 | Before 1997 | Transcendental number| | ||
| Komornik–Loreti constant | 1.78723 16501 82965 93301 | tk = Thue–Morse sequence | 1998 | Transcendental number| | |
| Regular paperfolding sequence | 0.85073 61882 01867 26036 | Before 1998 | |||
| Artin constant | 0.37395 58136 19202 28805 | 1999 | |||
| MRB constant | 0.18785 96424 62067 12024 | 1999 | |||
| Somos' quadratic recurrence constant | 1.66168 79496 33594 12129 | 1999 | Transcendental number|? |
2000 onwards
| Name | Symbol | Decimal Expansion | Formula | Year | Set |
| Foias constant α | 1.18745 23511 26501 05459 | Foias constant is the unique real number such that if x1 = α then the sequence diverges to ∞. When x1 = α, | 2000 | ||
| Foias constant β | 2.29316 62874 11861 03150 | 2000 | |||
| Raabe's formula | 0.91893 85332 04672 74178 | Before 2011 | |||
| Kepler–Bouwkamp constant | 0.11494 20448 53296 20070 | Before 2013 | |||
| Prouhet–Thue–Morse constant | 0.41245 40336 40107 59778 | where is the Thue–Morse sequence and Where | Before 2014 | Transcendental number| | |
| Heath-Brown–Moroz constant | 0.00131 76411 54853 17810 | Before 2002 | Transcendental number|? | ||
| Lebesgue constant | 0.98943 12738 31146 95174 | Before 2002 | |||
| :es:Constante Du Bois Reymond|2nd du Bois-Reymond constant | 0.19452 80494 65325 11361 | Before 2003 | Transcendental number| | ||
| Stephens constant | 0.57595 99688 92945 43964 | Before 2005 | Transcendental number|? | ||
| Taniguchi constant | 0.67823 44919 17391 97803 | Before 2005 | Transcendental number|? | ||
| Copeland–Erdős constant | 0.23571 11317 19232 93137 | Before 2012 | |||
| Hausdorff dimension, Sierpinski triangle | 1.58496 25007 21156 18145 | Before 2002 | Transcendental number| | ||
| Magic angle | 0.95531 66181 245092 78163 | Before 2003 | Transcendental number| | ||
| Landau–Ramanujan constant | 0.76422 36535 89220 66299 | Before 2005 | Transcendental number|? | ||
| Brun 4 constant = Σ inv.prime quadruplets | 0.87058 83799 75 | Before 2002 | |||
| Ramanujan nested radical | 2.74723 82749 32304 33305 | Before 2001 | Algebraic number| |