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Table of selected mathematical constants

Main article: List of mathematical constants

Abbreviations used:

R – Rational number, I – Irrational number (may be algebraic or transcendental), A – Algebraic number (irrational), T – Transcendental number (irrational)

Gen – General, NuT – Number theory, ChT – Chaos theory, Com – Combinatorics, Inf – Information theory, Ana – Mathematical analysis

Symbol	Value	Name	Field	N	First described	# of known digits
0	= 0	Zero	Gen	R	c. 7th–5th century BC	N/A
1	= 1	One, Unity	Gen	R		N/A
i	= √–1	Imaginary unit, unit imaginary number	Gen, Ana	A	16th century	N/A
π	≈ 3.14159 26535 89793 23846 26433 83279 50288	Pi, Archimedes' constant or Ludolph's number	Gen, Ana	T	by c. 2000 BC	12,100,000,000,000
e	≈ 2.71828 18284 59045 23536 02874 71352 66249	e, Napier's constant, or Euler's number	Gen, Ana	T	1618	100,000,000,000
√2	≈ 1.41421 35623 73095 04880 16887 24209 69807	Pythagoras' constant, square root of 2	Gen	A	by c. 800 BC	137,438,953,444
√3	≈ 1.73205 08075 68877 29352 74463 41505 87236	Theodorus' constant, square root of 3	Gen	A	by c. 800 BC
√5	≈ 2.23606 79774 99789 69640 91736 68731 27623	square root of 5	Gen	A	by c. 800 BC
$\gamma$	≈ 0.57721 56649 01532 86060 65120 90082 40243	Euler–Mascheroni constant	Gen, NuT		1735	14,922,244,771
$\phi$	≈ 1.61803 39887 49894 84820 45868 34365 63811	Golden ratio	Gen	A	by 3rd century BC	100,000,000,000
$\Lambda$	≥ –2.7 • 10−9	de Bruijn–Newman constant	NuT		1950?	none
M1	≈ 0.26149 72128 47642 78375 54268 38608 69585	Meissel–Mertens constant	NuT		1866 1874	8,010
$\beta$	≈ 0.28016 94990 23869 13303	Bernstein's constant	Ana
$\lambda$	≈ 0.30366 30028 98732 65859 74481 21901 55623	Gauss–Kuzmin–Wirsing constant	Com		1974	385
$\sigma$	≈ 0.35323 63718 54995 98454	Hafner–Sarnak–McCurley constant	NuT		1993
L	≈ 0.5	Landau's constant	Ana			1
Ω	≈ 0.56714 32904 09783 87299 99686 62210 35555	Omega constant	Ana	T
$\lambda$, $\mu$	≈ 0.62432 99885 43550 87099 29363 83100 83724	Golomb–Dickman constant	Com, NuT		1930 1964
	≈ 0.64341 05463	Cahen's constant		T	1891	4000
C2	≈ 0.66016 18158 46869 57392 78121 10014 55577	Twin prime constant	NuT			5,020
	≈ 0.66274 34193 49181 58097 47420 97109 25290	Laplace limit
$\beta$*	≈ 0.70258	Embree–Trefethen constant	NuT
K	≈ 0.76422 36535 89220 66299 06987 31250 09232	Landau–Ramanujan constant	NuT			30,010
	≈ 0.80939 40205	Alladi–Grinstead constant	NuT
B4	≈ 0.87058 83800	Brun's constant for prime quadruplets	NuT
K	≈ 0.91596 55941 77219 01505 46035 14932 38411	Catalan's constant	Com			15,510,000,000
B´L	= 1	Legendre's constant	NuT	R		N/A
$\Lambda$	≈ 1.09868 58055	Lengyel's constant	Com		1992
K	≈ 1.13198 824	Viswanath's constant	NuT			8
$\zeta (3)$	≈ 1.20205 69031 59594 28539 97381 61511 44999	Apéry's constant		I	1979	15,510,000,000
$\theta$	≈ 1.30637 78838 63080 69046 86144 92602 60571	Mills' constant	NuT		1947	6850
$\rho$	≈ 1.32471 79572 44746 02596 09088 54478 09734	Plastic constant	NuT	A	1928
$\mu$	≈ 1.45136 92348 83381 05028 39684 85892 02744	Ramanujan–Soldner constant	NuT	I		75,500
	≈ 1.45607 49485 82689 67139 95953 51116 54356	Backhouse's constant
	≈ 1.46707 80794	Porter's constant	NuT		1975
	≈ 1.53960 07178	Lieb's square ice constant	Com	A	1967
EB	≈ 1.60669 51524 15291 76378 33015 23190 92458	Erdős–Borwein constant	NuT	I
	≈ 1.70521 11401 05367 76428 85514 53434 50816	Niven's constant	NuT		1969
B2	≈ 1.90216 05823	Brun's constant for twin primes	NuT		1919	10
P2	≈ 2.29558 71493 92638 07403 42980 49189 49039	Universal parabolic constant	Gen	T
$\alpha$	≈ 2.50290 78750 95892 82228 39028 73218 21578	Feigenbaum constant	ChT
K	≈ 2.58498 17595 79253 21706 58935 87383 17116	Sierpiński's constant
	≈ 2.68545 20010 65306 44530 97148 35481 79569	Khinchin's constant	NuT		1934	7350
F	≈ 2.80777 02420 28519 36522 15011 86557 77293	Fransén–Robinson constant	Ana
	≈ 3.27582 29187 21811 15978 76818 82453 84386	Lévy's constant	NuT
$\psi$	≈ 3.35988 56662 43177 55317 20113 02918 92717	Reciprocal Fibonacci constant		I
$\delta$	≈ 4.66920 16091 02990 67185 32038 20466 20161	Feigenbaum constant	ChT		1975