Name	Mathematical constant	Value	Notation
One	$$1$$	1	M_ONE
Two	$$2$$	2	M_TWO
One half	$$1/2$$	0.5	M_ONE_HALF
Ludolph's number	$$π$$	3.1415926535898	M_PI
Tau	$$τ=2\cdot π$$	6.2831853071796	M_TAU
Euler's number	$$e=\sum_{n=0}^{\infty}\cfrac{1}{n!}=1+\cfrac{1}{1}+\cfrac{1}{1\cdot 2}+\cfrac{1}{1\cdot 2\cdot 3}+\cdots$$	2.718281828459	M_E
Euler's constant	$$γ=\lim_{n\rightarrow\infty}\left(-\log{n}+\sum_{k=1}^{n}\right)\cfrac{1}{k}$$	0.57721566490153	M_EULER
Apéry's constant	$$ζ(3)=\sum_{n=1}^{\infty}\cfrac{1}{n^3}=1+\cfrac{1}{2^3}+\cfrac{1}{3^3}+\cfrac{1}{4^3}+\cfrac{1}{5^3}+\cdots$$	1.2020569031596	M_APERY
Catalan's constant	$$G=\sum_{n=0}^{\infty}\cfrac{\left(-1\right)^n}{\left(2n+1\right)^2}=\cfrac{1}{1^2}-\cfrac{1}{3^2}+\cfrac{1}{5^2}-\cfrac{1}{7^2}+\cfrac{1}{9^2}-\cdots$$	0.91596559417722	M_CATALAN
Feigenbaum constant α	$$α$$	2.5029078750959	M_FEIGENBAUM_ALPHA
Feigenbaum constant δ	$$δ$$	4.669201609103	M_FEIGENBAUM_DELTA
Lemniscate constant	$$ϖ=2\int_{0}^{1}\cfrac{\text{d}t}{\sqrt{1-t^4}}$$	2.6220575542921	M_LEMNISCATE
Glaisher–Kinkelin constant	$$A$$	1.2824271291006	M_GLAISHER
Khinchin's constant	$$K_0=\lim_{n\rightarrow\infty}\left(a_1a_2\ldots a_n\right)^{1/n}$$	2.6854520010653	M_KHINCHIN
Golden Ratio	$$φ=\cfrac{1+\sqrt{5}}{2}$$	1.6180339887499	M_GOLDEN_RATIO
Silver Ratio	$$δ_S=\sqrt{2}+1$$	2.4142135623731	M_SILVER_RATIO
Supergolden Ratio	$$ψ=\cfrac{1+\sqrt[3]{\cfrac{29+3\cdot\sqrt{93}}{2}}+\sqrt[3]{\cfrac{29-3\cdot\sqrt{93}}{2}}}{3}$$	1.4655712318768	M_SUPERGOLDEN_RATIO
Connective constant	$$μ=\sqrt{2+\sqrt{2}}$$	1.8477590650226	M_CONNECTIVE
Kepler–Bouwkamp constant	$$K'=\prod_{n=3}^{\infty}\cos\left(\cfrac{π}{n}\right)=\cos\left(\cfrac{π}{3}\right)\cos\left(\cfrac{π}{4}\right)\cos\left(\cfrac{π}{5}\right)\cdots$$	0.1149420448533	M_KEPLER_BOUWKAMP
Erdős–Borwein constant	$$E=\sum_{n=1}^{\infty}\cfrac{1}{2^n-1}=\cfrac{1}{1}+\cfrac{1}{3}+\cfrac{1}{7}+\cfrac{1}{15}\cdots$$	1.6066951524153	M_ERDOS_BORWEIN
Omega constant	$$Ω=\cfrac{1}{π}\int_{0}^{π}\log\left(1+\cfrac{\sin t}{t}e^{t \cot t}\right)dt$$	0.56714329040978	M_OMEGA
Gauss's constant	$$G=\cfrac{1}{\text{agm}\left(1, \sqrt{2}\right)}=\cfrac{1}{4π}\sqrt{\cfrac{2}{π}}Γ\left(\cfrac{1}{4}\right)^2=\cfrac{ϖ}{π}$$	0.83462684167407	M_GAUSS
Second Hermite constant	$$γ_2=\cfrac{2}{\sqrt{3}}$$	1.1547005383793	M_SECOND_HERMITE
Liouville's constant	$$L=\sum_{n=1}^{\infty}\cfrac{1}{10^{n!}}=\cfrac{1}{10^{1!}}+\cfrac{1}{10^{2!}}+\cfrac{1}{10^{3!}}+\cfrac{1}{10^{4!}}+\cdots$$	0.110001	M_LIOUVILLE
Ramanujan's constant	$${e}^{π\cdot\sqrt{163}}$$	2.6253741264077E+17	M_RAMANUJAN
Dottie number	$$D$$	0.73908513321516	M_DOTTIE
Meissel-Mertens constant	$$M=\lim_{n\rightarrow\infty}\left(\sum_{p\le n}\cfrac{1}{p}-\ln\left(\ln n\right)\right)=γ+\sum_{p}\left(\ln\left(1-\cfrac{1}{p}\right)+\cfrac{1}{p}\right)$$	0.26149721284764	M_MEISSEL_MERTENS
Universal parabolic constant	$$ \ln{\left(1+\sqrt{2}\right)}+\sqrt{2}$$	2.2955871493926	M_UNIVERSAL_PARABOLIC
Cahen's constant	$$C=\sum_{k=1}^{\infty}\cfrac{\left(-1\right)^k}{s_k-1}=\cfrac{1}{1}-\cfrac{1}{2}+\cfrac{1}{6}-\cfrac{1}{42}+\cfrac{1}{1806}\pm\cdots$$	0.64341054628834	M_CAHEN
Gelfond's constant	$${e}^π$$	23.140692632779	M_GELFOND
Gelfond-Schneider constant	$$2^{\sqrt{2}}$$	2.6651441426902	M_GELFOND_SCHNEIDER
Second Favard constant	$$K_2=\cfrac{π^2}{8}$$	1.2337005501362	M_SECOND_FAVARD
Golden angle	$$g=π\cdot\left(3-\sqrt{5}\right)$$	2.3999632297287	M_GOLDEN_ANGLE
Sierpiński's constant	$$K=π\left(2γ+\ln\cfrac{4π^3}{Γ\left(\cfrac{1}{4}\right)^4}\right)=π\left(2γ+4\ln Γ\left(\cfrac{3}{4}\right)-\ln π\right)=π\left(2\ln2+3\ln π+2γ-4\ln Γ\left(\cfrac{1}{4}\right)\right)$$	2.5849817595793	M_SIERPINSKI
Landau-Ramanujan constant	$$b=\cfrac{1}{\sqrt{2}}\prod_{p\equiv 3\ (\mod 4)}\left(1-\cfrac{1}{p^2}\right)^{-\cfrac{1}{2}}=\cfrac{π}{4}\prod_{p\equiv 1\ (\mod 4)}\left(1-\cfrac{1}{p^2}\right)^{\cfrac{1}{2}}$$	0.76422365358922	M_LANDAU_RAMANUJAN
First Nielsen-Ramanujan constant	$$a_1=\cfrac{π^2}{12}$$	0.82246703342411	M_FIRST_NIELSEN_RAMANUJAN
Gieseking constant	$$G=\cfrac{3\sqrt{3}}{4}\left(1-\sum_{n=0}^{\infty}\cfrac{1}{\left(3n+2\right)^2}+\sum_{n=1}^{\infty}\cfrac{1}{\left(3n+1\right)^2}\right)=\cfrac{\sqrt{3}}{4}\left(\cfrac{ψ_1\left(1/3\right)}{2}-\cfrac{π^2}{3}\right)$$	1.0149416064097	M_GIESEKING
Bernstein's constant	$$β=\lim_{n\rightarrow\infty}2nE_{2n}\left(f\right)$$	0.28016949902387	M_BERNSTEIN
Tribonacci constant	$$\cfrac{1+\sqrt[3]{19+3\cdot\sqrt{33}}+\sqrt[3]{19-3\cdot\sqrt{33}}}{3}$$	1.8392867552142	M_TRIBONACCI
Brun's constant	$$B_2=\sum_{p}\left(\cfrac{1}{p}+\cfrac{1}{p+2}\right)=\left(\cfrac{1}{3}+\cfrac{1}{5}\right)+\left(\cfrac{1}{5}+\cfrac{1}{7}\right)+\left(\cfrac{1}{11}+\cfrac{1}{13}\right)\cdots$$	1.902160583104	M_BRUN
Twin primes constant	$$C_2=\prod_{p\ \text{prime,}\ p\geq3}\left(1-\cfrac{1}{\left(p-1\right)^2}\right)$$	0.66016181584687	M_TWIN_PRIMES
Plastic Ratio	$$ρ=\sqrt[3]{\cfrac{1}{2}+\cfrac{\sqrt{69}}{18}}+\sqrt[3]{\cfrac{1}{2}-\cfrac{\sqrt{69}}{18}}$$	1.3247179572447	M_PLASTIC_RATIO
Zero	$$0$$	0	M_ZERO
Negative one	$$-1$$	-1	M_NEGATIVE_ONE
Square Root of 2	$$\sqrt{2}$$	1.4142135623731	M_SQRT2
Square Root of 3	$$\sqrt{3}$$	1.7320508075689	M_SQRT3
Square Root of 5	$$\sqrt{5}$$	2.2360679774998	M_SQRT5
Cube Root of 2	$$\sqrt[3]{2}$$	1.2599210498949	M_CURT2
Cube Root of 3	$$\sqrt[3]{3}$$	1.4422495703074	M_CURT3
Twelfth Root of 2	$$\sqrt[12]{2}$$	1.0594630943593	M_TWRT2
Natural Log of 2	$$\ln(2)$$	0.69314718055995	M_LN2
Natural Log of 10	$$\ln(10)$$	2.302585092994	M_LN10
Natural Log of Pi	$$\ln(π)$$	1.1447298858494	M_LNPI
Base 10 Log of e	$$\log10(e)$$	0.43429448190325	M_LOG10E
Base 2 Log of e	$$\log2(e)$$	1.442695040889	M_LOG2E
Half of Pi	$$π/2$$	1.5707963267949	M_PI_2
Quarter of Pi	$$π/4$$	0.78539816339745	M_PI_4
Inverse of Pi	$$1/π$$	0.31830988618379	M_1_PI
Two over Pi	$$2/π$$	0.63661977236758	M_2_PI
Square Root of Pi	$$\sqrt{π}$$	1.7724538509055	M_SQRTPI
Two over Square Root of Pi	$$2/\sqrt{π}$$	1.1283791670955	M_2_SQRTPI
Inverse of Square Root of 2	$$1/\sqrt{2}$$	0.70710678118655	M_SQRT1_2

Name

Mathematical constant

Value

Notation

One

$$1$$

M_ONE

Two

$$2$$

M_TWO

One half

$$1/2$$

0.5

M_ONE_HALF

Ludolph's number

$$π$$

3.1415926535898

M_PI

Tau

$$τ=2\cdot π$$

6.2831853071796

M_TAU

Euler's number

$$e=\sum_{n=0}^{\infty}\cfrac{1}{n!}=1+\cfrac{1}{1}+\cfrac{1}{1\cdot 2}+\cfrac{1}{1\cdot 2\cdot 3}+\cdots$$

2.718281828459

M_E

Euler's constant

$$γ=\lim_{n\rightarrow\infty}\left(-\log{n}+\sum_{k=1}^{n}\right)\cfrac{1}{k}$$

0.57721566490153

M_EULER

Apéry's constant

$$ζ(3)=\sum_{n=1}^{\infty}\cfrac{1}{n^3}=1+\cfrac{1}{2^3}+\cfrac{1}{3^3}+\cfrac{1}{4^3}+\cfrac{1}{5^3}+\cdots$$

1.2020569031596

M_APERY

Catalan's constant

$$G=\sum_{n=0}^{\infty}\cfrac{\left(-1\right)^n}{\left(2n+1\right)^2}=\cfrac{1}{1^2}-\cfrac{1}{3^2}+\cfrac{1}{5^2}-\cfrac{1}{7^2}+\cfrac{1}{9^2}-\cdots$$

0.91596559417722

M_CATALAN

Feigenbaum constant α

$$α$$

2.5029078750959

M_FEIGENBAUM_ALPHA

Feigenbaum constant δ

$$δ$$

4.669201609103

M_FEIGENBAUM_DELTA

Lemniscate constant

$$ϖ=2\int_{0}^{1}\cfrac{\text{d}t}{\sqrt{1-t^4}}$$

2.6220575542921

M_LEMNISCATE

Glaisher–Kinkelin constant

$$A$$

1.2824271291006

M_GLAISHER

Khinchin's constant

$$K_0=\lim_{n\rightarrow\infty}\left(a_1a_2\ldots a_n\right)^{1/n}$$

2.6854520010653

M_KHINCHIN

Golden Ratio

$$φ=\cfrac{1+\sqrt{5}}{2}$$

1.6180339887499

M_GOLDEN_RATIO

Silver Ratio

$$δ_S=\sqrt{2}+1$$

2.4142135623731

M_SILVER_RATIO

Supergolden Ratio

$$ψ=\cfrac{1+\sqrt[3]{\cfrac{29+3\cdot\sqrt{93}}{2}}+\sqrt[3]{\cfrac{29-3\cdot\sqrt{93}}{2}}}{3}$$

1.4655712318768

M_SUPERGOLDEN_RATIO

Connective constant

$$μ=\sqrt{2+\sqrt{2}}$$

1.8477590650226

M_CONNECTIVE

Kepler–Bouwkamp constant

$$K'=\prod_{n=3}^{\infty}\cos\left(\cfrac{π}{n}\right)=\cos\left(\cfrac{π}{3}\right)\cos\left(\cfrac{π}{4}\right)\cos\left(\cfrac{π}{5}\right)\cdots$$

0.1149420448533

M_KEPLER_BOUWKAMP

Erdős–Borwein constant

$$E=\sum_{n=1}^{\infty}\cfrac{1}{2^n-1}=\cfrac{1}{1}+\cfrac{1}{3}+\cfrac{1}{7}+\cfrac{1}{15}\cdots$$

1.6066951524153

M_ERDOS_BORWEIN

Omega constant

$$Ω=\cfrac{1}{π}\int_{0}^{π}\log\left(1+\cfrac{\sin t}{t}e^{t \cot t}\right)dt$$

0.56714329040978

M_OMEGA

Gauss's constant

$$G=\cfrac{1}{\text{agm}\left(1, \sqrt{2}\right)}=\cfrac{1}{4π}\sqrt{\cfrac{2}{π}}Γ\left(\cfrac{1}{4}\right)^2=\cfrac{ϖ}{π}$$

0.83462684167407

M_GAUSS

Second Hermite constant

$$γ_2=\cfrac{2}{\sqrt{3}}$$

1.1547005383793

M_SECOND_HERMITE

Liouville's constant

$$L=\sum_{n=1}^{\infty}\cfrac{1}{10^{n!}}=\cfrac{1}{10^{1!}}+\cfrac{1}{10^{2!}}+\cfrac{1}{10^{3!}}+\cfrac{1}{10^{4!}}+\cdots$$

0.110001

M_LIOUVILLE

Ramanujan's constant

$${e}^{π\cdot\sqrt{163}}$$

2.6253741264077E+17

M_RAMANUJAN

Dottie number

$$D$$

0.73908513321516

M_DOTTIE

Meissel-Mertens constant

$$M=\lim_{n\rightarrow\infty}\left(\sum_{p\le n}\cfrac{1}{p}-\ln\left(\ln n\right)\right)=γ+\sum_{p}\left(\ln\left(1-\cfrac{1}{p}\right)+\cfrac{1}{p}\right)$$

0.26149721284764

M_MEISSEL_MERTENS

Universal parabolic constant

$$ \ln{\left(1+\sqrt{2}\right)}+\sqrt{2}$$

2.2955871493926

M_UNIVERSAL_PARABOLIC

Cahen's constant

$$C=\sum_{k=1}^{\infty}\cfrac{\left(-1\right)^k}{s_k-1}=\cfrac{1}{1}-\cfrac{1}{2}+\cfrac{1}{6}-\cfrac{1}{42}+\cfrac{1}{1806}\pm\cdots$$

0.64341054628834

M_CAHEN

Gelfond's constant

$${e}^π$$

23.140692632779

M_GELFOND

Gelfond-Schneider constant

$$2^{\sqrt{2}}$$

2.6651441426902

M_GELFOND_SCHNEIDER

Second Favard constant

$$K_2=\cfrac{π^2}{8}$$

1.2337005501362

M_SECOND_FAVARD

Golden angle

$$g=π\cdot\left(3-\sqrt{5}\right)$$

2.3999632297287

M_GOLDEN_ANGLE

Sierpiński's constant

$$K=π\left(2γ+\ln\cfrac{4π^3}{Γ\left(\cfrac{1}{4}\right)^4}\right)=π\left(2γ+4\ln Γ\left(\cfrac{3}{4}\right)-\ln π\right)=π\left(2\ln2+3\ln π+2γ-4\ln Γ\left(\cfrac{1}{4}\right)\right)$$

2.5849817595793

M_SIERPINSKI

Landau-Ramanujan constant

$$b=\cfrac{1}{\sqrt{2}}\prod_{p\equiv 3\ (\mod 4)}\left(1-\cfrac{1}{p^2}\right)^{-\cfrac{1}{2}}=\cfrac{π}{4}\prod_{p\equiv 1\ (\mod 4)}\left(1-\cfrac{1}{p^2}\right)^{\cfrac{1}{2}}$$

0.76422365358922

M_LANDAU_RAMANUJAN

First Nielsen-Ramanujan constant

$$a_1=\cfrac{π^2}{12}$$

0.82246703342411

M_FIRST_NIELSEN_RAMANUJAN

Gieseking constant

$$G=\cfrac{3\sqrt{3}}{4}\left(1-\sum_{n=0}^{\infty}\cfrac{1}{\left(3n+2\right)^2}+\sum_{n=1}^{\infty}\cfrac{1}{\left(3n+1\right)^2}\right)=\cfrac{\sqrt{3}}{4}\left(\cfrac{ψ_1\left(1/3\right)}{2}-\cfrac{π^2}{3}\right)$$

1.0149416064097

M_GIESEKING

Bernstein's constant

$$β=\lim_{n\rightarrow\infty}2nE_{2n}\left(f\right)$$

0.28016949902387

M_BERNSTEIN

Tribonacci constant

$$\cfrac{1+\sqrt[3]{19+3\cdot\sqrt{33}}+\sqrt[3]{19-3\cdot\sqrt{33}}}{3}$$

1.8392867552142

M_TRIBONACCI

Brun's constant

$$B_2=\sum_{p}\left(\cfrac{1}{p}+\cfrac{1}{p+2}\right)=\left(\cfrac{1}{3}+\cfrac{1}{5}\right)+\left(\cfrac{1}{5}+\cfrac{1}{7}\right)+\left(\cfrac{1}{11}+\cfrac{1}{13}\right)\cdots$$

1.902160583104

M_BRUN

Twin primes constant

$$C_2=\prod_{p\ \text{prime,}\ p\geq3}\left(1-\cfrac{1}{\left(p-1\right)^2}\right)$$

0.66016181584687

M_TWIN_PRIMES

Plastic Ratio

$$ρ=\sqrt[3]{\cfrac{1}{2}+\cfrac{\sqrt{69}}{18}}+\sqrt[3]{\cfrac{1}{2}-\cfrac{\sqrt{69}}{18}}$$

1.3247179572447

M_PLASTIC_RATIO

Zero

$$0$$

M_ZERO

Negative one

$$-1$$

-1

M_NEGATIVE_ONE

Square Root of 2

$$\sqrt{2}$$

1.4142135623731

M_SQRT2

Square Root of 3

$$\sqrt{3}$$

1.7320508075689

M_SQRT3

Square Root of 5

$$\sqrt{5}$$

2.2360679774998

M_SQRT5

Cube Root of 2

$$\sqrt[3]{2}$$

1.2599210498949

M_CURT2

Cube Root of 3

$$\sqrt[3]{3}$$

1.4422495703074

M_CURT3

Twelfth Root of 2

$$\sqrt[12]{2}$$

1.0594630943593

M_TWRT2

Natural Log of 2

$$\ln(2)$$

0.69314718055995

M_LN2

Natural Log of 10

$$\ln(10)$$

2.302585092994

M_LN10

Natural Log of Pi

$$\ln(π)$$

1.1447298858494

M_LNPI

Base 10 Log of e

$$\log10(e)$$

0.43429448190325

M_LOG10E

Base 2 Log of e

$$\log2(e)$$

1.442695040889

M_LOG2E

Half of Pi

$$π/2$$

1.5707963267949

M_PI_2

Quarter of Pi

$$π/4$$

0.78539816339745

M_PI_4

Inverse of Pi

$$1/π$$

0.31830988618379

M_1_PI

Two over Pi

$$2/π$$

0.63661977236758

M_2_PI

Square Root of Pi

$$\sqrt{π}$$

1.7724538509055

M_SQRTPI

Two over Square Root of Pi

$$2/\sqrt{π}$$

1.1283791670955

M_2_SQRTPI

Inverse of Square Root of 2

$$1/\sqrt{2}$$

0.70710678118655

M_SQRT1_2

Privacy

Eng-Calculations Privacy Policy describes how Eng-Calculations collects, uses, and shares your personal data.

What Is Personal Data at Eng-Calculations?
At Eng-Calculations, we believe strongly in fundamental privacy rights and that those fundamental rights should not differ depending on where you live in the world. That’s why we treat any data that relates to an identified or identifiable individual or that is linked or linkable to them by Eng-Calculations as “personal data,” no matter where the individual lives.

Your Privacy Rights
At Eng-Calculations we respect your ability to know, access, correct, transfer, restrict the processing of, and delete your personal data. And if you choose to exercise these privacy rights, you have the right not to be treated in a discriminatory way nor to receive a lesser degree of service from Eng-Calculations. If you wish to exercise your rights and privacy options, please contact us by email support@Eng-Calculations.com.
There may be situations where we cannot grant your request - for example, if you ask us to delete your transaction data and Eng-Calculations is legally obligated to keep a record of that transaction to comply with law. We may also decline to grant a request where doing so would undermine our legitimate use of data for antifraud and security purposes, such as when you request deletion of an account that is being investigated for security concerns. Other reasons your privacy request may be denied are if it jeopardizes the privacy of others, is frivolous or vexatious, or would be extremely impractical.

Personal Data Eng-Calculations Collects from You
At Eng-Calculations, we believe that you can have great product and great privacy. This means that we strive to collect only the personal data that we need. The personal data Eng-Calculations collects depends on how you interact with Eng-Calculations. Eng-Calculations, we may collect a variety of information, including. Data such as name, email address and payment Information.
You are not required to provide the personal data that we have requested. However, if you choose not to do so, in many cases we will not be able to provide you with our product or services or respond to requests you may have.

Eng-Calculations Use of Personal Data
Eng-Calculations uses personal data to power our services, to process your transactions, to communicate with you, for security and fraud prevention, and to comply with law. We may also use personal data for other purposes with your consent. Eng-Calculations uses your personal data only when we have a valid legal basis to do so. Depending on the circumstance, Eng-Calculations may rely on your consent or the fact that the processing is necessary to fulfill a contract with you, protect your vital interests or those of other persons, or to comply with law. We may also process your personal data where we believe it is in our or others’ legitimate interests, taking into consideration your interests, rights, and expectations.
Eng-Calculations retains personal data only for so long as necessary.

Eng-Calculations Sharing of Personal Data
Eng-Calculations does not share personal data with third parties for their own marketing purposes.

Cookies and Other Technologies
Eng-Calculations websites, online services, interactive applications may use “cookies” and other technologies such as web beacons. These technologies help us to better understand user behavior including for security and fraud prevention purposes, tell us which parts of our websites people have visited, and facilitate and measure the effectiveness of advertisements and web searches.
- Communications Cookies. These cookies are used to enable network traffic to and from Eng-Calculations systems, including by helping us detect any errors.
- Strictly Necessary Cookies. These cookies are set as required to provide a specific feature or service that you have accessed or requested. For example, they allow us to display our websites in the proper format and language, to authenticate and verify your transactions.
- Other Cookies. These cookies are used to understand how visitors interact with our websites and online services, including by helping us to assess the effectiveness of advertisements and web searches. Eng-Calculations also uses these cookies to remember choices you make while browsing, so we can provide you with a customized experience.
If you want to disable cookies, choose “Block all cookies” privacy in browser settings. Certain features of the Eng-Calculations website may not be available if all cookies are disabled.

Menu

Privacy