formula.expert

Constants library

7 values, each with its units, its uncertainty, and where it came from.

Mathematical 7

Euler's Number exact

e=2.718281828459045e = 2.718281828459045

dimensionlessThe base of the natural logarithm, e = 2.71828182845905 — the unique number whose exponential function is its own derivative.

Euler–Mascheroni Constant exact

γ=0.5772156649015329\gamma = 0.5772156649015329

dimensionlessThe limiting gap between the harmonic series and the natural logarithm, γ = 0.577215664901533 — still not known to be irrational.

Natural Logarithm of Two exact

ln⁡2=0.6931471805599453\ln 2 = 0.6931471805599453

dimensionlessThe natural logarithm of 2, ln 2 = 0.693147180559945 — the number that converts a decay constant into a half-life.

Natural Logarithm of Ten exact

ln⁡10=2.302585092994046\ln 10 = 2.302585092994046

dimensionlessThe natural logarithm of 10, ln 10 = 2.30258509299405 — the factor that converts between natural and common logarithms.

Common Logarithm of e exact

log⁡10e=0.4342944819032518\log_{10} e = 0.4342944819032518

dimensionlessThe base-10 logarithm of e, 0.434294481903252 — the modulus of common logarithms, and the reciprocal of ln 10.

Catalan's Constant exact

G=0.915965594177219G = 0.915965594177219

dimensionlessCatalan's constant G = 0.915965594177219 — the alternating sum of reciprocal odd squares, of unknown irrationality after 160 years.

Apéry's Constant exact

ζ(3)=1.2020569031595942\zeta(3) = 1.2020569031595942

dimensionlessApéry's constant ζ(3) = 1.20205690315959 — the sum of reciprocal cubes, proved irrational in 1978 and still with no closed form.