Reference data and engineering information about numerical constants for mathematics applications.
Engineering reference data for Numerical Constants in mathematics.
x = − b ± b 2 − 4 a c 2 a x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} x = 2 a − b ± b 2 − 4 a c
Roots of ax² + bx + c = 0.
c 2 = a 2 + b 2 c^2 = a^2 + b^2 c 2 = a 2 + b 2
Right triangle relationship.
A = π r 2 A = \pi r^2 A = π r 2
Area of a circle.
log b ( x ) = ln ( x ) ln ( b ) \log_b(x) = \frac{\ln(x)}{\ln(b)} log b ( x ) = l n ( b ) l n ( x )
Change of base formula.
Symbol
Description
Unit
π \pi π Pi
3.14159...
e e e Euler's number
2.71828...
The following constants complete the set of fundamental logarithmic and radical values referenced in engineering calculations:
2 1 / 3 = 1.25992 10498 94873 16476 72106 07278 22836 05702 51464 ( 6 ) 2^{1/3} = 1.25992\ 10498\ 94873\ 16476\ 72106\ 07278\ 22836\ 05702\ 51464 \quad (6) 2 1/3 = 1.25992 10498 94873 16476 72106 07278 22836 05702 51464 ( 6 ) 3 1 / 3 = 1.44224 95703 07408 38232 16383 10780 10958 83918 69253 ( 7 ) 3^{1/3} = 1.44224\ 95703\ 07408\ 38232\ 16383\ 10780\ 10958\ 83918\ 69253 \quad (7) 3 1/3 = 1.44224 95703 07408 38232 16383 10780 10958 83918 69253 ( 7 ) log 10 ( 3 ) = 0.47712 12547 19662 43729 50279 03255 11530 92001 28864 ( 8 ) \log_{10}(3) = 0.47712\ 12547\ 19662\ 43729\ 50279\ 03255\ 11530\ 92001\ 28864 \quad (8) log 10 ( 3 ) = 0.47712 12547 19662 43729 50279 03255 11530 92001 28864 ( 8 ) These values are derived from the definitions of radical and logarithmic functions. The cube root (x 1 / 3 x^{1/3} x 1/3 log 10 \log_{10} log 10
