# Mathematical Constants

Many mathematical constants and expressions involving small integers occur time and again in numerical calculations. The Constants class contains static fields for many of these values.

The constants fall into four categories:

This topic contains the following sections:

The following example shows a method that evaluates the probability density function of a normal distribution with mean mean and standard deviation stdDev.

C#
``````public double NormalPDF(double x, double mean, double stdDev)
{
double z = (x - mean) / stdDev;
return Constants.OneOverSqrtTwoPi / stdDev
* Math.Exp(-0.5 * z * z);
}``````

The tables below list the constants in each of the four categories.

## Fundamental constants

Value

Description

E

The base for the natural logarithm, e (2.718...).

EulersConstant

Euler's constant, which is important in number theory and some engineering calculations (0.577...).

GoldenRatio

The Golden Ratio (1.618...).

Pi

The number Pi, the ratio between the circumference and the diameter of a circle (3.1415...).

## Expressions involving fundamental constants

Value

Description

TwoPi

Two times Pi (6.283...).

PiOverTwo

0.5 times Pi (1.570...).

PiOverFour

0.25 times Pi (0.785...).

LogTwoPi

The natural logarithm of two times Pi (1.837...).

PiSquared

The square of Pi (9.869...).

SqrtPi

The square root of Pi (1.772...).

SqrtTwoPi

The square root of two times Pi (2.506...).

OneOverSqrtPi

The reciprocal of the square root of Pi (0.564...).

OneOverSqrtTwoPi

The reciprocal of the square root of two times Pi (0.399...).

## Square roots of small integers.

Value

Description

Sqrt2

The square root of two (1.414...).

Sqrt3

The square root of three (1.732...).

Sqrt5

The square root of five (2.236...).

Sqrt7

The square root of seven (2.646...).

Sqrt17

The square root of seventeen (4.123...).

## Logarithms of small integers.

Value

Description

Log2

The natural logarithm of two (0.693...).

Log3

The natural logarithm of three (1.098...).

Log10

The natural logarithm of ten (2.305...).

Log17

The natural logarithm of seventeen (2.833...).

InvLog10

The base-10 logarithm of E.