Gaussian (Normal) Distribution Calculator

Standard Deviation
P(X < X1)  =  0.6915
P(X > X1)  =  0.3085
P(X < X2)  =  0.5987
P(X > X2)  =  0.4013
P(X1 to X2)  =  0.0928
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Normal (Gaussian) Distribution Calculator is an online statistics tool for data analysis programmed to calculate the normal probability density function for a given mean and standard deviation. Gaussian distribution is a continous probability distribution also called as Gaussian function and the curve associated with it is known as Bell Curve.


Gaussian distribution is also known as Normal distribution, the most prominent continuous probability function in statistics was introduced by Gauss to estimate the errors in huge observations. Wherein the Bell shaped curve known as Bell curve or Gaussian function is used to represent the distribution of probability density function.

Normal or Gaussian Distribution Formula

The term Normal or Gaussian Distribution in probability and statistics can be derived from the formula.


where parameter μ is the mean, location of the peak and σ2 is the variance, the measure of the width of the distribution. The distribution with μ = 0 and σ2 = 1 is called the standard normal distribution.

This Normal or Gaussian distribution is the most widely known and used of all distributions. Because the normal distribution approximates many natural phenomena so well, it has developed into a standard of reference for many probability problems. To make your calculations easy, this online normal distribution calculator will help you to figure out the probability density function value for the given values of mean, standard deviation and other variables.