Normal Distribution Calculator

Explore probabilities and percentiles of the normal distribution. Enter the mean and standard deviation to get started.

Input Parameters

Mean (

\mu

Standard Deviation (

\sigma

Calculation Type:

Value (x):

Value 2 (b):

Result

Calculated Result:

P(X < > between and ) =

Percentile for P(X < x) = is:

Enter parameters and calculate to see the result.

Visualization

Understanding Normal Distribution

The normal distribution, also known as the Gaussian distribution or bell curve, is a continuous probability distribution that is symmetric about the mean. It shows that data near the mean are more frequent in occurrence than data far from the mean.

Mean ( $\mu$ ): The average value of the distribution. It determines the center of the bell curve.
Standard Deviation ( $\sigma$ ): A measure of the spread or dispersion of the distribution. A larger standard deviation means a wider curve.
Probability: The likelihood of a random variable falling within a certain range.
Percentile: The value below which a given percentage of observations in a group of observations falls. For example, the 90th percentile is the value below which 90% of the observations may be found.

This calculator helps you find probabilities for different ranges under a normal distribution curve and also calculate percentile values. Use it to explore and understand normal distribution concepts.

Learn more about normal distribution on Wikipedia.