Gaussian Distribution Calculator

Analyze data using the Gaussian distribution with our calculator.


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The Gaussian Distribution Calculator, also known as the Normal Distribution Calculator, is a powerful tool that can analyze and visualize data following a Gaussian distribution. The Gaussian distribution, often called the normal distribution, is a fundamental statistical distribution widely employed in various fields, including statistics, natural sciences, social sciences, and engineering.

The formula for the probability density function (PDF) of the Gaussian distribution is:

\[ f(x) = \frac{1}{\sigma \sqrt{2\pi}} \cdot e^{-\frac{(x - \mu)^2}{2\sigma^2}} \]


  • \( f(x) \) represents the probability density function.
  • \( x \) is the variable of interest.
  • \( \mu \) is the mean (average) of the distribution.
  • \( \sigma \) is the standard deviation, representing the spread or dispersion of the data.

Using the Calculator

This calculator enables you to perform the following tasks:

  • Calculate the probability density function (\( f(x) \)) for a given \( x \), mean (\( \mu \)), and standard deviation (\( \sigma \)).
  • Visualize the Gaussian distribution curve based on the specified parameters.
  • Calculate the cumulative probability (cumulative distribution function) for a value \( x \) under the Gaussian distribution.
  • Find the inverse cumulative probability, which corresponds to the value \( x \) for a given cumulative probability.


The Gaussian distribution is fundamental in statistics and finds a wide range of applications:

  • Data Analysis: Analysts use it to study and describe data distribution, facilitating the understanding of data patterns.
  • Hypothesis Testing: Various statistical tests and hypothesis testing procedures assume a Gaussian distribution.
  • Quality Control: In manufacturing and quality control, it's used to evaluate product quality and process performance.
  • Physics and Natural Sciences: It describes the distribution of various physical phenomena, like particle velocities and measurement errors.
  • Finance and Economics: Financial modeling and risk assessment rely on the Gaussian distribution.

The Gaussian Distribution Calculator simplifies the analysis and interpretation of Gaussian distributions. Whether you're a statistician, researcher, or student, this calculator serves as a valuable tool for comprehending Gaussian distributions and their real-world applications.