Normal Distribution Calculator

Calculate normal distribution probabilities. Free online Gaussian distribution calculator.

The Normal Distribution Calculator computes probabilities for the normal (Gaussian) distribution. Find the probability of values falling within ranges, between z-scores, or in tail regions. Enter mean, standard deviation, and your values to get precise probabilities. Essential for statistics, quality control, and data analysis.

Common use cases

  • Statistical inference
  • Quality control limits
  • Grading on a curve
  • Financial modeling
  • Scientific data analysis

How to use

  1. Enter the mean (μ) and standard deviation (σ)
  2. Enter the x value(s) for probability
  3. Select probability type (less than, greater than, between)
  4. Click calculate for probability
  5. View the normal curve visualization

FAQ

What is the normal distribution?

A symmetric, bell-shaped probability distribution defined by mean (μ) and standard deviation (σ).

What is the 68-95-99.7 rule?

In a normal distribution, 68% falls within 1σ, 95% within 2σ, and 99.7% within 3σ of the mean.

What is the standard normal distribution?

A normal distribution with mean = 0 and standard deviation = 1. Used for z-score tables.

When is data normally distributed?

Many natural phenomena follow normal distribution. Check with histograms or normality tests.