ClarityKitFind a tool
Statistics

Normal Distribution Probability Calculator

Find the probability between two bounds for a normal distribution, plus the probabilities in both outside tails.

Data stays on this deviceConvention explained below
Data explorer
Data explorer

Check the dataset and sample convention before interpreting results.

See the method

Add your observations

Runs on your device

Your statistical summary

Your result

Let’s calculate.

Use the Calculate button to see your result.

Review the method below for assumptions and conventions.

How to use this tool

  1. Enter lower bound, upper bound, population mean, population standard deviation.
  2. Select Calculate to view the result.
  3. Check the method and assumptions below before using the result.

The method, explained

Standardize each bound using z = (x−mean)/SD. Subtract normal cumulative probabilities, using survival tails to avoid cancellation in the right tail.

A WORKED EXAMPLE

Using lower bound = -1, upper bound = 1, population mean = 0, population standard deviation = 1, the result is 0.682689492 probability. Change these example inputs to match your task; use the method above to check each step.

What to keep in mind

Assumes the stated normal population model, not merely a dataset with a known mean and standard deviation. A descriptive or probability calculation under the stated assumptions. Check the sample design and model before interpreting results.

Reference: NIST: statistical methods handbook

Common questions

Can I use a normal curve for any dataset?

No. The shape assumption matters. A mean and standard deviation alone do not establish that your population is normally distributed.

Why is a single exact value assigned zero probability?

The normal distribution is continuous. Probability corresponds to an interval of values; the density at one point is a height, not a point probability.

Methodology maintained by ClarityKit. How these tools are built and checked.