Math

Normal Distribution Calculator

Find the cumulative probability below, above or between values in a normal distribution.

How to use this normal distribution calculator

Enter the values requested above and select Calculate. Change any input to compare another scenario. The calculation runs locally in your browser and does not require an account.

Formula and method

Convert x to a z-score using z = (x − mean) ÷ standard deviation, then evaluate the standard normal cumulative distribution.

Example

With mean 100 and standard deviation 15, a value of 115 corresponds to z = 1.

Tips for a useful result

This uses a numerical approximation to the standard normal cumulative distribution.

What this calculator is useful for

Find the cumulative probability below, above or between values in a normal distribution. The result is intended for quick estimates, checking arithmetic and comparing scenarios. When a result affects a contract, tax filing, medical decision, building-code requirement or other high-stakes situation, verify the result with the appropriate professional or authoritative source.

Frequently asked questions

What does the Normal Distribution Calculator calculate?

Find the cumulative probability below, above or between values in a normal distribution.

How does the Normal Distribution Calculator work?

Convert x to a z-score using z = (x − mean) ÷ standard deviation, then evaluate the standard normal cumulative distribution.

Is the Normal Distribution Calculator free to use?

Yes. ERICH Calculators is free to use and does not require an account.