MihsabaHow to use
A normal distribution is a continuous distribution defined by mean μ and standard deviation σ. The calculator standardizes values to z-scores, evaluates cumulative probability, and can invert a percentile back to x.
- Enter the mean and a positive standard deviation.
- Choose left-tail, right-tail, between-values, or inverse-percentile mode.
- Enter x, interval bounds, or the desired percentile.
- Review the z-score and probability in decimal and percent form.
How it is calculated
Example
Standard-normal example: P(−1.96≤Z≤1.96) is about 95%, while the 97.5th percentile corresponds to z≈1.96.
Important notes
Results are numerical approximations from high-accuracy browser algorithms for the normal CDF and inverse CDF. Using this tool does not establish that real data are actually normally distributed.
Frequently asked questions
What is a z-score?
It is the number of standard deviations x lies from the mean: z=(x−μ)/σ.
How is a between probability computed?
The lower cumulative probability is subtracted from the upper cumulative probability.
Can I use μ=0 and σ=1?
Yes. That is the standard normal distribution.
Is this calculator free?
Yes. It is free to use and requires no account.