Normal Distribution Calculator
Find probabilities, percentiles, values, and z-scores for a normal distribution.
Why use this calculator
Turn a distribution into a probability or cutoff
The normal distribution is used to describe variation, standardize a value with a z-score, and approximate sampling distributions. This calculator turns a mean, standard deviation, and a value or percentile into an answer you can inspect on the curve.
What is a normal distribution?
A normal distribution is a symmetric bell-shaped distribution defined by its mean and standard deviation. The mean sets the center, while the standard deviation controls the spread. A z-score expresses how many standard deviations a value lies from the mean.
Under an exactly normal distribution, about 68% of values lie within one standard deviation of the mean, about 95% lie within two, and about 99.7% lie within three.
Using normal probabilities in experimentation
Sampling distributions, not always raw data
Revenue and other user-level metrics may be skewed even when the sampling distribution of their mean is approximately normal with sufficient data. Distinguish the raw metric distribution from the distribution of an estimator.
Percentiles and confidence intervals
Normal quantiles are used in many large-sample confidence intervals and sample-size formulas. The familiar 1.96 cutoff is the two-sided 95% standard-normal quantile.
Do not assume normality by default
Small samples, heavy tails, dependence between observations, or a ratio metric can invalidate a simple normal model. Use a method that matches the metric and experiment design.