Calculate probabilities, z-scores, and percentiles for any normal distribution
Enter parameters and calculate
The normal distribution (also called Gaussian distribution or bell curve) is the most important probability distribution in statistics.
Standardize any normal distribution to standard normal (μ=0, σ=1):
The distribution of sample means approaches normal as sample size increases, regardless of the population distribution. This makes the normal distribution fundamental to inferential statistics.
Every coffee helps keep the servers running. Every book sale funds the next tool I'm dreaming up. You're not just supporting a site — you're helping me build what developers actually need.
μ is the mean (center) and σ is the standard deviation (spread) of the normal distribution.
Enter a value and choose left tail P(X ≤ x), right tail P(X ≥ x), or between/outside ranges to shade the curve and compute areas.
Use the inverse option to enter a percentile and get the corresponding x value for your specified μ and σ.
Consider transformations or non‑parametric methods; the normal model assumptions may not apply to heavily skewed or multimodal data.