📈Z-Score Calculator

About this tool

Start from a raw value with its mean and standard deviation, from a z-score, or from a percentile. The calculator shows the z-score, the percentile, the left-tail, right-tail and two-tailed probabilities and, given a mean and standard deviation, the matching raw value. A normal curve shades the area below your z.

What a z-score tells you

A z-score measures how many standard deviations a value lies from the mean: z = (x − μ) ÷ σ. That puts scores from different scales on a common footing. On an IQ scale with a mean of 100 and a standard deviation of 15, a score of 130 is z = 2. For normally distributed data, z converts to a percentile through the normal cumulative distribution, so z = 2 is higher than about 97.7% of values. In hypothesis testing, z converts to a p-value. The two-tailed p-value is the chance of a result at least that extreme in either direction, so z = 1.96 gives the familiar p = 0.05. One-tailed tests use a single tail. Working backwards, the 95th percentile is z ≈ 1.645, and the middle 95% of a normal distribution lies within ±1.96 standard deviations. Honest limits: these conversions assume the data follow a normal distribution, and heavily skewed data, such as incomes, need other methods. The standard deviation calculator finds μ and σ from raw data, the confidence interval calculator builds ranges and the A/B test calculator applies the same ideas to experiments. Standard deviation explained: what it measures, how it's calculated, and the 68–95–99.7 rule explains the spread.

Frequently asked questions