Z-Score Calculator

How to use

1. 1Pick a mode. Direct uses values you already know, Dataset takes a list of numbers, and Inverse looks up z from a probability or percentile.
2. 2In Direct mode, enter the raw value (x), the mean (μ), and the standard deviation (σ). The z-score, p-values, and percentile update as you type.
3. 3In Dataset mode, paste a column of numbers separated by commas, spaces, or newlines, then enter the raw value to score against the dataset. Switch the standard deviation type to sample (n − 1) for inferential statistics or population (n) when your data covers the whole group.
4. 4In Inverse mode, enter a probability (0 to 1) or a percentile (0 to 100) and pick a tail (two-tailed, left, or right). The matching critical z value is returned along with a reference table of common α levels.
5. 5Click Copy summary to grab a one-line description of the result for homework, a lab report, a spec, or a chat message.

About this tool

Z-Score Calculator standardizes a raw value against a normal distribution and returns the matching p-values and percentile, with three working modes built into the same page. In Direct mode you supply the raw value, the mean, and the standard deviation that you already know (from a textbook problem, a published study, a quality control specification, or an exam rubric); the tool returns z = (x − μ) / σ along with the left-tailed p-value Φ(z), the right-tailed p-value 1 − Φ(z), the two-tailed p-value 2 × (1 − Φ(|z|)), and the percentile rank as a percentage. In Dataset mode you paste a column of numbers and one raw value to score against them; the tool computes the dataset mean, computes the sample standard deviation (n − 1, Bessel's correction, the default for inferential statistics) or the population standard deviation (n), and then standardizes the raw value using the same formulas as Direct mode. Sample and population are both available because students, biologists, and quality engineers often pick the wrong one by accident; the tool labels each choice and explains the difference. In Inverse mode you supply a probability between 0 and 1 (or a percentile between 0 and 100) and pick a tail; the tool returns the matching critical z value, which is what you need for confidence intervals (95% CI uses z = 1.96, 99% CI uses z = 2.5758) and for hypothesis tests at common α levels. The standard normal cumulative distribution function uses the Abramowitz and Stegun 26.2.17 polynomial approximation of erf, accurate to about 7.5 × 10⁻⁸ across the real line, which is more precision than any classroom z-table will offer. The inverse normal uses Peter Acklam's rational approximation, accurate to about 1.15 × 10⁻⁹ in the body of the distribution. Each mode shows a step-by-step explanation of the calculation so students can copy the working into their homework, plus a built-in reference table of the most-used critical values (α = 0.10, 0.05, 0.01, 0.001) and a short explainer covering what a z-score means, when to use two-tailed vs one-tailed p-values, and the rough 68-95-99.7 empirical rule for normal distributions. Useful for exam revision, hypothesis testing in psychology and biology, six-sigma quality work, finance risk modelling, education grading on a curve, comparing measurements with different units, computing standardized residuals, and any moment when you would otherwise reach for a printed z-table. Everything runs locally in your browser; nothing you type is uploaded.

Free to use. Works in your browser. No signup, no login.