Z Test Calculator
Last updated: July 2026 · Free · No sign-up required
Enter values above and click Calculate to see your result instantly.
About the Z Test Calculator
Under the hood, this calculator applies z = (x-bar – mu) / (sigma / sqrt(n)); p-value from the standard normal distribution, so the z test calculator result you see is genuine math, not a lookup table.
Scroll past the calculator for a quick-reference table, a step-by-step methodology with a fully worked example, and answers to the questions people most often ask about z test calculator.
From our guides
Quick reference
Z critical values:
| Test | 0.05 level | 0.01 level |
|---|---|---|
| Two-tailed | +/-1.96 | +/-2.576 |
| One-tailed | 1.645 | 2.326 |
functions Shows the working, not just the answer
For students and teachers, the final number is only half the value. Every math tool here exposes the formula it applied, the intermediate steps, and the rounding rule, so you can follow along, check your homework, or use the answer in a proof or report with confidence.
calculate Accurate to the spec
Calculations use 64-bit floating point with sensible rounding for the domain (currency to 2 decimals, percentages to 4 decimals, algebra to 6 significant figures). Where exact rational arithmetic matters — fractions, factorials, simplification — we use a dedicated BigNumber path so 1/3 + 1/6 returns ½, not 0.49999.
school Free for classroom use
Educators are welcome to link to any math calculator on CalcaTools from a class site, Google Classroom, or worksheet. The pages are mobile-friendly, free, ad-supported (so we can keep them free) and have no sign-up wall — students just click and use them in class or at home.
tips_and_updates Pair with the spoke articles
Below the calculator we link a small set of plain-English explainer pages — "What is a percentage?", "Why does PEMDAS matter?", and so on. They cover the underlying concept in 4–6 short paragraphs. Read those before the calculator if the topic is new, or after if you want the extra context.
Interpretation guide
Reading the result:
| Condition | Conclusion |
|---|---|
| p < alpha | Reject the null hypothesis |
| p >= alpha | Fail to reject the null |
| |z| large | Sample far from the null value |
| |z| near 0 | Sample consistent with the null |
Formula & methodology
Formula: z = (x-bar - mu) / (sigma / sqrt(n)); p-value from the standard normal distribution
A z-test compares a sample mean or proportion to a hypothesized value when the population standard deviation is known (or the sample is large). The calculator computes the z-statistic — how many standard errors the sample sits from the null value — and the corresponding p-value. If the p-value is below your significance level (alpha), you reject the null hypothesis. Use the t-test instead for small samples with an unknown population standard deviation.
Frequently asked questions
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