P-Value from Z-Score Calculator
Last updated: June 2026 · Free · No sign-up required
Enter values above and click Calculate to see your result instantly.
Quick reference
| z-score | Two-tailed p |
|---|---|
| 1.645 | 0.10 |
| 1.96 | 0.05 |
| 2.576 | 0.01 |
| 3.291 | 0.001 |
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.
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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.
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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.
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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
| p-value | Conventional reading |
|---|---|
| p < 0.01 | Strong evidence against H₀ |
| 0.01 ≤ p < 0.05 | Significant at the 5% level |
| 0.05 ≤ p < 0.10 | Marginal — often called suggestive |
| p ≥ 0.10 | No evidence against H₀ at usual levels |
Formula & methodology
Formula: Left: p = Φ(z); Right: p = 1 − Φ(z); Two-tailed: p = 2 × min(Φ(z), 1 − Φ(z))
- Enter the z-score from your test statistic.
- Choose the tail that matches your alternative hypothesis.
- The standard normal CDF Φ gives the tail area — the p-value — compared against α = 0.05 and 0.01.
Worked example: z = 1.96, two-tailed → p = 2 × (1 − 0.975) = 0.05 — right at the classic significance threshold. z = −2.5 left-tailed → p = 0.0062.
Frequently asked questions
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