CalcaTools

P-Value from Z-Score Calculator

Convert a z-score to its left-, right- or two-tailed p-value with significance verdicts.

Last updated: June 2026 · Free · No sign-up required

Results

Enter values above and click Calculate to see your result instantly.

Quick reference

z-scoreTwo-tailed p
1.6450.10
1.960.05
2.5760.01
3.2910.001

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.

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

p-valueConventional reading
p < 0.01Strong evidence against H₀
0.01 ≤ p < 0.05Significant at the 5% level
0.05 ≤ p < 0.10Marginal — often called suggestive
p ≥ 0.10No 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))

  1. Enter the z-score from your test statistic.
  2. Choose the tail that matches your alternative hypothesis.
  3. 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

How do I find the p-value from a z-score?
Take the standard normal tail area beyond your z. Left-tailed uses Φ(z), right-tailed 1 − Φ(z), and two-tailed doubles the smaller tail.
What is the p-value for z = 1.96?
Two-tailed p = 0.05 exactly (to 3 decimals) — which is why ±1.96 is the cutoff for 95% confidence.
When do I use one-tailed vs two-tailed?
Two-tailed tests "different from"; one-tailed tests a direction ("greater than" or "less than") chosen before seeing the data. Two-tailed is the safer default.
Is my result significant?
Compare p to your α: p < 0.05 rejects H₀ at the 5% level, p < 0.01 at the 1% level. The calculator prints both verdicts.
Can a z-score be negative?
Yes — negative z just means the statistic fell below the mean. Two-tailed p-values are identical for +z and −z.

Explore the full statistics toolkit

Every CalcaTools statistics calculator — descriptive measures, probability distributions, hypothesis tests, confidence intervals, and Six Sigma process metrics — with step-by-step workings on each result.

Process quality