A walkthrough, end to end.
- 1
Enter the z-score (standardized test statistic).
- 2
Pick test type: left-tailed, right-tailed, or two-tailed.
- 3
The calculator returns the p-value from the standard-normal CDF.
P-value from z
Right-tailed: p = 1 − Φ(z). Left-tailed: p = Φ(z). Two-tailed: p = 2 × (1 − Φ(|z|)). Φ is the standard normal CDF; the calculator uses an Abramowitz-Stegun approximation accurate to ~10⁻⁷.
What you can do with this.
Hypothesis testing
Reject H₀ if p < α (typically 0.05). p < 0.001 = strong evidence; 0.05–0.001 = moderate; > 0.05 = fail to reject. The calculator just computes p; interpretation depends on your test.
Two-tailed test
When you don't have a directional hypothesis (e.g., 'is the mean different from 100?'). Use two-tailed; doubles the one-tailed p-value.
One-tailed test
When you have a directional hypothesis (e.g., 'is the mean GREATER than 100?'). Right-tailed: p = P(Z ≥ z). Left-tailed: p = P(Z ≤ z).
Effect-size warning
Statistical significance ≠ practical importance. With huge n, even tiny effects can produce p < 0.001. Always report effect size alongside p-value.
Interpreting p < 0.05
Doesn't mean 'there's a 5% chance H₀ is true' (Bayesian misinterpretation). Means 'if H₀ is true, we'd see this z or more extreme < 5% of the time'.
Multiple testing correction
Running 20 tests at α=0.05 means ~1 false positive expected by chance. Use Bonferroni (α/n) or FDR correction. The calculator gives raw p; correction is on you.
Pre-registration
Pick your test type (one- vs two-tailed) BEFORE seeing data. Picking based on observed direction is p-hacking.
P-value 2026 — what's current
p-values remain the dominant statistical-significance metric in most fields. ASA's 2016 statement urged caution; complementary effect sizes and CIs are increasingly required alongside p.
Frequently asked.
Field-dependent. Generally p < 0.05 considered statistically significant. Medical: often p < 0.01 or p < 0.001. Physics: 5σ standard (~10⁻⁷ p-value).
Two-tailed by default — more conservative. Use one-tailed only when you have a strong directional hypothesis pre-registered before seeing data.
This calculator is z-based. For t, F, χ² tests, use the appropriate distribution calculator (typically built into stats software like R, Python's scipy).
No. Calculations run entirely in your browser.