P-Value Calculator (z to p)
Convert a z-score to one-tail or two-tail p-value via the standard normal CDF.
Result
p-value
0.049996
two-tailed at z = 1.96.
- z-score1.96
- CDF Φ(z)0.975002
- Tailtwo
- p-value0.04999565
- Sig at α = 0.05?✓ Significant at α = 0.05
- Sig at α = 0.01?✗
Step-by-step
- Φ(1.96) = 0.975002 (cumulative normal).
- Two-tailed: p = 2 × (1 − Φ(|z|)) = 2 × (1 − 0.975002) = 0.049996.
How to use this calculator
- Compute z-score from your data.
- Pick tail type.
- Read p and significance.
About this calculator
A p-value is the probability of seeing test results at least as extreme as observed, assuming the null hypothesis is true. Smaller p ⇒ stronger evidence against H₀. Conventional threshold: p < 0.05 for "significant"; p < 0.01 for "highly significant". Two-tailed test (|z|) is appropriate when alternative is two-sided; one-tailed when direction is pre-specified. Calculator uses Abramowitz-Stegun normal CDF approximation (~7 decimal accuracy).
Frequently asked
Convention from Fisher (1925). Loosely: 1-in-20 false positive rate is acceptable for many fields. Increasingly criticized in favor of pre-registration and effect-size emphasis.
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