P-Value Calculator (from z-Score or t-Score)
By Santaji GadepatilinUpdated November 7, 2026
A p-value is the probability of getting a test statistic at least as extreme as the one observed if the null hypothesis were true. This p-value calculator converts a z-score (normal distribution) or a t-score with its degrees of freedom (Student t distribution) into two-tailed, left-tailed and right-tailed p-values.
How to use the p-value calculator
Choose the distribution of your test statistic — standard normal for a z-test, Student t for a t-test — then enter the statistic and, for t, its degrees of freedom. The calculator returns the two-tailed, left-tailed and right-tailed p-values. Use the two-tailed value when the alternative hypothesis is “not equal”, the right-tailed value for “greater than” and the left-tailed value for “less than”.
P-value formulas
left-tailed p = F(x) · right-tailed p = 1 − F(x) · two-tailed p = 2 × min(F(x), 1 − F(x))
F is the cumulative distribution function of the standard normal (Φ) or of Student’s t with df degrees of freedom.
Worked example
A z-test gives z = 1.96:
- Right-tailed p = 1 − Φ(1.96) = 0.0250
- Two-tailed p = 2 × 0.0250 = 0.0500 — right on the 5% threshold
If the same value were a t-score with 20 degrees of freedom, the two-tailed p-value would be 0.0641 — not significant at 5%, because the t distribution has heavier tails.
z-score to p-value table
| z | one-tailed p | two-tailed p |
|---|---|---|
| 1 | 0.1587 | 0.3173 |
| 1.282 | 0.0999 | 0.1998 |
| 1.645 | 0.0500 | 0.1000 |
| 1.96 | 0.0250 | 0.0500 |
| 2 | 0.0228 | 0.0455 |
| 2.326 | 0.0100 | 0.0200 |
| 2.576 | 0.0050 | 0.0100 |
| 3 | 0.0013 | 0.0027 |
| 3.291 | 0.0005 | 0.0010 |
| 4 | 3.17e-05 | 6.33e-05 |
Two-tailed p-value for a t-score by degrees of freedom
| df | t = 2.0 | t = 2.5 | t = 3.0 |
|---|---|---|---|
| 2 | 0.1835 | 0.1296 | 0.0955 |
| 5 | 0.1019 | 0.0545 | 0.0301 |
| 10 | 0.0734 | 0.0314 | 0.0133 |
| 20 | 0.0593 | 0.0212 | 0.0071 |
| 30 | 0.0546 | 0.0181 | 0.0054 |
| 60 | 0.0500 | 0.0152 | 0.0039 |
| 120 | 0.0478 | 0.0138 | 0.0033 |
| ∞ (z) | 0.0455 | 0.0124 | 0.0027 |
Practical notes
- Report the exact p-value (for example p = 0.031) rather than just “p < 0.05”.
- A two-tailed p-value is twice the smaller one-tailed value — never halve it after seeing which way the result went.
- Running many tests inflates false positives; with m tests a Bonferroni correction compares each p-value with α ÷ m.
Frequently asked questions
How do I get a p-value from a z-score?
For a right-tailed test p = 1 − Φ(z), for a left-tailed test p = Φ(z), and for a two-tailed test p = 2 × (1 − Φ(|z|)), where Φ is the standard normal cumulative distribution. z = 1.96 gives a two-tailed p of 0.05.
Why does the t distribution give a bigger p-value?
The t distribution has heavier tails than the normal, reflecting the extra uncertainty of estimating the standard deviation from the sample. As degrees of freedom grow, t approaches the normal distribution.
What is a significant p-value?
By convention p < 0.05, but the threshold α should be chosen before the test. Fields such as particle physics use far stricter thresholds (5σ, about p < 3×10⁻⁷).
Is the p-value the probability that the null hypothesis is true?
No. It is the probability of data this extreme assuming the null hypothesis is true. A small p-value says the data are surprising under the null, not how likely the null is.