P Value Calculator

1. **Pick the distribution** your test statistic comes from: z (standard normal), t, chi-square (χ²) or F. 2. **Enter the statistic**, for example `t = 2.45`. 3. **Enter the degrees of freedom** if the distribution needs them: one value (`df`) for t and χ², two values (`df1`, `df2`) for F. A z statistic needs none. 4. **Choose one- or two-tailed** for z and t. χ² and F tests are right-tailed by nature, so the calculator uses the upper tail for them. 5. Read the p value, then copy the APA 7 report sentence with the copy button.

You can also paste several statistics or upload a CSV to get p values for a whole column at once. Nothing is uploaded to a server: the calculation runs entirely in your browser.

A p value is the probability of getting a test statistic at least as extreme as the one you observed, **assuming the null hypothesis is true**. Small p values mean your data would be unusual if there were really no effect or no difference.

You need this calculator when you already have a test statistic but not its p value, for example:

• a textbook or exam question gives you `t = 2.45, df = 18`;
• an article reports a statistic but only `p < .05`, and you want the exact value;
• your software printed the statistic and you want to double-check the p value;
• you computed a z score by hand for a proportion or a large-sample test.

If you still need to compute the statistic itself from raw data, start with the [t test calculator](/tools/t-test-calculator), the [chi square calculator](/tools/chi-square-calculator) or the [z score calculator](/tools/z-score-calculator). Each of those reports the p value too.

The p value is an area under the probability distribution of the statistic:

• **z, two-tailed:** `p = 2 × (1 − Φ(|z|))`, where Φ is the standard normal CDF.
• **z, one-tailed (upper):** `p = 1 − Φ(z)`.
• **t, two-tailed:** `p = 2 × (1 − T_df(|t|))`, where T_df is the t distribution CDF with df degrees of freedom.
• **χ²:** `p = 1 − F_χ²(χ², df)` (upper tail only).
• **F:** `p = 1 − F_F(F, df1, df2)` (upper tail only).

The calculator evaluates these CDFs numerically, so you get an exact value rather than a range from a printed table.

**Assumptions belong to the test, not to the p value.** The p value is only valid if the test that produced the statistic was appropriate: independent observations, the right test for your design, and that test's own distribution assumptions (for example approximate normality for a t test, or expected counts of at least 5 for a chi-square test).

A study compares reaction times between two groups and reports **t = 2.45 with df = 18**. You want the two-tailed p value.

1. Distribution: t. Statistic: 2.45. df: 18. Tails: two. 2. Area above 2.45 in a t distribution with 18 df ≈ 0.0124. 3. Two-tailed p = 2 × 0.0124 ≈ **0.0247**, reported as *p* = .025.

Since .025 < .05, the result is statistically significant at α = .05. For comparison, the two-tailed critical t value for df = 18 is 2.101, and 2.45 exceeds it.

The same calculator gives these values for other statistics:

| Statistic | Tails | p value | |---|---|---| | z = 2.17 | two-tailed | .030 | | z = 2.17 | one-tailed | .015 | | χ²(3) = 7.82 | upper | .0499 | | F(2, 27) = 3.89 | upper | .033 |

Note that the one-tailed z p value is exactly half the two-tailed one.

• **p ≤ α (usually .05):** reject the null hypothesis. The data are unlikely under "no effect".
• **p > α:** you fail to reject the null hypothesis. This is **not** evidence that the null is true; your study may simply lack power.

A p value says nothing about how large or important an effect is. Always report an effect size (Cohen's d, Cramér's V, η², r) and, where possible, a confidence interval alongside it. The [t test calculator](/tools/t-test-calculator) gives you Cohen's d and a 95% CI automatically.

APA 7 asks for exact p values to two or three decimals, with no leading zero (because p cannot exceed 1), and the statistic in italics with its degrees of freedom:

> The difference between groups was statistically significant, *t*(18) = 2.45, *p* = .025.

Other formats:

• *z* = 2.17, *p* = .030
• χ²(3, *N* = 120) = 7.82, *p* = .050
• *F*(2, 27) = 3.89, *p* = .033

When p is very small, write *p* < .001 instead of a long string of zeros. The calculator's copy button produces this format for you.

If you are writing up a whole study and already have the full dataset, Data2Paper's [Generate Paper](/generate-paper) can run the analyses and draft the complete paper, including the results section, tables and figures. You can preview the first part for free before deciding to unlock it.

• **Using a two-tailed p for a one-tailed hypothesis (or the reverse).** Decide on the direction before you see the data. Halving a two-tailed p after the fact is not legitimate.
• **Wrong degrees of freedom.** For a one-sample or paired t test df = n − 1; for Student's independent t test df = n1 + n2 − 2; Welch's test uses a fractional df.
• **Using one tail for χ² or F incorrectly.** These tests are upper-tailed; do not double the p value.
• **Writing p = .000.** Software rounds; report *p* < .001.
• **Saying "p = .06 shows a trend" or "proves no effect".** Report the exact value and interpret it with the effect size and CI.
• **Treating p as the probability the null is true.** It is the probability of the data (or more extreme) given the null.