P-Value Calculator

StatisticsLast updated: August 17, 2026

The p-value is the probability of observing a result at least as extreme as the test statistic you obtained, assuming the null hypothesis (H₀) is true. A small p-value is the numerical way of saying "if H₀ were true, data like this would be very surprising"; when p falls below the significance level α chosen in advance (usually 0.05), H₀ is rejected.

This calculator turns a test statistic you already have into an exact p-value. Use it when a paper reports only t(28) = 2.31, when you want to check the significance of a z value you worked out by hand in Excel, or when your table gives you nothing more precise than "p < 0.05". The z, t, chi-square (χ²), and F distributions are supported, and because APA 7 asks for exact p-values, the result is also given to three decimals.

Pick the distribution that matches the test your statistic came from.
E.g. z = 1.96; t = 2.31; χ² = 15.2; F = 4.35. Either a point or a comma may be used as the decimal separator.
Use a two-tailed test for z and t unless you have a directional prediction; for χ² and F the p-value always comes from the right tail.

Thresholds for Interpreting a p-Value

A p-value is interpreted by comparing it with the significance level (α) fixed in advance. The thresholds below are the ones this calculator uses in its decision table, and they are the boundaries commonly accepted in academic publishing.

p < 0.05
Significant
The standard threshold in the social sciences; H₀ is rejected. APA 7 asks for the exact value to be reported whatever the decision (e.g. p = 0.028).
p < 0.01
Highly significant
A stricter α; preferred in medical research and in analyses that involve multiple comparisons
p < 0.001
Very highly significant
Values that appear as "Sig. = .000" in SPSS output are reported as p < 0.001 under APA 7; p is never exactly zero
p ≥ 0.05
Not significant
H₀ cannot be rejected. This result is not evidence that "there is no difference"; it only shows that the data at hand do not provide enough evidence.
What the p-value does not measure
Effect size
p does not show the size of the effect, its practical importance, the probability that the hypothesis is true, or the probability that the finding will replicate. Effect size measures such as Cohen d or r² and a confidence interval should be reported alongside it.

Reporting criteria in force with the 7th edition of the APA Publication Manual (2020)Kaynak: American Psychological Association — Publication Manual (7th edition, 2020)

Formula

Two-tailed (z, t): p = 2 · [ 1 − F(|statistic|) ]
One-tailed, right: p = 1 − F(statistic)
One-tailed, left:  p = F(statistic)
χ² and F: p = 1 − F(statistic)   (always the right tail)
F: the cumulative distribution function (CDF) of the relevant distribution

The "Sig. = .000" line in SPSS output does not mean p is zero; under APA 7 that value must be reported as p < 0.001. Switching from a two-tailed to a one-tailed test after seeing the result is another common mistake.

How to Calculate

  1. Choose the type of your test statistic: z, t, chi-square (χ²), or F.
  2. Enter the value of the statistic; add the degrees of freedom for t, or the numerator and denominator degrees of freedom for F.
  3. Choose the tail type: two-tailed is the standard when you have no directional prediction (χ² and F switch to the right tail automatically).
  4. Read the exact p-value, the decisions at α = 0.10 / 0.05 / 0.01, and the distribution plot in the results section.

Worked Examples

z = 1.96 (two-tailed)

For z = 1.96 the two-tailed p-value is 0.050 — the classic boundary of the α = 0.05 level. The exact value is displayed as 0.05000 and the result counts as significant at α = 0.05.

p-value: p = 0.050 · Exact p (5 decimals): 0.05000 · Decision (α = 0.05): Significant — H₀ is rejected

t(28) = 2.31 (two-tailed)

For a t statistic of t(28) = 2.31 coming out of a t-test, the two-tailed p-value is 0.028; since p < 0.05 the difference is significant at the 5% level, but it is not significant at the 1% level.

p-value: p = 0.028 · Exact p (5 decimals): 0.02848 · Decision (α = 0.05): Significant — H₀ is rejected

χ²(6) = 15.2 (right tail)

In a chi-square test with 6 degrees of freedom, χ² = 15.2 gives p = 0.019; the relationship between the variables is statistically significant at the α = 0.05 level.

p-value: p = 0.019 · Exact p (5 decimals): 0.01876 · Decision (α = 0.05): Significant — H₀ is rejected

Frequently Asked Questions

What exactly does a p-value tell you?
The p-value is the probability of observing a test statistic at least as extreme as yours, given that the null hypothesis is true. It is not the probability that the hypothesis is true, not the probability that the result will replicate, and not the size of the effect. If p < α, H₀ is rejected; but a p-value on its own says nothing about practical importance, so it should always be reported alongside an effect size.
Can a p-value really be 0.000?
No; a p-value is never exactly zero. The "Sig. = .000" output in SPSS means the value rounded to 0.000 at three decimals. Under APA 7 this is reported as p < 0.001, and this calculator displays values below 0.001 the same way.
What is the difference between a one-tailed and a two-tailed p-value?
A two-tailed test looks for departures in both directions, while a one-tailed test looks only in the predicted direction; for symmetric distributions the one-tailed p is half the two-tailed value. A one-tailed test is justified only when the directional hypothesis was argued for before the data were collected; switching to one tail after seeing the result artificially shrinks the p-value.
Why do chi-square and F tests use only the right tail?
Chi-square and F statistics are built from squared quantities, so they cannot be negative, and any departure from the null hypothesis in any direction makes the statistic larger. Significance is therefore always judged by the area in the right tail of the distribution; the left tail is used only in special scenarios such as a variance ratio.
What is the difference between the p-value and α (alpha)?
α is the error rate the researcher fixes before collecting data (the probability of a Type I error; usually 0.05). The p-value is computed from the data. The decision rule is simple: if p < α the result is called significant and H₀ is rejected; if p ≥ α, H₀ cannot be rejected.
Is there really a big difference between p = 0.049 and p = 0.051?
In practice, no; the two values carry almost identical evidential weight. The 0.05 threshold is a convention, and reducing the p-value to a binary decision throws information away. This is why APA 7 asks for the exact p-value, together with an effect size and a confidence interval, whatever the decision turns out to be.