P-Value Calculator
Turn a z, t, chi-square, or F test statistic into an exact p-value for a left, right, or two-tailed hypothesis test.
Distribution
Tail
Significant at α = 0.05 (reject H0)
How does this calculator work?
A p-value is the probability of getting a test statistic at least as extreme as the one observed, assuming the null hypothesis is true. Enter your z, t, chi-square, or F value with its degrees of freedom and tail, and this tool returns the exact p-value and whether it is significant at α = 0.05.
Formula
How this is calculated
Pick the distribution that matches your test, enter the observed test statistic, and (for t, χ², and F) the degrees of freedom — F also needs a denominator df. The calculator evaluates the cumulative distribution function exactly: the normal CDF uses an erf approximation, the t and F tails use the regularized incomplete beta function I_x(a,b), and the chi-square upper tail uses the regularized lower incomplete gamma function via p = 1 − P(χ² < x; df).
The tail setting decides which probability becomes the p-value. A right-tailed test returns the upper-tail area P(X > stat); a left-tailed test returns P(X < stat); a two-tailed test doubles the smaller tail, p = 2·min(upper, lower), capped at 1. The result is then compared against the conventional α = 0.05 threshold to report whether the null hypothesis is rejected. The shaded curve shows the density with only the rejection (tail) region filled.
Assumptions: the statistic is computed correctly under the null hypothesis and the chosen reference distribution is valid (e.g., normality or large samples for z). Degrees of freedom must be positive; χ² and F statistics must be non-negative since those distributions have support on [0, ∞). Series and continued-fraction expansions converge to roughly 1e-15, so p-values are accurate to many decimals across typical ranges.
Frequently asked questions
Use two-tailed when your alternative hypothesis is simply "different" (≠), and one-tailed when you predict a specific direction (> or <) before seeing the data. Two-tailed doubles the one-tailed p-value for symmetric distributions like z and t.
Chi-square goodness-of-fit and ANOVA F tests measure discrepancy, where larger statistics mean stronger evidence against the null. Only large values are surprising, so the standard p-value is the right (upper) tail P(X > stat).
No. A small p-value means the data would be unlikely if the null hypothesis were true, so you reject the null. It does not measure effect size or the probability that the alternative is true.
Also known as
TG we-Calculate Editorial Team. (2026). P-Value Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/p-value-calculator
TG we-Calculate Editorial Team. "P-Value Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/p-value-calculator.
TG we-Calculate Editorial Team, "P-Value Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/p-value-calculator
@misc{wecalculate_p_value_calculator, title = {P-Value Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/p-value-calculator}}, year = {2026}, note = {TG we-Calculate} }
Did this calculator help you?