P Value Calculator

Formula

Uses the relationship between the t distribution and the incomplete beta function for stable tail probabilities.

Worked Example

How P-Values Are Calculated from t Statistics

• This calculator uses the Student t cumulative distribution function (CDF) via the regularized incomplete beta function for numerically stable tail probabilities
• Two-tailed p-values test for deviation in either direction from the null. They double the smaller single-tail probability
• One-tailed p-values test for deviation in a specific direction only (upper or lower), producing a smaller p-value than two-tailed for the same t statistic
• The standard significance threshold is alpha = 0.05, meaning you reject the null if p is less than 0.05. Some fields use stricter thresholds (0.01 or 0.001)
• Degrees of freedom (df) affect the shape of the t distribution. Lower df produces heavier tails, making it harder to achieve small p-values from the same t statistic

P-values tell you the strength of evidence against the null hypothesis, not the probability that the null is true. Always interpret p-values in the context of effect size, sample size, and study design.

You can also calculate changes using our Two-Tailed P Value Calculator, One-Tailed P Value Calculator, Test Statistic to P Value Calculator or T-Test Calculator.

Frequently Asked Questions