T Distribution Calculator

What is the t-distribution?

The t-distribution is a bell-shaped curve used for hypothesis testing when the population standard deviation is unknown. It's wider than the normal distribution and depends on degrees of freedom. Degrees of freedom are a measure of how certain you are in the shape of the distribution. As df increases, it gets closer to the standard normal (z) distribution.

How to use this calculator

• T → P mode: Enter your t-statistic and df to get the exact, corresponding p-value. The shaded area on the graph equals the p-value.
• P → T mode: Enter a significance level (α, e.g. 0.05) and df to find the critical t-value.
• Two-tailed is used for H₁: μ ≠ μ₀. Use one-tailed when your hypothesis specifies a direction (e.g. μ > μ₀ or μ < μ₀).