T Table Calculator (T Distribution)

What Is T Table?

The t distribution is the bell-shaped distribution used for small samples when the population standard deviation is unknown. It has heavier tails than the normal distribution, and approaches it as the degrees of freedom increase.

Choose critical value to get the t* for a confidence interval or test, or p-value to turn a t statistic into a probability. The calculator also gives a t table for your degrees of freedom at the common confidence levels from 80 % to 99.9 %, so it works as a complete t table.

The article below covers the formulas, variables, a worked confidence interval and answers to common questions about reading a t table.

How to Use the T Table Calculator

1. Choose critical value or p-value.
2. Enter the degrees of freedom.
3. Enter the confidence level or the t statistic.
4. Read the result and the table of common critical values.

T Table Formula

T Table Variables Explained

T Table Worked Example

For a 95% confidence interval from a sample of 16 values, df = 15 and the two-tailed critical value is t* = 2.1314. The margin of error is 2.1314 × s ÷ 4. A z-based interval would use 1.96, which is too narrow for a sample this small.

With the example values loaded in the calculator above, the steps are:

1. α = 1 − 95 ÷ 100 = 0.05.
2. Two-tailed: t* = t(1 − α/2, df = 15) = 2.13145.
3. One-tailed: t = t(1 − α, df = 15) = 1.75305.

Result: Two-tailed critical value t* = ±2.13145; One-tailed critical value = 1.75305.

Where T Table Is Used

Common T Table Mistakes to Avoid

• df for a one-sample t-test is n − 1.
• Use the two-tailed value for confidence intervals.
• Non-integer df (Welch test) are allowed.

T Table Terms and Definitions

Degrees of freedom

The number of independent pieces of information used to estimate the spread.

Critical value

The cut-off t where the tail area equals α.

T Table FAQs