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
- Choose critical value or p-value.
- Enter the degrees of freedom.
- Enter the confidence level or the t statistic.
- Read the result and the table of common critical values.
T Table Formula
Standardised t
Confidence interval
T Table Variables Explained
| Symbol | Meaning | Notes |
|---|---|---|
| df | Degrees of freedom | n − 1 for one sample |
| t* | Critical t value | |
| t | Observed t statistic | |
| α | Significance level | 1 − confidence |
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:
- α = 1 − 95 ÷ 100 = 0.05.
- Two-tailed: t* = t(1 − α/2, df = 15) = 2.13145.
- One-tailed: t = t(1 − α, df = 15) = 1.75305.
Result: Two-tailed critical value t* = ±2.13145; One-tailed critical value = 1.75305.
How to Read a t Critical Value
The t distribution has heavier tails than the normal, especially for small samples. For a 95% interval from 16 values, df = 15 and the two-tailed critical value is 2.1314, compared with 1.96 for a z-based interval. The larger value widens the interval to allow for the uncertainty in the estimated standard deviation.
As degrees of freedom grow, t approaches z. At df = 30 the 95% value is 2.042, and at infinity it is 1.96. The table on this page lists the critical values for your degrees of freedom at the usual confidence levels.
Where T Table Is Used
Confidence intervals
Get the multiplier t* for a mean with an unknown standard deviation.
t-tests
Find the critical value to compare with a t statistic.
Finding a p-value
Convert a t statistic and its degrees of freedom into a p-value.
Replacing a printed table
Get exact values for any degrees of freedom, with no interpolation.
Common T Table Mistakes to Avoid
- Degrees of freedom for a one-sample t are n − 1.
- Check whether your table is one-tailed or two-tailed. The same value of α gives different cut-offs.
- For df above about 100, t* is very close to z*.
- Use the t value, not z, whenever the standard deviation is estimated from a small sample.
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
How do I read a t table?
Find the row for your degrees of freedom and the column for your confidence level or tail area. The entry is the critical value t*.
What is the critical t value for 95% with df = 10?
It is 2.228 for a two-tailed 95% interval. The z value for the same level is 1.96.
Why is t larger than z?
The sample standard deviation is only an estimate, which adds uncertainty. The t distribution has heavier tails to reflect that, and it is the larger the smaller the sample.
How do I get a p-value from t?
Find the area in the tail or tails beyond your t statistic with the correct degrees of freedom. The calculator does this from the t statistic you enter.