T-Test Calculator
Run a one-sample t-test from a sample mean, hypothesized mean, sample standard deviation, and sample size, with the p-value shown.
T-Test Calculator
Run a one-sample t-test from a sample mean, hypothesized mean, sample standard deviation, and sample size, with the p-value shown.
Enter values and compute the result.
A t-test calculator checks whether a sample mean differs significantly from a hypothesized value. This one-sample t-test takes your sample mean, the hypothesized mean, the sample standard deviation, and the sample size, then returns the t statistic, its degrees of freedom, and a two-tailed p-value. It is the right tool when the population standard deviation is unknown and your sample is small.
How to use this calculator
- Enter the sample mean — the average of your observed data.
- Enter the hypothesized mean — the value you are testing against (often a target or historical figure).
- Enter the sample standard deviation of your data.
- Enter the sample size (
n), then read the t statistic, the degrees of freedom (n − 1), and the two-tailed p-value.
A p-value below your significance level (commonly 0.05) is evidence that the sample mean differs from the hypothesized mean.
Worked example
Suppose a sample of 25 values has a mean of 105 and a standard deviation of 15, and you are testing against a hypothesized mean of 100.
First find the standard error, then the t statistic:
standard error = sd / √n = 15 / √25 = 15 / 5 = 3
t = (sample mean − hypothesized mean) / SE = (105 − 100) / 3 ≈ 1.667
degrees of freedom = n − 1 = 24
With t ≈ 1.667 on 24 degrees of freedom, the two-tailed p-value is about 0.109. Because 0.109 is greater than 0.05, you would not reject the hypothesis that the true mean is 100 — the difference could plausibly be chance. For the method and assumptions behind the one-sample t procedure, see the OpenStax single population mean using the Student t distribution.
Frequently asked questions
When should I use a t-test instead of a z-test?
Use a t-test when the population standard deviation is unknown and you estimate it from the sample, especially with small samples. As the sample size grows, the t distribution approaches the normal, and the two tests give similar answers.
What does the t statistic mean?
The t statistic measures how many standard errors the sample mean sits from the hypothesized mean. Larger absolute values indicate a bigger, less likely-by-chance gap between the sample and the hypothesized value.
Why is this a two-tailed p-value?
A two-tailed test asks whether the mean differs in either direction. The calculator doubles the one-tailed tail area so that a difference above or below the hypothesized mean both count toward significance.