🧪T-Test Calculator
Run one-sample, two-sample, or paired t-tests and get the test statistic, degrees of freedom, and p-value.
Free T-Test Calculator
Our free t-test calculator runs one-sample, two-sample independent (Welch's), and paired t-tests, returning the t-statistic, degrees of freedom, and two-tailed p-value instantly. Enter your sample statistics — mean, standard deviation, and sample size — and the test type handles the rest.
The one-sample test compares a sample mean against a hypothesized value. The two-sample test compares means from two independent groups using Welch's t-test, which doesn't assume equal variances. The paired test compares before-and-after measurements on the same subjects using the mean and standard deviation of the differences.
Every result shows the formula and substitution used to compute the t-statistic and p-value, so you can verify the calculation for coursework, research, or a quick significance check. No sign-up, no downloads — everything runs instantly in your browser.
About the T-Test Calculator
Features
Three test types
One-sample, two-sample (Welch's), and paired t-tests in one tool.
Accurate p-values
Uses the regularized incomplete beta function for an accurate Student's t-distribution CDF.
Significance flag
Instantly see whether the result is significant at the common α=0.05 threshold.
Step-by-step working
See the exact formula and substitution used to compute the t-statistic and degrees of freedom.
Frequently Asked Questions
What is a t-test used for?
A t-test determines whether there is a statistically significant difference between means — either a sample mean and a hypothesized value, two independent group means, or paired before-and-after measurements.
What's the difference between one-sample, two-sample, and paired t-tests?
A one-sample test compares a sample mean to a fixed value. A two-sample test compares means from two independent groups. A paired test compares the same subjects measured twice, using the differences between pairs.
Why does the two-sample test use Welch's formula?
Welch's t-test doesn't assume the two groups have equal variances, which makes it more robust and reliable than the pooled-variance t-test for most real-world data.
What is degrees of freedom?
Degrees of freedom (df) describes how many independent values went into the estimate. For one-sample and paired tests, df = n − 1. Welch's two-sample test uses the Welch–Satterthwaite equation, which can produce a non-integer df.
What does the p-value mean?
The p-value is the probability of observing a t-statistic this extreme if there were truly no difference between the means. A p-value below your significance level (commonly 0.05) suggests the difference is statistically significant.
Is this a one-tailed or two-tailed test?
This calculator reports the two-tailed p-value, which tests for a difference in either direction. For a one-tailed test, divide the reported p-value by 2 (if the observed direction matches your hypothesis).
What inputs does the paired t-test need?
The paired test needs the mean and standard deviation of the differences between each pair of measurements, plus the number of pairs.
Can sample size be very small?
The calculator requires at least 2 observations per group so a standard deviation and degrees of freedom can be computed, but t-tests are most reliable with larger samples.
What counts as statistically significant?
This calculator flags results as significant when the two-tailed p-value is below 0.05, the most common threshold, though your context may call for a different significance level.
Is this calculator free to use?
Yes, the t-test calculator is completely free with no sign-up, and all calculations run instantly in your browser.