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An online t-test calculator that quickly tells whether the difference between two group means is significant — enter the means, standard deviations, and sample sizes to get the t-value and p-value.
Both samples require at least 2 valid numbers.
Enter at least 2 numbers per sample. For paired tests, sample sizes must be equal. Separate numbers with commas, spaces, or newlines. Non-numeric input will be ignored.
Enter sample data to see T-test results
Overview
Understand what the tool solves, how it works, and the boundaries of its data.
A t-test compares a sample mean with a reference value or compares two means under a stated model. Choose one-sample when one group is compared with a hypothesized mean, paired when each value in one list corresponds to a value in the other, and independent two-sample when the groups contain different, unrelated observations. The calculator takes raw numeric observations, not summary-only inputs such as a mean, standard deviation, and sample size.
For two independent samples, Welch is the default. It uses each group’s sample variance and does not assume equal population variances. The alternative pooled Student method assumes equal variances. NIST describes the corresponding one-sample, paired, and two-sample calculations and their test statistics.
The t statistic expresses the observed mean difference relative to its estimated standard error. Degrees of freedom determine the reference t distribution used for the p-value. Select a left-tailed, right-tailed, or two-tailed alternative to match the question you set before examining the result; the default is two-tailed. The default significance level is α = 0.05.
A p-value is the probability, assuming the null hypothesis is true, of observing a test statistic at least as extreme as the one obtained under the selected alternative. Compare it with your preselected α. A p-value below α leads to rejecting that null hypothesis for this test; a p-value at or above α means the result did not cross that decision threshold. It does not prove the null is true or that the groups are identical.
One sample: t = (x̄ − μ₀) / (s / √n), df = n − 1.
Paired: calculate dᵢ = xᵢ − yᵢ, then t = d̄ / (sᵈ / √n), df = n − 1.
Independent Welch: t = (x̄₁ − x̄₂) / √(s₁²/n₁ + s₂²/n₂), with Welch–Satterthwaite degrees of freedom.
Guide
Follow the workflow and verify inputs and outputs with practical examples.
Select one-sample, paired, or two-sample based on the study design. For one-sample, also enter the hypothesized mean μ₀.
Paste the observations into the sample box or boxes. Separate values with commas, spaces, semicolons, tabs, or line breaks. At least two valid numeric observations are needed per sample. Paired lists must have equal lengths and matching order.
For an independent two-sample test, keep Welch unless an equal-variance assumption is supported for your analysis; pooled Student is available as an explicit alternative.
Choose the tail and α, then read t, degrees of freedom, p-value, descriptive statistics, distribution plot, and the calculation steps together. Alpha must be between 0 and 1; if the entered value is invalid, the calculation falls back to 0.05.
Example for a paired test: enter 4, 7, 9 in the first list and 3, 5, 6 in the second. Pairwise differences are 1, 2, and 3; their mean is 2 and sample standard deviation is 1. This gives t ≈ 3.464 and df = 2. With a two-tailed test, p is about 0.074, above α = 0.05, so this example does not reject the null at that threshold.
Use cases
See how the tool fits into real work and everyday tasks.
When the same participants are measured twice, enter values in corresponding order and use paired mode to test the mean of within-person differences.
For observations from distinct groups, use independent two-sample mode. Welch is the default when equal population variance has not been established.
When a set of measurements is compared with a stated benchmark, use one-sample mode and enter that benchmark as μ₀. Keep the measurement units and sampling method alongside the result.
Q&A
Find concise answers to common questions and confusing cases.
No. The input fields parse raw observations. This calculator does not have a summary-statistics entry mode.
Use paired mode and keep the two lists in matching participant order. If the groups contain different people without one-to-one pairing, use independent two-sample mode.
No. It means the observed result did not cross the chosen α threshold for rejecting the null under the selected model. It is not proof that the means are equal.
Pooled Student assumes equal population variances. Use it only when that assumption is appropriate for the study; otherwise the default Welch method avoids imposing it.
Notes
Review scope, result limitations, and important precautions before use.
Check independence for separate observations and preserve the correct one-to-one relationship for paired measurements. Strong skew or influential outliers can make a small-sample mean comparison difficult to interpret; consider whether the method fits the data and study design. Statistical significance does not measure practical importance and does not establish causation. Do not use this result alone for medical, legal, engineering-safety, or other high-impact decisions.
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