T-Test Calculator
Run one-sample, two-sample (Welch's), and paired t-tests online for free. Enter your data as comma-separated numbers to get the t-statistic, degrees of freedom, exact p-value, Cohen's d effect size, 95% confidence interval, and a complete step-by-step solution. Free, private, and 100% client-side. No signup required.
Enter your data as comma- or space-separated numbers, choose the test type and tail, then click Calculate. Supports one-sample, two-sample (Welch), and paired t-tests with t-statistic, degrees of freedom, p-value, Cohen's d, and 95% CI. All calculations run locally in your browser.
Separate values with commas, spaces, or newlines
- p < 0.05 → statistically significant at α = 0.05 (*)
- p < 0.01 → highly significant at α = 0.01 (**)
- p < 0.001 → very highly significant at α = 0.001 (***)
- Cohen's d: <0.2 negligible, 0.2–0.5 small, 0.5–0.8 medium, >0.8 large
The most complete t-test calculator online — supports all three t-test types with exact p-values, Cohen's d effect size, 95% confidence intervals, and step-by-step solutions.
Three T-Test Types in One Tool
Run one-sample, two-sample (Welch's), and paired t-tests from a single interface. The t-test calculator automatically applies the correct formula and degrees of freedom for each test type.
Exact P-Values & Effect Size
Computes exact p-values using the t-distribution CDF (regularized incomplete beta function), Cohen's d effect size, and 95% confidence intervals for the mean difference — not just a pass/fail result.
Secure T-Test Calculator Online
Every calculation runs entirely in your browser using client-side JavaScript. Your data never leaves your device — complete privacy, zero server uploads, no tracking.
100% Free — No Signup Required
The t-test calculator is completely free with no account, no ads, and no usage limits. Run as many t-tests as you need, any time, on any device.
See how researchers, students, engineers, and analysts use the t-test calculator in their daily work.
Scientific Research & Experiments
Researchers use the t-test calculator to determine whether an experimental treatment produces a statistically significant effect compared to a control group. The two-sample Welch's t-test handles unequal group sizes and variances.
Clinical Trials & Medical Studies
Medical researchers use the paired t-test to compare patient measurements before and after treatment. The t-test calculator computes the exact p-value and Cohen's d to assess both statistical and clinical significance.
Statistics Homework & Education
Students use the t-test calculator to verify homework answers and understand the step-by-step calculation of t-statistics, degrees of freedom, and p-values. The solution breakdown shows every formula substitution.
Quality Control & Manufacturing
Quality engineers use the one-sample t-test to check whether a production batch meets a target specification. Enter the sample measurements and the target value to instantly see if the difference is statistically significant.
A/B Testing & Product Analytics
Product managers use the two-sample t-test to compare conversion rates, session durations, or revenue between two user groups. The t-test calculator provides the p-value and 95% CI needed to make data-driven decisions.
Psychology & Social Science
Psychologists use the paired t-test to compare pre- and post-intervention scores for the same participants. The t-test calculator computes Cohen's d to report effect size alongside statistical significance.
A complete reference guide to the three t-test types, when to use each, and how the t-statistic and p-value are computed.
What is a T-Test?
A t-test is a statistical hypothesis test used to determine whether there is a significant difference between means. It computes a t-statistic — the ratio of the observed mean difference to the standard error — and then uses the t-distribution to compute a p-value. If the p-value is below your significance level (typically α = 0.05), you reject the null hypothesis and conclude the difference is statistically significant. The t-test is appropriate when the population standard deviation is unknown and the sample size is small to moderate.
How Our T-Test Calculator Works
- 1Enter your data: Paste your numbers as comma- or space-separated values. For two-sample and paired tests, enter both groups. For one-sample, enter the sample and the hypothesized mean μ₀.
- 2Choose test type and tail:Select one-sample, two-sample (Welch), or paired. Choose two-tailed for "is there any difference?", right-tailed for "is Group 1 larger?", or left-tailed for "is Group 1 smaller?"
- 3Read the results:The t-test calculator shows the t-statistic, degrees of freedom, exact p-value, significance badge, Cohen's d effect size, 95% CI, and a step-by-step solution. All calculations run locally in your browser — your data never leaves your device.
What Gets Computed
- t-Statistic: The ratio of the mean difference to the standard error. Larger |t| values indicate stronger evidence against the null hypothesis.
- Degrees of Freedom (df):For one-sample and paired: df = n − 1. For Welch's two-sample: df is computed using the Welch-Satterthwaite equation, which accounts for unequal variances.
- p-Value: Computed using the exact t-distribution CDF via the regularized incomplete beta function. Not an approximation — the same method used by R, Python scipy, and SPSS.
- Cohen's d:A standardized effect size measure. d = mean difference / pooled standard deviation. Values: <0.2 negligible, 0.2–0.5 small, 0.5–0.8 medium, >0.8 large.
One-Sample T-Test
Tests whether a sample mean differs from a known or hypothesized population mean μ₀. Formula: t = (x̄ − μ₀) / (s / √n). Use when you have one group and a reference value.
Two-Sample Welch's T-Test
Tests whether two independent group means differ. Uses Welch-Satterthwaite df to handle unequal variances. More robust than Student's t-test. Use when comparing two separate groups.
Paired T-Test
Tests whether the mean difference between paired observations is zero. Equivalent to a one-sample t-test on the differences. Use for before/after, matched pairs, or repeated measures designs.
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A t-test calculator is a tool that performs statistical hypothesis tests to determine whether observed differences between means are statistically significant. Our t-test calculator supports one-sample, two-sample (Welch's), and paired t-tests, computing the t-statistic, degrees of freedom, exact p-value, Cohen's d, and 95% confidence interval — all in your browser with no signup required.
A one-sample t-test compares a sample mean to a known value (e.g. "is the average weight different from 70 kg?"). A two-sample t-test compares two independent group means (e.g. "do treatment and control groups differ?"). A paired t-test compares two related measurements from the same subjects (e.g. "did scores improve after training?").
The p-value is the probability of observing a t-statistic as extreme as the one computed, assuming the null hypothesis is true. A p-value < 0.05 means there is less than a 5% chance of seeing this result by chance — conventionally considered statistically significant. A p-value < 0.01 is considered highly significant.
Welch's t-test is a variant of the two-sample t-test that does not assume equal variances between groups. It uses the Welch-Satterthwaite equation to compute adjusted degrees of freedom. It is more robust than Student's t-test and is recommended as the default for two-sample comparisons when you cannot verify equal variances.
Cohen's d is a standardized effect size that measures the magnitude of the difference in standard deviation units. Values: d < 0.2 = negligible, 0.2–0.5 = small, 0.5–0.8 = medium, > 0.8 = large. A statistically significant result with a small Cohen's d may not be practically meaningful, especially with large sample sizes.
The 95% confidence interval (CI) for the mean difference gives a range of plausible values for the true population mean difference. If the CI does not include 0, the result is statistically significant at α = 0.05. The CI is computed as: mean difference ± t_{0.025, df} × SE.
The p-values are computed using the exact t-distribution CDF via the regularized incomplete beta function with Lentz's continued fraction algorithm. This is the same numerical method used by R, Python scipy.stats, and SPSS. Results are accurate to at least 4 decimal places for all practical sample sizes.
Yes, completely. All calculations are performed locally in your web browser using client-side JavaScript. No data, values, or results are ever sent to any server. Your data stays entirely on your device.
Yes. The t-test calculator is 100% free with no account registration, no payment, and no usage limits. Run as many t-tests as you need, any time, on any device.