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T-Test Calculator (Welch and Student)

Paste two independent samples and get t, the degrees of freedom, the p-value, the critical value and the decision — computed BOTH ways, Welch and Student's pooled variance, with Welch as the default because it does not assume the two variances are equal. The Welch–Satterthwaite degrees of freedom are computed exactly, not rounded down. Sample means, standard deviations, the confidence interval of the difference and Cohen's d come with it.

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Open T-Test Calculator (Welch and Student) and you get an answer straight away, with no account to create. You will find it under Statistics & probability, with Chi-Square Test Calculator and F-Test Calculator for the neighbouring cases.

How to use it

  1. Open the tool — no signup or install needed.
  2. Enter your input or adjust the available options.
  3. Get your result instantly, then copy or download it.

Frequently asked questions

What is T-Test Calculator (Welch and Student)?

Paste two independent samples and get t, the degrees of freedom, the p-value, the critical value and the decision — computed BOTH ways, Welch and Student's pooled variance, with Welch as the default because it does not assume the two variances are equal. The Welch–Satterthwaite degrees of freedom are computed exactly, not rounded down. Sample means, standard deviations, the confidence interval of the difference and Cohen's d come with it.

When would I actually use this?

Summarising a dataset before drawing conclusions from it, checking whether a difference between two groups is real, and putting an interval around an estimate.

What is the most common mistake?

Reading a p-value as the probability that the hypothesis is wrong. It is the probability of seeing data at least this extreme if the null were true — a different statement, and a much weaker one.

How is T-Test Calculator (Welch and Student) different from Chi-Square Test Calculator?

They sit next to each other but answer different questions: Chi-Square Test Calculator is the one to open when you need it to χ² test of independence on any contingency table, showing observed, expected, the contribution and the standardised residual of every cell, plus Cramér's V. Cells with an expected count below 5 are flagged, because that is when the test stops being valid. Pick whichever matches what you're starting from — both are free.

Is there a tool for the next step?

F-Test Calculator is the closest one after this: Three ways in: a one-way ANOVA from raw groups, a two-sample variance ratio, or a bare F with its two degrees of freedom. Each gives the p-value, the critical value at your α and the decision, from the same exact F distribution.

What else is worth having open alongside it?

Fisher's Exact Test Calculator and Kruskal-Wallis Test Calculator — they come up in the same task often enough to be worth a second tab.

Where do the figures come from?

Distributions and test statistics are computed from their standard definitions, not from a lookup table, so results carry more digits than a printed table would. The assumptions each test makes are stated with it.

Further reading

All guides →
ExplainerA 1 % Drop Rate Does Not Mean One Hundred RunsAt 1 %, a hundred attempts give you 63.4 % — not certainty. Ninety per cent takes 230 attempts and ninety-nine takes 459, and more than a third of players are still empty-handed at a hundred.ExplainerWhat Is a Z-Score? Standard Deviations Above the MeanA z-score is z = (x − μ) / σ — how many standard deviations a value sits from the mean. Learn how to compute it, read the standard normal curve, and turn it into a percentile.ExplainerMean, Median and Mode: What's the Difference?Mean, median and mode all describe the 'middle' of your data — but answer different questions. Here's what each means, with examples and when to use which.ExplainerGeometric vs Arithmetic Mean: Which to UseThe arithmetic mean adds and divides; the geometric mean multiplies and takes a root. Learn which fits growth rates, ratios, and averages.How-toHow to Calculate Standard Deviation (Step by Step)Standard deviation measures how spread out your data is. Here's the formula, a worked example, and the difference between population and sample.ExplainerProbability Basics, With ExamplesProbability measures how likely something is, from 0 to 1. Here's the basic idea, how to combine events with AND and OR, and the complement.