t-Distribution
Student's t PDF, CDF, and critical values
About this calculator
The t-Distribution Calculator evaluates Student's t-distribution for any positive degrees of freedom. In point mode it returns the probability density, the left-, right-, and two-tailed probabilities, and the percentile of a given t value; in critical-value mode it inverts the distribution to find the one- or two-tailed critical t* for a significance level α, along with the matching confidence level. Fractional degrees of freedom are accepted, and probabilities are clamped to [0, 1] against numerical overshoot.
How to use the t-Distribution calculator
- Enter the values for your problem into the input fields.
- Read the result — it updates instantly as you type.
- Check the formula and the visual explanation to follow how the answer was found.
- Copy the page URL to share the exact calculation.
Common examples
- Two-tailed critical value, df = 10, α = 0.05 → t* ≈ 2.2281 (the classic 95% CI multiplier)
- One-tailed critical value, df = 20, α = 0.05 → t* ≈ 1.7247
- t = 2 with df = 15 → CDF ≈ 0.968, two-tailed p ≈ 0.0639, right tail ≈ 0.032
- t = 0 with df = 5 → density ≈ 0.3796 at the peak, CDF exactly 0.5 by symmetry
Frequently asked questions
How does the t-Distribution calculator work?
Enter your values and the calculator applies the exact mathematical method for this problem, showing the result together with the formula it used. Everything is computed with high-precision arithmetic, so the answer you see is not limited by ordinary floating-point rounding.
When would I use the t-Distribution calculator?
It is useful for homework and exam preparation, for checking work done by hand, and whenever a step in a larger problem needs this calculation done quickly and reliably.
How accurate are the results?
Calculations run at 30 significant digits of precision internally. Displayed values are rounded for readability, but the underlying result is far more precise than a typical hand or pocket-calculator computation.
Can I share a specific calculation with someone else?
Yes. Every value you enter updates the URL, so copying the address bar and sharing the link reopens the exact same calculation for whoever clicks it.