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Updated 2026-03-07 UTC
t Distribution Calculator — CDF and Inverse (Critical Values)
Compute Student’s t CDF and inverse t quantiles (critical values) with GetCalcMaster. Includes verification tips (educational).
Student’s t distribution is common for confidence intervals and hypothesis tests when σ is unknown. This guide shows how to compute probabilities and critical values (quantiles).
Important: This content and tool are for educational purposes only. Outputs are estimates; always cross‑verify with official sources and/or a qualified professional.
What this calculator is
The Statistics Calculator is an interactive tool inside GetCalcMaster. It’s designed to help you explore scenarios, understand formulas, and document assumptions.
Key features
- Immediate results as you change inputs
- Transparent assumptions and explainable outputs
- Works well with the built‑in Notebook for saving scenarios
Formula
CDF: tcdf(t, df)
Inverse CDF (quantile): tinv(p, df)Quick examples
tcdf(0, 10) # should be ~0.5 by symmetrytinv(0.975, 10) # two-sided 95% critical value# Symmetry check: tcdf(-t,df) = 1 - tcdf(t,df) t = 2 df = 10 tcdf(-t, df) - (1 - tcdf(t, df))
Verification tips
- By symmetry, tcdf(0, df) should be ~0.5 for valid df.
- For 95% two-sided intervals, the critical value is tinv(0.975, df).
- As df increases, the t distribution approaches the standard normal.
Common mistakes
- Using df incorrectly (common choice is df=n−1).
- Mixing up one-sided vs two-sided critical values.
- Using p as a percent (97.5 instead of 0.975).
How to use it (quick steps)
- Choose degrees of freedom df (often n−1).
- Open the Statistics Calculator.
- Use tcdf(t, df) for left-tail probability P(T ≤ t).
- Use tinv(p, df) to find the t value with CDF=p (critical values).
- For two-sided tests, use p = 1 − α/2.
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FAQ
What does tcdf(t,df) return?
The left-tail probability P(T ≤ t) for a t random variable with df degrees of freedom.
How do I get a two-sided 95% critical t?
Use tinv(0.975, df).
When should I use t instead of z?
Commonly when the population σ is unknown and the sample size is small/moderate (educational rule of thumb).
Tip: For reproducible work, save your inputs and reasoning in Notebook.