invT Calculator (Inverse t)
Find the t critical value that cuts off a given area of Student's t-distribution. This is the TI-84 invT(area, df) function — the reverse of tcdf — with right-tail and two-tailed options added so you never have to convert the area by hand.
Part of the TI-84 statistics functions guide, which shows when to use invT and every other DISTR-menu function.
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Estimate confidence intervals for means and proportions with visible assumptions.
What invT Does
invT is the quantile (inverse CDF) function of the t-distribution. Give it the area to the left of a point and the degrees of freedom, and it returns that point. Its everyday use is finding t* — the multiplier in a confidence interval or the rejection cutoff in a t-test.
C% confidence interval → t* = invT((1 + C) / 2, df)
Right-tailed test at α → t* = invT(1 − α, df)
Two-tailed test at α → t* = invT(1 − α/2, df)
How to Use invT on a TI-84
- Press 2nd then VARS (DISTR).
- Choose 4:invT(. It is missing on the TI-83 and TI-84 before OS 2.30 — use the t-table instead.
- Enter the left-tail area and df, then select Paste and press ENTER.
Unlike invNorm, invT on the calculator has no tail option: always convert to a left-tail area first. This page does that conversion for you. In Excel use =T.INV(area, df) or =T.INV.2T(α, df) for a two-tailed critical value.
Worked Example: t* for a 95% Confidence Interval
You have a sample of n = 25 and want a 95% confidence interval for the mean.
- df = n − 1 = 24.
- 95% in the middle leaves 2.5% in each tail, so the left-tail area is 0.975.
- invT(0.975, 24) = 2.0639.
The interval is x̄ ± 2.0639 × s/√25. Compare with the z multiplier 1.96: the t value is larger because the standard deviation was estimated from the sample. Build the full interval with the confidence interval calculator.
Common t* Values
df = 10: 90% → 1.8125 95% → 2.2281 99% → 3.1693
df = 20: 90% → 1.7247 95% → 2.0860 99% → 2.8453
df = 30: 90% → 1.6973 95% → 2.0423 99% → 2.7500
df = ∞ (z): 90% → 1.6449 95% → 1.9600 99% → 2.5758
Frequently Asked Questions
What area do I enter into invT for a 95% confidence interval?
0.975. A 95% interval leaves 5% outside, split into 2.5% per tail, so the area to the left of the upper cutoff is 0.975. Or choose the Center tail here and enter 0.95 directly.
Why does invT give a negative number?
invT expects the area to the left. Any left area below 0.5 lies below the center of the distribution, so the t value is negative: invT(0.05, 10) = −1.8125. Enter 0.95 (or pick the right tail) to get the positive cutoff.
My TI-84 does not have invT. What can I do?
invT was added in TI-84 Plus OS 2.30. On older calculators and the TI-83, read the value from a t-table or use this page. Updating the calculator's OS from Texas Instruments' website also adds it.
What is the difference between invT and invNorm?
invNorm uses the normal curve and needs a mean and standard deviation; invT uses the t-distribution and needs degrees of freedom. Use invT when the population standard deviation is unknown and estimated from the sample.
Can the degrees of freedom be a decimal?
Yes. Welch's two-sample t procedure produces fractional degrees of freedom, and both the TI-84 and this calculator accept them.
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