t Confidence Interval Calculator
t confidence interval for one mean or the difference between two means (Welch or pooled), with t*, SE, df, steps, and a number-line picture.
Known σ? See the z confidence interval calculator. Paired designs: paired t-test.
Related Calculators
One-Sample t-Test Calculator
Test a mean against a hypothesized value from data or x̄, Sx, and n: the TI-84 T-Test output.
Confidence Interval Calculator
Build a z confidence interval for a population mean at 90%, 95%, or 99% confidence.
invT Calculator
Find t critical values with invT(area, df) for left, right, or two-tailed areas.
One mean vs difference of means
TInterval covers one μ. 2-SampTInt covers μ₁ − μ₂; if the interval for the difference contains 0, a two-sided Welch test at the same α typically does not reject H₀: μ₁ = μ₂.
Worked examples
One sample: x̄ = 52.3, Sx = 4.8, n = 16 → 95% CI (49.7423, 54.8577).
Two samples (Welch): (78.2, 6.1, 25) vs (74.5, 8.3, 22) → 95% CI for μ₁−μ₂ (−0.6505, 8.0505).
Related guides and calculators
The interval is the estimate plus or minus a margin of error. For a proportion use the proportion confidence interval calculator, for a mean with a known standard deviation the confidence interval calculator, and the sample size calculator finds how many observations a target width needs. To test a mean against a value use the one-sample t-test, and look up critical values in the t-table. Read confidence intervals and how to read a t-table.
Frequently Asked Questions
When do I use a t interval instead of z?
Whenever σ is unknown and estimated by Sx: the usual case.
Welch or pooled?
Welch (Pooled: No) is valid without equal-variance assumptions; pool only with strong prior reason.
Why is df a decimal?
Welch–Satterthwaite df is rarely an integer; it is expected.
How do I read an interval that contains 0?
For a difference, 0 inside the CI aligns with no significant difference at that confidence level for a two-sided test.
Excel / R / Python?
R/Python t.test confidence intervals; Excel lacks a one-step 2-SampTInt: use formulas or this calculator.
Does raw data work?
Yes, paste lists and the page computes x̄ and Sx before the interval.
What is t*?
The two-sided critical value t_{(1+C)/2, df} multiplying SE to form the margin of error.
Paired measurements?
Compute differences first or use the paired t-test tool: do not treat pairs as independent groups.
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