99% Confidence Interval Calculator
The 99% confidence interval for a mean — wider than the usual 95%, and the right choice when a false positive is expensive.
The construction is identical to the 95% interval; only the critical value changes.
How the 99% confidence interval calculator works
The construction is identical to the 95% interval; only the critical value changes. At 99% the normal cut-off is 2.576 rather than 1.960, so the interval is about 31% wider.
That extra width is the price of certainty, and it is paid in sample size: matching a 95% interval's precision at 99% confidence needs about 73% more data.
Formula: CI = x̄ ± t₀.₉₉₅ × s / √n
Worked examples
| Inputs | Margin of error | Note |
|---|---|---|
| Mean 50, SD 10, n 40 | 4.281587 | ±4.28, against ±3.20 at 95% |
| A large sample | 0.816108 | t approaches 2.576 |
| A small sample | 20.590138 | t = 4.60 — very wide |
FAQFrequently asked questions
When should I use 99% instead of 95%?
When a false positive is costly — safety-critical work, regulatory submissions, or any analysis running many tests at once.
How much wider is it?
About 31% in a large sample, and considerably more in a small one where the t distribution has heavy tails.
What does it cost in sample size?
Roughly 73% more observations to reach the same precision, because the required n scales with the square of the critical value.
Does a wider interval mean a worse study?
No — it means a more cautious claim from the same data. The data has not changed.
Is 99% "more correct"?
No. Both are correct statements of different things. Choosing the level after seeing the data, however, is not.
Where these figures come from
- NIST Digital Library of Mathematical Functions — reference definitions for elementary and special functions
- Wolfram MathWorld — definitions and formulas for every topic on this page
- NIST/SEMATECH e-Handbook of Statistical Methods — the statistical formulas (mean, variance, z, confidence intervals, sample size)
- Common Core State Standards — Mathematics — the terms and methods taught in US schools
Last checked: September 2026. Formulas are fixed by mathematics and do not change with tax years or regulations.