Confidence interval calculator
Calculate a confidence interval for a sample mean.
The confidence interval calculator takes a sample's mean, standard deviation, and size, and computes a confidence interval using the standard normal (Z) critical value for the chosen confidence level — showing the margin of error and the resulting lower and upper bounds.
How to use
- Enter your sample's mean, standard deviation, and size, then pick a confidence level.
- Click "Calculate" to get the margin of error and the resulting confidence interval.
Common use scenarios
- Reporting a confidence interval alongside a sample mean in a study or report.
- Checking how much a margin of error narrows as sample size increases.
- Verifying a confidence interval calculated elsewhere by hand or in a spreadsheet.
- Comparing intervals across different confidence levels for the same sample.
✓Content & verification reviewed: 2026-08-25
How we verify Confidence interval calculator
How to confirm the interval matches what you'd expect.
Margin of error = Z × (standard deviation ÷ √n)
The margin of error shrinks as sample size grows (since it's divided by the square root of n) and grows as the chosen confidence level increases (since a higher confidence level uses a larger Z critical value).
This uses a Z critical value, not a t-distribution
That makes it most accurate for larger samples (roughly n ≥ 30); for small samples, a proper t-interval would be slightly wider than what this tool reports, since it accounts for extra uncertainty in a small sample's standard deviation estimate.
A higher confidence level always produces a wider interval
Moving from 90% to 99% confidence, for the same sample data, increases the Z critical value and therefore widens the interval — there's a direct tradeoff between how confident you are and how precise the interval is.
Before you rely on the result
- Your sample size is large enough (roughly 30+) for the Z-based interval to be a good approximation.
- You've picked the confidence level appropriate for your reporting context, not just the default.
- You're reporting the interval alongside the mean, not the margin of error alone.
- You understand a wider interval at higher confidence is expected, not a sign of a mistake.
Who this is for
- Students and researchers reporting a confidence interval alongside a sample mean.
- Analysts checking how margin of error changes with sample size.
- Anyone verifying a confidence interval calculated by hand or in a spreadsheet.
- People comparing intervals across different confidence levels for the same data.
Real-world examples
Reporting a study result
A researcher computes the confidence interval for a sample mean to report alongside the point estimate in a study or paper.
Planning around sample size
An analyst tries a few different sample sizes to see how much narrower the interval becomes as more data is collected.
Comparing confidence levels
Someone compares the 90%, 95%, and 99% intervals for the same sample to understand the confidence/precision tradeoff before choosing which to report.
Limitations
- This uses the standard normal (Z) critical value rather than the t-distribution, so it's most accurate for larger samples (roughly n ≥ 30) — for small samples a t-interval would be slightly wider.
Frequently asked questions
Why does the interval get wider at a higher confidence level?
A higher confidence level requires a larger critical value, which increases the margin of error — you trade precision for confidence.
Is this accurate for a small sample size?
It's most accurate for larger samples (roughly n ≥ 30). For smaller samples, a t-distribution-based interval would be slightly wider than this Z-based result.
What does the confidence level actually mean?
If you repeated the sampling process many times, that percentage of the resulting intervals would contain the true population mean — it's not the probability that this specific interval contains it.
Can I use this for a proportion instead of a mean?
This tool is built for a sample mean with a standard deviation. For estimating a proportion, use the sample size calculator, which is designed for that case.
🔒 Runs in your browser — nothing is uploaded. Results are for reference only; see the disclaimer. Last updated: 2026-08-25
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