Confidence Interval Calculator Online
Compute a confidence interval for a mean from sample statistics, entirely on your device. Enter a mean, standard deviation, and sample size to get an instant interval.
The Confidence Interval Calculator runs entirely in your browser. The sample mean, standard deviation, and sample size you enter stay on your device and are never uploaded to ArrayKit.
Open the Sample Size Calculator
About Confidence Interval Calculator
Confidence Interval Calculator turns a sample mean, standard deviation, and sample size into a confidence interval for the true population mean, using the standard normal (z) critical value for 90%, 95%, or 99% confidence. Type in your sample statistics and the tool instantly returns the margin of error, the lower and upper bounds of the interval, and the z critical value it used, so you can see exactly how the range was built. It is useful for statistics coursework, A/B test readouts, survey results, and any quick sanity check on how precise a sample mean estimate is. A wider interval means less certainty; a larger sample size or lower confidence level narrows it. Everything is computed locally in your browser, so your sample numbers never leave your device.
Features
- Computes a 90%, 95%, or 99% confidence interval for a mean from sample statistics
- Reports the margin of error and the z critical value used in the calculation
- Instant recalculation as you edit the mean, standard deviation, or sample size
- Segmented control to switch confidence level without retyping anything
- Copy a plain-text summary of the inputs and the resulting interval
- Clear error messages for a negative standard deviation or an invalid sample size
- Uses the standard z-interval formula so results match textbook calculations
- Runs entirely in your browser — no sample data is sent anywhere
How to use the Confidence Interval Calculator
- Enter the sample mean
- Enter the sample standard deviation
- Enter the sample size (n)
- Choose a confidence level: 90%, 95%, or 99%
- Read the interval, margin of error, and z critical value
Example
Input
μ=100, σ=15, n=36, 95%
Output
95% CI: [95.1, 104.9]
Common errors & troubleshooting
- The interval looks far too wide. — Check that the standard deviation was entered as the sample SD, not the variance (SD squared) — squaring instead of using SD directly inflates the margin of error.
- Confidence Interval Calculator shows an error for the sample size. — Sample size (n) must be a positive whole number greater than 0 — a blank, zero, or negative value cannot produce an interval.
- Switching from 95% to 99% confidence made the interval wider, not tighter. — That is expected — a higher confidence level uses a larger z critical value, which widens the interval so it is more likely to contain the true mean.
- Interval seems unrealistically narrow for a very small sample. — This tool uses the z (normal) interval, which assumes a reasonably large sample; for small samples (roughly n < 30) a t-interval with more degrees-of-freedom uncertainty is usually more appropriate.
Frequently asked questions
- What does the Confidence Interval Calculator compute?
- It computes a confidence interval for a population mean from a sample mean, sample standard deviation, and sample size, using the z critical value for the confidence level you choose (90%, 95%, or 99%).
- How does the Confidence Interval Calculator find the margin of error?
- Margin of error equals the z critical value times the sample standard deviation divided by the square root of the sample size: ME = z × sd ÷ √n. The interval is the mean plus or minus that margin.
- Why does a 99% confidence interval look wider than a 95% one?
- A higher confidence level uses a larger z critical value (2.576 for 99% versus 1.96 for 95%), which increases the margin of error so the interval is more likely to capture the true mean.
- Does the Confidence Interval Calculator use a z-interval or a t-interval?
- It uses the z (normal) interval with fixed critical values for 90%, 95%, and 99% confidence. This is the standard large-sample approximation; very small samples are better served by a t-interval.
- Can I use the Confidence Interval Calculator for a proportion instead of a mean?
- This tool is built for a mean from sample mean, standard deviation, and size. For a proportion confidence interval you would need a separate proportion-based formula.
- Is my sample data uploaded when I use the Confidence Interval Calculator?
- No. The Confidence Interval Calculator runs entirely in your browser. The numbers you type are never uploaded or sent to a server.
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