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A confidence interval gives a range that likely contains the true population mean, based on a sample — a more honest way to report a result than a single estimated number alone.
This calculator finds a confidence interval for a population mean at 90%, 95%, or 99% confidence.
How it works
Enter the sample mean, sample standard deviation, sample size, and desired confidence level. The calculator finds the standard error, multiplies it by the critical z-value for the chosen confidence level to get the margin of error, and adds/subtracts that from the mean.
- Enter sample mean.
- Enter sample standard deviation.
- Enter sample size (n).
- Enter confidence level.
- Click Calculate to see your results.
Examples
A survey result
A sample of 50 people with a mean score of 100 and standard deviation of 15 gives a 95% confidence interval of approximately [95.84, 104.16].
Who should use it
- Reporting the precision of a survey or experiment's sample mean.
- Understanding how much a sample statistic might differ from the true population value.
Industry applications
- Statistics and research methodology
- Market research and survey analysis
Advantages
- Supports the three most commonly used confidence levels: 90%, 95%, and 99%.
- Shows the full standard error and margin of error calculation, not just the final range.
Limitations
- Uses the z-distribution rather than the t-distribution, which is a simplification for smaller sample sizes.
Common mistakes to avoid
- Interpreting a confidence interval as "there's a 95% chance the true mean is in this range" — the more precise interpretation is about the reliability of the method over repeated sampling.
- Using a very small sample size with the z-distribution approach, which technically calls for a t-distribution and would produce a slightly wider, more accurate interval.
Best practices
- Report the sample size alongside any confidence interval, since a narrow interval from a tiny sample can be misleading about how precisely the true mean is actually known.
Tips
- A larger sample size shrinks the confidence interval without changing the confidence level — if you need a tighter estimate, increasing sample size is often more effective than changing the confidence level.