Confidence Interval Calculator
Calculate a confidence interval around a sample mean using the sample standard deviation, sample size and chosen confidence level.
Your results
Calculation breakdown
- Standard error
- SE = s / √n
- Margin of error
- E = z × SE
- Confidence interval
- CI = mean ± E
Worked example
A sample of 30 customers has a mean spend of $50 with a standard deviation of $10. At 95% confidence (z ≈ 1.96), the interval is roughly $46.42 to $53.58.
Assumptions
- Uses the normal (z) approximation, which is reasonable for sample sizes of about 30 or more; smaller samples should use a t-distribution.
- Assumes the sample is randomly selected and reasonably representative of the population.
How this calculator works
Enter your sample mean, sample standard deviation, sample size and desired confidence level. The calculator uses the normal (z) approximation to return the confidence interval and margin of error around your sample mean.
Frequently asked questions
What does a 95% confidence interval mean?
If you repeated the sampling many times, about 95% of the resulting intervals would contain the true population mean.
Should I use this for small samples?
This tool uses the z (normal) approximation, which works best for sample sizes of about 30 or more; smaller samples are more accurately handled with a t-distribution.
Why does a higher confidence level widen the interval?
A higher confidence level requires a larger margin of error to be more certain the true value falls within the range.