Confidence Interval Calculator
Margin of error and interval around a sample mean.
Enter your values
Results update instantly as you type — no submit needed.
Results
- Confidence interval
- 66.4636 to 70.3364
- Margin of error
- ± 1.9364
- Standard error
- 0.98796
- Relative margin
- 2.83%
Working
- 1SE = 12.1 ÷ √150 = 0.98796
- 2MOE = 1.96 × 0.98796 = 1.9364
Quick answer
A confidence interval is the sample mean plus or minus z × the standard error, giving a plausible range for the population mean.
CI = x̄ ± z·(s ÷ √n)
How to use the Confidence Interval Calculator
- 1Enter your sample mean and standard deviation.
- 2Add the sample size.
- 3Pick a confidence level.
Frequently asked questions
What does 95% confidence mean?
If you repeated the study many times, about 95% of the intervals produced would contain the true population mean.
How do I halve the margin of error?
Quadruple the sample size — the margin shrinks with the square root of n.