Margin of Error Calculator

Calculate margin of error step by step

The calculator will find the margin of error from the given sample size and distribution, with steps shown.

Sample size: `n=`

Confidence level: %

standard deviation:

Distribution used:
If the population standard deviation is known or the sample size is `n>30`, normal distribution will be chosen automatically. To force another distribution, choose it explicitly.

If the calculator did not compute something or you have identified an error, or you have a suggestion/feedback, please write it in the comments below.


Your input: find the margin of error for the sample size $$$n=64$$$, standard deviation $$$\sigma=7$$$, and confidence level $$$95.0 \%$$$ using normal distribution.

First, find the critical value: $$$z_{\frac{\alpha}{2}}=1.95996398454005$$$

Next, find the standard error of the mean: $$$SE=\frac{\sigma}{\sqrt{n}}=\frac{7}{8}$$$

Finally, the margin of error is $$$ME=z_{\frac{\alpha}{2}} \cdot SE=1.95996398454005 \cdot \left(\frac{7}{8}\right) \approx 1.71496848647255$$$

Answer: $$$ME=1.71496848647255$$$