Confidence Interval Calculator
Find the confidence interval for a mean from the sample mean, standard deviation and size. The result updates as you type, with the working underneath so you can check it.
Your details
Result
95% confidence interval
48.04 to 51.96
- Margin of error
- 1.95996
- Standard error
- 1
- Critical z
- 1.960
Good to know: CI = x̄ ± z × s ÷ √n
About this tool
Formula
CI = x̄ ± z × s ÷ √n
Questions people ask
What does a 95% confidence interval mean?
If you repeated the sampling many times, about 95% of such intervals would contain the true mean. It is not a 95% chance that this one does.
Related tools
- Z-Score CalculatorFind how many standard deviations a value is from the mean, with percentile.
- Normal Distribution CalculatorFind probabilities for a normal distribution.
- Sample Size CalculatorFind how many survey responses you need for a chosen margin of error.
- Standard DeviationMean, variance & spread of data
How we calculate this
We use the standard published formula or definition for this calculation, and we show the working so you can check it.
Spotted a mistake? Tell us and we'll check it. How we check our calculators