Confidence interval calculator
Gives the range likely to contain the true population mean, with the margin of error and the critical value used.
Loading the tool…
Processing and privacy: The result is calculated inside your browser and your data is not sent to any server.
How to use it
- Enter sample mean (x̄), standard deviation, sample size (n), confidence level and distribution.
- The result appears straight away and updates as you edit.
- Copy the result, or copy a link that keeps the same values to share it.
How it is calculated
Interval = x̄ ± critical value × (s ÷ √n). The critical value comes from the t distribution with n - 1 degrees of freedom, or from z when the population SD is known.
Example
Inputs: Sample mean (x̄) = 50, Standard deviation = 10, Sample size (n) = 25, Confidence level = 95%, Distribution = t (SD from the sample). Result: 95% confidence interval: 45.8722 to 54.1278; Lower bound: 45.872203; Upper bound: 54.127797.
Limits and caveats
- Assumes a random sample and roughly normal data, or a large sample (about 30 or more).
- This is an interval for a mean; for a survey percentage use the margin of error calculator.
Questions about this tool
When do I use t and when z?
Use t when the standard deviation comes from the sample itself, which is the usual case. Use z only when the population SD is known in advance.
What does 95% confidence mean?
If you repeated the sampling many times, about 95% of the intervals built this way would contain the true mean.
How can I make the interval narrower?
Use a larger sample or accept a lower confidence level. Quadrupling the sample size roughly halves the margin of error.