Statistics
Confidence Interval Calculator
Enter a sample mean, standard deviation, size, and confidence level to see the margin of error plus lower and upper bounds.
Compute a two-sided z-interval for a population mean using your sample mean, spread, and size.
Mean confidence interval
CI = x̄ ± Z × (σ / √n)
Z is the standard normal critical value for the selected confidence, σ is the sample (or population) standard deviation, and n is the sample size.
How to use
- Provide your sample mean and standard deviation.
- Enter the sample size that produced those statistics.
- Pick a confidence level to update the Z-score and interval bounds.
Example
Input: Mean = 72, σ = 10.5, n = 40, Confidence = 95%
Output: Margin of error ≈ 3.25, Interval ≈ [68.75, 75.25]
FAQ & notes
Does this use a t-score for small samples?
This calculator focuses on z-intervals. For very small samples where σ is unknown, consider substituting a t critical value manually.
Can I interpret the interval as probability?
Not directly. A 95% interval means that if you repeatedly sampled and built intervals the same way, about 95% would capture the true mean.