How it works
Compute the confidence interval for a mean from a sample mean, standard deviation, size, and confidence level.
Enter the sample mean, standard deviation, sample size, and a confidence level. The calculator finds the critical z-value and reports the lower/upper bounds and the margin of error.
Formula
CI = mean ± z × (sd ÷ √n), where z is the two-sided critical value for the chosen confidence level.
x̄- Sample mean (number)
sd- Standard deviation (number)
n- Sample size (count)
Examples
- Mean 100, sd 15, n 100, 95%Mean 100 · sd 15 · n 100 · 95%≈ [97.06, 102.94] · margin of error ≈ 2.94
Frequently asked questions
z or t interval?
This uses the normal (z) critical value. For small samples with an estimated (sample) standard deviation, a t-interval is more appropriate.
What does 95% mean?
Over many repeated samples, about 95% of such intervals would contain the true mean.
How to read the result
The interval is an estimate of where the true population mean lies, given the sample and confidence level.
Limitations
Uses the z-distribution and assumes the sample mean is approximately normal. It does not cover proportions, medians, or small-sample t-intervals.
Source: Standard confidence-interval formula with normal critical values.