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Confidence Interval Calculator

95% (or 80–99.9%) CI for a sample mean.

95% confidence interval
[94.632, 105.368]
100.00 ± 5.368
Standard error
2.7386
Margin of error
5.3677
Critical z
1.960

Uses the z-distribution, which is appropriate when the population standard deviation is known or n is large enough (often n ≥ 30). For small samples with unknown σ, use a t-interval instead.

About

Enter your sample mean, standard deviation, sample size, and the confidence level you want. Get the lower and upper bounds, the margin of error, and the standard error. Uses the z-distribution, appropriate for n ≥ 30 or known σ.

How to use

  1. Enter sample mean, SD, and n.
  2. Pick a confidence level.
  3. Read the interval and margin of error.

FAQ

Z or t?+

This uses z. For small samples (n < 30) with unknown population SD, the t-distribution is more correct; the result is wider. For most rough work the difference is small.

What does 95% CI mean exactly?+

If you repeated the sampling many times, about 95% of the constructed intervals would contain the true population mean. It's not a probability about your specific interval.