This confidence interval calculator builds a z-based interval around a sample mean using the sample standard deviation and size.
Statistics
Confidence Interval Calculator
Compute a confidence interval for a mean with known or sample SD.
Calculator
About this calculator
Formula notes
CI = x̄ ± z·(s / √n). For 95% confidence, z ≈ 1.96.
Worked examples
- Example: mean 100, SD 15, n = 100 gives 100 ± 1.96·(15/10) = 100 ± 2.94, i.e. 97.06 to 102.94.
- For a sample mean of 50, standard deviation 12, and n = 100, a normal-approximation 95% interval is about 50 +/- 2.35, or 47.65 to 52.35.
How to use it
- Enter the sample mean and sample standard deviation.
- Enter the sample size and pick the confidence level.
- Read the margin of error and both interval bounds.
Frequently asked questions
Why does a bigger sample narrow the interval?
The standard error s/√n shrinks as n grows, so the margin of error tightens.
When should I use a t-interval instead?
With small samples (roughly n < 30) and unknown population SD, a t-interval is more accurate.
Limits and interpretation
- The interval relies on the selected standard-error model, confidence level, sampling design, independence, and distribution assumptions.
- A 95% confidence interval does not mean a fixed parameter has a 95% probability of lying inside this one computed interval.