Confidence Interval Calculator
Calculate the confidence interval for a population mean with known or unknown standard deviation. Enter your sample data and confidence level to get results with a visual representation.
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About Confidence Intervals
A confidence interval is a range of values that likely contains the true population parameter. A 95% CI means that if the same population is sampled multiple times, 95% of the intervals would contain the true mean.
Use Z-distribution when population standard deviation (σ) is known. Use T-distribution when only sample standard deviation (s) is known, especially for smaller sample sizes (n < 30).
For known σ: CI = x̄ ± Z*(σ/√n)
For unknown σ: CI = x̄ ± T*(s/√n)
Where Z/T is the critical value based on confidence level.
A wider interval indicates more uncertainty about the population mean. Higher confidence levels (99% vs 95%) produce wider intervals. Larger sample sizes produce narrower intervals.