Confidence Interval Calculator
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Calculate 90%, 95%, 99%, or 99.9% confidence intervals from sample mean, standard deviation, and sample size.
Enter your values below and click Calculate for instant results.
A confidence interval is a range of values that likely contains the true population parameter based on sample data. A 95% confidence interval means that if you repeated the same sampling process 100 times, approximately 95 of the resulting intervals would contain the true population mean.
A common misinterpretation: a 95% confidence interval does not mean there is a 95% probability that the population parameter lies within this specific interval. The parameter is fixed; it is either in the interval or it is not. The 95% refers to the reliability of the method, not the probability for this particular result.
The margin of error is the half-width of the confidence interval. If the 95% confidence interval is (68, 82), the margin of error is 7 and the sample mean is 75. Political polls commonly report results with a margin of error: "47% approve, margin of error plus or minus 3 percentage points" means the 95% confidence interval for true approval is 44% to 50%.
Larger samples produce narrower confidence intervals. Higher standard deviations produce wider intervals. Higher confidence levels (99% vs 95%) produce wider intervals. The tradeoff between confidence level and interval width reflects a fundamental principle: you can be more certain about a wider claim than a narrower one.