Confidence Interval Calculator
Enter your sample mean, standard deviation, sample size, and confidence level below to instantly get the confidence interval.
How a Confidence Interval Is Calculated
Confidence interval = sample mean ± z × (standard deviation ÷ √n), where z depends on the confidence level (1.96 for 95%, 2.576 for 99%, and so on).
Worked example
Sample mean 100, standard deviation 15, n = 30, 95% confidence (z = 1.96).
Margin = 1.96 × (15 ÷ √30) = 1.96 × 2.7386 ≈ 5.3676
Interval: 100 − 5.37 to 100 + 5.37 = [94.63, 105.37]
Frequently Asked Questions
What is a confidence interval?
A confidence interval is a range of values likely to contain the true population value, built around a sample estimate. A 95% confidence interval means that if you repeated the sampling process many times, about 95% of the resulting intervals would contain the true population mean.
Why does a higher confidence level make the interval wider?
Being more certain that the true value falls inside your range requires casting a wider net. A 99% confidence interval has to be wider than a 90% one for the same data, since it needs to capture the true value more reliably.
What is the margin of error in a confidence interval?
The margin of error is the amount added and subtracted from the sample mean to build the interval — z × (standard deviation ÷ √n). A smaller margin means a tighter, more precise estimate.
Does a bigger sample size make the confidence interval narrower?
Yes. The sample size appears under a square root in the denominator of the margin of error, so a larger sample shrinks the margin — though with diminishing returns, since you'd need to quadruple the sample size to cut the margin in half.
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