Use this free online confidence interval calculator to estimate the range within which a true population mean likely falls, based on your sample mean, standard deviation, and sample size. Choose a 90%, 95%, or 99% confidence level to see the margin of error and interval calculated instantly.
How to Use the Confidence Interval Calculator
Enter your "Sample Mean" - the average value from your sample data.
Enter your "Sample Standard Deviation" - must be zero or greater.
Enter your "Sample Size (n)" - must be a positive whole number.
Select your desired "Confidence Level" (90%, 95%, or 99%).
Click "Calculate" to see the margin of error and confidence interval.
Frequently Asked Questions
The calculator computes the margin of error as MOE = Z x (s / √n), where Z is the z-score for your chosen confidence level, s is the sample standard deviation, and n is the sample size. The interval is then [mean - MOE, mean + MOE].
90% confidence uses Z = 1.645, 95% confidence uses Z = 1.96, and 99% confidence uses Z = 2.576. These values come from the standard normal distribution.
The calculator rejects negative standard deviations and requires the sample size to be a positive whole number, showing an error message like "Sample size must be a positive integer" instead of calculating a result.
For a sample mean of 50, standard deviation of 12, sample size of 30, and 95% confidence: MOE = 1.96 x (12 / √30) ≈ 4.29, giving a confidence interval of roughly [45.71, 54.29].