Confidence Interval Calculator
Calculate the confidence interval for a mean or proportion.
Tip: A 95% confidence interval means: we are 95% sure the true value falls within this interval.
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About this digital tool
The confidence interval calculator estimates the limits within which the true mean of a population lies, from the data of a sample. Enter the sample mean, the standard deviation, the sample size (n) and the confidence level (90%, 95% or 99%) and get the lower limit, the upper limit and the maximum error.
The formula is mean ± z × s ÷ √n, where z is 1.645 for 90%, 1.96 for 95% and 2.576 for 99%. For a mean of 50, s = 10, n = 100 and 95% confidence, the maximum error is 1.96 × 10 ÷ 10 = 1.96, so the interval is from 48.04 to 51.96. It is used in surveys, in scientific research, in quality control and in business analysis.
How to use
- Enter the sample mean.
- Enter the sample standard deviation and the sample size (n).
- Choose the confidence level: 90%, 95% or 99%.
- Read the lower limit, the upper limit and the maximum error.
Frequently asked questions
How is a 95% confidence interval interpreted?
If we repeated the survey 100 times, in ~95 of them the true value would fall within the interval. It does not mean a 95% chance that the true value is inside.
How is the confidence interval for the mean calculated?
Find the maximum error E = z × s ÷ √n, then the interval is mean − E to mean + E. For 50, s = 10, n = 100, 95%: 48.04 to 51.96.
How does sample size affect the interval?
The larger the sample, the narrower the interval. The error is proportional to 1 ÷ √n, so to halve it you have to quadruple the sample.
What z value is used for 90%, 95% and 99%?
1.645, 1.96 and 2.576 respectively. A higher confidence level gives a wider interval.