Confidence Interval Calculator for Standard Deviation

Estimate the range for your population's standard deviation with our intuitive calculator. Just enter your sample data and confidence level.

Sample Standard Deviation

Sample Size

Confidence Level (%)

Results

Confidence Interval: (, )

Chi-Square Distribution Visualization

This plot shows the Chi-Square distribution for your sample's degrees of freedom. The green and red dashed lines indicate the Chi-Square values corresponding to the lower and upper bounds of your chosen confidence level.

Understanding Confidence Intervals for Standard Deviation

A confidence interval for the standard deviation estimates a range within which the true population standard deviation is likely to fall. It's based on your sample data and a chosen confidence level, like 95%, indicating the reliability of the estimate.

We use the chi-square (χ²) distribution because the sample standard deviation's distribution relates to chi-square, especially when data is normally distributed. The formula involves chi-square values corresponding to your confidence level and degrees of freedom (sample size minus 1).

For example, if you calculate a 95% confidence interval for standard deviation to be (10, 15), it means you are 95% confident that the true population standard deviation lies between 10 and 15. This tool is useful in quality control, finance, and research to understand the variability in a population.

Learn more about Confidence Intervals and Chi-Square Distribution.