Lower And Upper Fence Calculator

Calculate Tukey’s lower and upper outlier fences from the first and third quartiles.

How the lower and upper fence calculator works

Interquartile range (IQR) = Q3 − Q1. Lower fence = Q1 − 1.5 × IQR; upper fence = Q3 + 1.5 × IQR. Values outside the fences are potential outliers, not automatically errors.

Example and useful facts

Example: Calculate Tukey’s lower and upper outlier fences from the first and third quartiles. Enter the sample values above, then change one input at a time to see how the result changes.

Formula and assumptions: Interquartile range (IQR) = Q3 − Q1. Lower fence = Q1 − 1.5 × IQR; upper fence = Q3 + 1.5 × IQR. Values outside the fences are potential outliers, not automatically errors.

Did you know? Box plots often use 1.5×IQR fences to flag potential outliers for further investigation.

Frequently asked questions

What does the lower and upper fence calculator calculate?

Calculate Tukey’s lower and upper outlier fences from the first and third quartiles.

Are the results exact?

The result follows the formula and assumptions shown on this page. Real-world rules, measurements, rates, and individual circumstances can affect the final answer.

Results are estimates for general information only. They are not a substitute for professional advice where applicable. Found a mistake? Report an error.