Research Tools

Outlier Calculator

Outlier Calculator

Outlier Calculator

Detect possible outliers with Tukey’s IQR fences, standard Z-scores, or robust modified Z-scores. Results update automatically as you edit the data or settings.

Data and detection settings

Separate values with commas, spaces, semicolons, or new lines. Scientific notation is supported.

Ready.
Live results
Observations —
Detected outliers —
Median —
Method result —
Box plot and Tukey fences
Outliers detected by method
Position Value IQR Modified Z Z-score Selected result
How this is calculated
Enter at least three numbers to see the formulas with your values.
Accuracy notes and verification tests

The IQR method uses lower and upper inner fences of Q1 − 1.5×IQR and Q3 + 1.5×IQR by default. Values beyond inner fences are potential outliers; the traditional outer fences use 3×IQR. The modified Z-score uses M = 0.6745(x − median)/MAD. Standard Z-scores use z = (x − mean)/SD.

Test A: [1,2,3,4,5,6,7,8,100] using median-of-halves → Q1=2.5, Q3=7.5, IQR=5, inner fences=[−5,15] → 100 is flagged. Modified Z for 100 = 32.03875. Sample Z for 100 ≈ 2.65979, so it is not flagged by a |z|>3 rule.
Test B: NIST 90-value outlier example using median-of-halves → Q1=436, Q3=739, IQR=303, upper inner fence=1193.5 → 1441 is flagged as an outlier.

Outlier rules are screening methods, not automatic instructions to delete data. Investigate data entry, measurement, study design, and domain context before excluding observations.

This Outlier Calculator helps researchers, students, and analysts identify unusual observations in a numerical dataset using the interquartile range (IQR), standard Z-score, and modified Z-score methods. Paste your data to instantly see potential outliers, quartiles, IQR fences, median absolute deviation, standardized scores, method agreement, and an interactive box-plot-style visualization. Because different outlier methods make different assumptions, the tool lets you compare results and inspect the exact formula values before deciding how an unusual observation should be handled in your analysis.

About the author

Muhammad Hassan

Muhammad Hassan writes about research design, academic methods and data-analysis concepts for ResearchMethod.net. His work focuses on presenting methodological topics in clear language for students and early-career researchers. Articles are developed from recognized methodological literature and official software documentation.