# Tukey Fence Outlier Calculator

> Find outliers with Tukey’s fences: Q1 − k×IQR and Q3 + k×IQR, with k = 1.5 for outliers and 3 for far-out values, and the quartile method stated.

Category: Statistics & probability · Applies to: Worldwide · Last updated: 2026-10-29
Interactive calculator: https://calculators.geekmidst.com/calculators/outlier-tukey-fence-calculator

Tukey’s rule flags any value more than 1.5 interquartile ranges below Q1 or above Q3, the same rule box plots use for their whiskers.

Also called: IQR outlier calculator, Upper and lower fence calculator.

## Inputs
- Numbers (default 2, 4, 4, 4, 5, 5, 7, 9, 30)
- Fence multiplier k (default 1.5)
- Quartile method (options: Inclusive / linear (Excel QUARTILE.INC, R default), Exclusive (Excel QUARTILE.EXC), Tukey hinges; default type7)

## Results
- Outliers found
- Outlying values
- Lower fence
- Upper fence
- Q1
- Q3
- IQR
- Far-out values (beyond 3 × IQR)

## Formula

```
IQR = Q3 − Q1;  lower fence = Q1 − k × IQR;  upper fence = Q3 + k × IQR;  outlier if x < lower or x > upper
```

Where:
- Q1, Q3: first and third quartiles
- k: multiplier: 1.5 (outlier) or 3 (far out)

## Worked example
1. Q1 = 4 and Q3 = 7 (inclusive method), so IQR = 3.
2. Fences: 4 − 1.5 × 3 = −0.5 and 7 + 1.5 × 3 = 11.5.
3. Only 30 lies outside; it is also beyond 7 + 3 × 3 = 16, so it is far out.

**Result:** One outlier, 30, lies above the upper fence of 11.5.

## What the result means

A flagged value is a prompt to investigate, not to delete: check for data-entry errors, unit mix-ups or a genuinely different case before deciding what to do.

## Assumptions and limits
- Tukey’s fences make no normality assumption; for normal data about 0.7% of values fall outside the 1.5 × IQR fences by chance.
- In small or heavily skewed samples the rule may flag legitimate values; the quartile method also shifts the fences slightly.

## Questions

### Why 1.5?

Tukey chose it as a practical compromise: for normal data the fences sit about 2.7 standard deviations from the mean.

### Should I remove outliers?

Only with a reason, such as a proven measurement error. Otherwise report results with and without them, or use robust statistics like the median.

## Related calculators
- [Interquartile Range Calculator](https://calculators.geekmidst.com/calculators/interquartile-range-calculator)
- [Median Absolute Deviation Calculator](https://calculators.geekmidst.com/calculators/median-absolute-deviation-calculator)
- [Z-score Calculator](https://calculators.geekmidst.com/calculators/z-score-calculator)
- [Statistics Calculator](https://calculators.geekmidst.com/calculators/statistics-calculator)

Source: GM¹X CalcVerse — https://calculators.geekmidst.com/calculators/outlier-tukey-fence-calculator