Calculator inputs
Formula used
General R quantile form
Q(p) = (1 − γ)xj + γxj+1, where h = np + m and j = floor(h).
Types 1–3 use discontinuous empirical rules. Types 4–9 use continuous interpolation rules. Type 7 matches R’s default quantile calculation.
| Type | Method | m or rule |
|---|---|---|
| 1 | Inverse empirical distribution | γ is zero only when g equals zero. |
| 2 | Averaged inverse distribution | γ is one-half when g equals zero. |
| 3 | Nearest even order statistic | Uses h = np − 0.5. |
| 4 | Linear empirical interpolation | m = 0 |
| 5 | Hydrologist method | m = 0.5 |
| 6 | Weibull method | m = p |
| 7 | Default R method | m = 1 − p |
| 8 | Median-unbiased method | m = (p + 1) / 3 |
| 9 | Normal-unbiased method | m = p / 4 + 3 / 8 |
How to use this calculator
- Paste values or upload a CSV text file.
- Select a calculation mode and input scale.
- Choose an R quantile type and cleaning rules.
- Set precision and display preferences.
- Calculate, inspect steps, then export the results.
Example data
| Dataset | Requested percentile | Type | Purpose |
|---|---|---|---|
| 12, 18, 21, 25, 29, 33, 38 | 90 | 7 | Find the default R 90th percentile. |
| 4, 7, 7, 10, 15, 21 | 25, 50, 75 | 8 | Compare quartiles using median-unbiased interpolation. |
| 2, 5, 9, 12, 20 | Target 10 | Rank mode | Calculate strict, inclusive, and R-style ranks. |
Frequently asked questions
What is a percentile?
A percentile divides ordered data into one hundred relative positions. It describes where a value sits within a distribution.
Is a percentile the same as a percentage?
No. A percentage measures a part of a whole. A percentile describes relative position within ordered observations.
What is a quantile?
A quantile is a cut point for a probability. Percentiles express the same probability on a 0–100 scale.
Why do R quantile types differ?
Each type defines sample positions and interpolation differently. Small datasets often reveal the largest differences.
Which R quantile type should I use?
Type 7 is R’s default. Use another type when your method requires it.
How are duplicate values handled?
Duplicates remain in the ordered sample. Rank mode also reports a duplicate-aware midrank.
Can the calculator ignore missing values?
Yes. It can remove NA, NaN, NULL, and blank entries.
What is percentile rank?
Percentile rank measures the percentage below or at a target. Several rank definitions are displayed together.
Can I compare all nine R methods?
Yes. Comparison mode calculates the same percentile using types one through nine.