# Decile Calculator

URL: https://speedycalculator.com/calculators/statistics/decile/
Last updated: 2026-10-30

> The decile calculator splits a data set into ten equal parts and returns the nine cut points D1 to D9 – the 10th, 20th, …, 90th percentiles – with their rank positions, using the (n + 1) rule or Excel's inclusive rule, plus a chart of the deciles.

## Inputs

- Data set
- Decile method

## Results

- First decile (D1, 10th percentile)
- D2 (20th percentile)
- D3 (30th percentile)
- D4 (40th percentile)
- D5 (50th percentile = median)
- D6 (60th percentile)
- D7 (70th percentile)
- D8 (80th percentile)
- Ninth decile (D9, 90th percentile)
- Interdecile range (D9 − D1)
- Number of values
- Note
- Decile table
- Decile values
- Sorted data

## Formula

```
Position of Dₖ = k(n + 1)/10 (or 1 + k(n − 1)/10) · Dₖ = x₍⌊r⌋₎ + (r − ⌊r⌋)(x₍⌊r⌋+1₎ − x₍⌊r⌋₎), k = 1 … 9
```

## Explanation

Deciles are the nine values that divide sorted data into ten groups with the same number of observations. The first decile D1 has 10% of the data below it, D5 is the median and D9 has 90% below it. They sit between quartiles (four groups) and percentiles (a hundred groups) in detail, and are a common way to report incomes, wealth and test results: "the top decile of earners", "pupils in the bottom decile".

The gap between D9 and D1, the interdecile range, covers the middle 80% of the data and is a useful measure of spread that is less sensitive to extremes than the full range. The ratio D9 ÷ D1 is widely used in economics to describe income inequality.

Because the decile positions are usually fractional, the value is interpolated between neighbouring observations. The default rule places Dₖ at position k(n + 1)/10; Excel's PERCENTILE.INC uses 1 + k(n − 1)/10. With fewer than nine values, the (n + 1) rule needs positions outside the data, which are clamped to the minimum or maximum.

### How to use the Decile Calculator

- **Data set**
- **Decile method**

Everything is calculated in your browser, so results appear instantly and nothing you type is sent to a server.

### How it works

Sort the data, compute the position of each decile with the chosen rule and interpolate between the values at the neighbouring ranks.

### Worked example

Twenty values: 35, 41, 44, 47, 50, 52, 55, 57, 58, 61, 63, 64, 67, 70, 72, 75, 79, 83, 88, 94. With the (n + 1) rule D1 is at position 2.1: 41 + 0.1 × 3 = 41.3. D5 is at position 10.5: (61 + 63)/2 = **62**, the median. D9 is at position 18.9: 83 + 0.9 × 5 = 87.5. The interdecile range is 87.5 − 41.3 = 46.2.

DecilePositionValueD12.141.3D24.247.6D36.352.9D48.457.4D510.562D612.665.8D714.771.4D816.878.2D918.987.5

### Where deciles are used

- Income and wealth statistics (D9/D1 ratio, "top 10%").
- School performance bands and exam grading.
- Ranking neighbourhoods by deprivation indices.
- Splitting customers into ten equal groups for marketing analysis.

## Worked example

Inputs — Data set: 35, 41, 44, 47, 50, 52, 55, 57, 58, 61, 63, 64, 67, 70, 72, 75, 79, 83, 88, 94; Decile method: (n + 1)·p rank, interpolated (NIST, Excel PERCENTILE.EXC).

Results — First decile (D1, 10th percentile) = 41.3; D2 (20th percentile) = 47.6; D3 (30th percentile) = 52.9; D4 (40th percentile) = 57.4; **D5 (50th percentile = median) = 62**; D6 (60th percentile) = 65.8.

## Key terms

- **Decile**: A cut point dividing the data into tenths.
- **Interdecile range**: D9 − D1, the spread of the middle 80% of the data.
- **D9/D1 ratio**: A common measure of inequality.

## FAQ

**What is a decile?**
One of nine values that split sorted data into ten equal-sized groups. D1 is the 10th percentile and D9 the 90th.

**How do I calculate deciles?**
Sort the data, find the position k(n + 1)/10 for the k-th decile and interpolate between the neighbouring values.

**How many deciles are there?**
Nine cut points (D1 to D9) create ten groups, sometimes also called deciles.

**Is the 5th decile the median?**
Yes, D5 is the 50th percentile, the median.

**What is the first decile of the example data?**
Its position is 21/10 = 2.1, so D1 = 41 + 0.1 × (44 − 41) = 41.3.

**What is the difference between deciles, quartiles and percentiles?**
They divide data into 10, 4 and 100 equal parts. D9 = P90, D5 = Q2 = P50.

**What does "top decile" mean?**
The 10% of observations above D9.

**How many values do I need?**
At least 9 for every decile to be inside the data with the (n + 1) rule; 20 or more for stable results.


## Sources

- [Wolfram MathWorld – Decile](https://mathworld.wolfram.com/Decile.html)
- [NIST/SEMATECH e-Handbook – Percentiles](https://www.itl.nist.gov/div898/handbook/prc/section2/prc262.htm)
- [OpenStax – Introductory Statistics 2e](https://openstax.org/details/books/introductory-statistics-2e)