# Percentile rank

Shape / rows

A variant of [Number or rank rows](https://meridian.online/operations/number-or-rank-rows).

Give each row its relative position within its partition as a fraction from 0 to 1.

Page: <https://meridian.online/operations/number-or-rank-rows/percentile-rank>

## Status

Runs as a SQL step.

arcform carries it as a `sql:` step today.

## The DuckDB step

give each row its percentile rank within its partition, from 0 to 1

It reads the `orders` table the proofs share. Create it first:

```sql
CREATE TABLE orders AS SELECT * FROM (VALUES
  (1,  'Alice Ng',      'north', DATE '2026-01-03', 120.00, 'widget', 'a|b',   '{"channel":"web","items":[1,2]}'),
  (2,  'alice ng',      'north', DATE '2026-01-05',  80.50, 'gadget', 'b',     '{"channel":"shop","items":[3]}'),
  (3,  'Bob  Okafor',   'south', DATE '2026-01-05', 300.00, 'widget', 'a|c',   '{"channel":"web","items":[4,5,6]}'),
  (4,  'Carla Díaz',    'east',  DATE '2026-01-09',  NULL,  'gizmo',  NULL,    '{"channel":"web","items":[]}'),
  (5,  'Bob Okafor',    'south', DATE '2026-01-12',  45.25, 'gadget', 'c',     '{"channel":"phone","items":[7]}'),
  (6,  'Dev Patel',     'west',  DATE '2026-01-12', 510.00, 'widget', 'a',     '{"channel":"web","items":[8,9]}'),
  (7,  'Carla Diaz',    'east',  DATE '2026-01-20',  99.99, 'gizmo',  'b|c',   '{"channel":"shop","items":[10]}'),
  (8,  'Dev Patel',     'west',  DATE '2026-02-02', 510.00, 'widget', 'a',     '{"channel":"web","items":[8,9]}'),
  (9,  'Eve Larsen',    NULL,    DATE '2026-02-03',  15.00, 'gadget', NULL,    '{"channel":"web","items":[11]}'),
  (10, 'Alice Ng',      'north', DATE '2026-02-10', 220.00, 'gizmo',  'a|b|c', '{"channel":"phone","items":[12,13]}')
) t(order_id, customer, region, order_date, amount, product, tags, meta);
```

Then run the statement:

```sql
CREATE TEMP TABLE result AS
SELECT product, order_id, amount,
       round(percent_rank() OVER (PARTITION BY product ORDER BY amount), 4) AS pct
FROM orders
WHERE amount IS NOT NULL;
SELECT * FROM result ORDER BY product, amount;
SELECT CASE WHEN ((SELECT list(pct ORDER BY order_id) FROM result WHERE product = 'widget') = [0.0, 0.3333, 0.6667, 0.6667] AND (SELECT list(pct ORDER BY amount) FROM result WHERE product = 'gadget') = [0.0, 0.5, 1.0] AND (SELECT list(pct ORDER BY amount) FROM result WHERE product = 'gizmo') = [0.0, 1.0]) THEN 'as expected' ELSE error('the percent ranks were not 0 to 1 within each product, with the tied 510.00 orders sharing 0.6667') END AS verdict;
```

It needs nothing installed beyond DuckDB itself.

## What other tools call it

Meridian's classification; an independent blind rating agreed on 95.7% of 324 rows (variant, version 3).

- Apache DataFusion: [`cume_dist`](https://datafusion.apache.org/user-guide/sql/window_functions.html) (read 2026-09-27)
- Apache DataFusion: [`percent_rank`](https://datafusion.apache.org/user-guide/sql/window_functions.html) (read 2026-09-27)
- DuckDB: [`cume_dist`](https://duckdb.org/docs/current/sql/functions/window_functions) (read 2026-09-27)
- DuckDB: [`percent_rank`](https://duckdb.org/docs/current/sql/functions/window_functions) (read 2026-09-27)
- Ibis: [`CumeDist`](https://github.com/ibis-project/ibis/blob/05d2b293344e86cb41c1a426071734f7e270335a/ibis/expr/operations/analytic.py) (read 2026-09-27)
- Ibis: [`PercentRank`](https://github.com/ibis-project/ibis/blob/05d2b293344e86cb41c1a426071734f7e270335a/ibis/expr/operations/analytic.py) (read 2026-09-27)
- Tableau Prep: [`RANK_PERCENTILE`](https://help.tableau.com/current/prep/en-us/prep_function_reference.htm) (read 2026-09-27)