Shape / rows · All operations

Percentile rank

A variant of Number or rank rows

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

Status

In arcform

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.
  • The statement checks its own result and raises an error when it is wrong: “the percent ranks were not 0 to 1 within each product, with the tied 510.00 orders sharing 0.6667”.
  • It passed on DuckDB v2.0.0 (Cyanoptera) d54cbbe3df.

What other tools call it

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

Apache DataFusion (2)
  • cume_distread 2026-09-27

    Window: Relative rank: rows preceding or peer with the current row over total rows

  • percent_rankread 2026-09-27

    Window: Percentage rank of the current row within its partition

DuckDB (2)
Ibis (2)
  • CumeDistread 2026-09-27

    Cumulative-distribution position of each row within its window

  • PercentRankread 2026-09-27

    Relative rank of each row within its window, as a fraction

Tableau Prep (1)
  • RANK_PERCENTILEread 2026-09-27

    Percentile rank from 0 to 1 within a partition

Background

In PostgreSQL, percent_rank gives each row its relative rank, (rank - 1) / (total partition rows - 1), a value from 0 to 1 inclusive.[1] In statistics, the percentile rank of a score is the percentage of scores in its frequency distribution that are less than that score.[2]

When to use it

Percentile ranks are commonly used to clarify the interpretation of scores on standardized tests.[2] In DuckDB, percent_rank returns 0 for a partition with a single row.[3]

Percentile ranks are not on an equal-interval scale: two pairs of scores whose percentile ranks differ by the same amount need not differ by the same amount in score.[2] Compare percent ranks as positions, and go back to the values themselves before averaging or subtracting. (Meridian's view)

The method

In statistics, the percentile rank is (CF − 0.5 × F) / N × 100, where CF counts the scores less than or equal to the score of interest, F is that score's frequency and N is the number of scores.[2] The 0.5 × F term counts half of the scores equal to the score of interest, so that the percentile rank reflects a percentage of scores less than it.[2] Say in the column's name or description which definition it holds, since a reader may expect the statistician's percentile rank rather than SQL's percent_rank. (Meridian's view)

Sources

  1. [1]PostgreSQL: Documentation: 18: 9.22. Window Functionsdocumentation
  2. [2]Percentile rank - Wikipediasecondary source
  3. [3]Window Functions – DuckDBdocumentation