--- title: "atan2" slug: "dev-database-reference-sql-functions-numeric-atan2" updated: 2026-10-30T18:18:51Z published: 2026-10-30T18:18:51Z canonical: "docs.vastdata.com/dev-database-reference-sql-functions-numeric-atan2" --- > ## Documentation Index > Fetch the complete documentation index at: https://docs.vastdata.com/llms.txt > Use this file to discover all available pages before exploring further. # atan2 *Applies to VAST Cluster 5.5.* *[Functions](/develop/docs/dev-database-reference-sql-functions-index) › [Numeric and math functions](/develop/docs/dev-database-reference-sql-functions-numeric) › Inverse trigonometry.* Returns the angle, in radians from -pi to pi, between the positive x axis and the point (x, y). It takes the y coordinate first. Unlike [atan](/develop/docs/dev-database-reference-sql-functions-numeric-atan)`(y / x)`, it tells the four quadrants apart and works when `x` is 0. ## Syntax ``` atan2(y, x) ``` | Argument | Type | Description | | --- | --- | --- | | `y` | Any number (`DOUBLE`, `REAL`, an integer or a `DECIMAL`) | The y coordinate (the vertical one). | | `x` | Any number | The x coordinate (the horizontal one). | **Returns:** `DOUBLE`, from -pi to pi. ## Set up the examples The examples connect with the ADBC driver, as in [VAST Query Engine (ADBC)](/develop/docs/dev-database-integrations-adbc), and work in a schema called `docs_sql_fn_numeric_atan2`. Set `QE_ENDPOINT`, `AWS_ACCESS_KEY_ID`, `AWS_SECRET_ACCESS_KEY` and `VASTDB_BUCKET` ([SQL reference](/develop/docs/dev-database-reference-sql-index#example-connect-and-use-a-transaction)), and run the blocks in order in one Python session. Below each block is the output you should see. This block connects, defines the `run()` and `plan()` helpers, and creates a table of seven points, one in each quadrant, one on an axis, one at the origin and one with no x coordinate: ``` import os import re import adbc_driver_manager import adbc_driver_manager.dbapi as dbapi import adbc_driver_vastdb BUCKET = os.environ["VASTDB_BUCKET"] SCHEMA = f'"{BUCKET}/docs_sql_fn_numeric_atan2"' conn = dbapi.connect( driver=adbc_driver_vastdb.get_driver_path(), db_kwargs={ "vast.db.endpoint": os.environ["QE_ENDPOINT"], "vast.db.access_key": os.environ["AWS_ACCESS_KEY_ID"], "vast.db.secret_key": os.environ["AWS_SECRET_ACCESS_KEY"], }, autocommit=True, ) def server_message(e): """The server's message in a driver error, without the request ID or the echoed statement.""" text = re.sub(r"\[req=0x[0-9a-f]+\]: ", "", str(e)) found = (re.search(r'message: "(.*?)", request_id', text, re.S) or re.search(r"description: (.*)\)", text, re.S)) message = found.group(1) if found else text.strip().splitlines()[-1] message = re.sub(r"^Plan query: '.*?' failed with: ", "", message, flags=re.S) message = re.split(r"\\n|\n", message)[0].replace('\\"', '"') return message.replace(BUCKET, "") def run(sql): """Run one statement. Print the rows it returns, or the error.""" try: with conn.cursor() as cur: cur.execute(sql) rows = cur.fetchall() if cur.description else [] except (adbc_driver_manager.Error, OSError) as e: print(f"{type(e).__name__}: {server_message(e)}") else: print(rows) def plan(sql): """Print the plan without its ~N Rows lines: the table's row count, which can still be 0 just after an insert.""" with conn.cursor() as cur: cur.execute("EXPLAIN " + sql) steps = cur.fetchall()[0][1] print("\n".join(line for line in steps.splitlines() if "Rows" not in line)) TABLE = f"{SCHEMA}.points" run(f"CREATE SCHEMA IF NOT EXISTS {SCHEMA}") run(f"CREATE TABLE IF NOT EXISTS {TABLE} (id BIGINT, x DOUBLE, y DOUBLE)") run(f"INSERT INTO {TABLE} VALUES " "(1, 1.0, 1.0), (2, -1.0, 1.0), (3, -1.0, -1.0), (4, 1.0, -1.0), " "(5, 0.0, 2.0), (6, 0.0, 0.0), (7, NULL, 1.0)") ``` ``` [] [] [(7,)] ``` ## What it does `atan2(y, x)` is the angle, measured counterclockwise from the positive x axis, of the line from the origin to the point (x, y). It's positive above the x axis (`y > 0`), negative below it, and pi or -pi on the negative x axis. When `x` is positive it's the same as `atan(y / x)`. | Call | Point | Result | | --- | --- | --- | | `atan2(1, 1)` | (1, 1), upper right | `0.7853981633974483` (pi/4) | | `atan2(1, -1)` | (-1, 1), upper left | `2.356194490192345` (3pi/4) | | `atan2(-1, -1)` | (-1, -1), lower left | `-2.356194490192345` | | `atan2(-1, 1)` | (1, -1), lower right | `-0.7853981633974483` | | `atan2(1, 0)` | (0, 1), on the y axis | `1.5707963267948966` (pi/2) | | `atan2(-1, 0)` | (0, -1) | `-1.5707963267948966` | | `atan2(0, -1)` | (-1, 0), on the negative x axis | `3.141592653589793` (pi) | The result is a `DOUBLE` for every numeric argument type. ``` run("SELECT atan2(1, 1), atan2(1, -1), atan2(-1, -1), atan2(-1, 1)") run("SELECT atan2(1, 0), atan2(-1, 0), atan2(0, -1)") run("SELECT typeof(atan2(1::INTEGER, 1::INTEGER)), atan2(1, 1) = atan(1)") ``` ``` [(0.7853981633974483, 2.356194490192345, -2.356194490192345, -0.7853981633974483)] [(1.5707963267948966, -1.5707963267948966, 3.141592653589793)] [('DOUBLE', True)] ``` ## NULLs and edge cases | Input | Result | | --- | --- | | `NULL` as either argument | `NULL` | | `atan2(0, 0)` (the origin) | `0.0`, not an error | | `atan2(-0.0::DOUBLE, 0)` | `-0.0` | | `atan2(0, -0.0::DOUBLE)` | `3.141592653589793` (pi) | | `atan2(-0.0::DOUBLE, -0.0::DOUBLE)` | `-3.141592653589793` (-pi) | | `atan2(-0.0::DOUBLE, -1)` | `-3.141592653589793`: the sign of a zero `y` picks pi or -pi | | `atan2('inf'::DOUBLE, 'inf'::DOUBLE)` | `0.7853981633974483` (pi/4) | | `atan2(1, 'inf'::DOUBLE)`, `atan2(1, '-inf'::DOUBLE)` | `0.0`, `3.141592653589793` | | `'nan'::DOUBLE` as either argument | `nan` | | `'12'` (a string literal holding a number) | Converted to `DOUBLE`: `atan2('12', 1)` is `1.4876550949064553` | | `'abc'` (a string that isn't a number) | Error: `Could not convert string 'abc' to DOUBLE` | | A `BLOB`, date, boolean, list or interval | Error: `No function matches the given name and argument types`, for example `'atan2(DATE, INTEGER_LITERAL)'` | A literal `-0.0` is a `DECIMAL`, which has no negative zero; write `-0.0::DOUBLE` to get one. The same cases, as the cluster returns them. They use the helpers from [Set up the examples](/develop/docs/dev-database-reference-sql-functions-numeric-atan2#set-up-the-examples): ``` run("SELECT atan2(NULL, 1), atan2(1, NULL), atan2(0, 0)") run("SELECT atan2(-0.0::DOUBLE, 0), atan2(0, -0.0::DOUBLE), atan2(-0.0::DOUBLE, -0.0::DOUBLE), atan2(-0.0::DOUBLE, -1)") run("SELECT atan2('inf'::DOUBLE, 'inf'::DOUBLE), atan2(1, 'inf'::DOUBLE), atan2(1, '-inf'::DOUBLE)") run("SELECT atan2('nan'::DOUBLE, 1), atan2(1, 'nan'::DOUBLE), atan2('12', 1)") run("SELECT atan2('abc', 1)") run("SELECT atan2(DATE '2026-10-16', 1)") ``` ``` [(None, None, 0.0)] [(-0.0, 3.141592653589793, -3.141592653589793, -3.141592653589793)] [(0.7853981633974483, 0.0, 3.141592653589793)] [(nan, nan, 1.4876550949064553)] OSError: Could not convert string 'abc' to DOUBLE InternalError: Binder Error: No function matches the given name and argument types 'atan2(DATE, INTEGER_LITERAL)'. You might need to add explicit type casts. ``` ## Examples The angle of each point, in radians and in degrees. Note the order of the arguments: `y` first, then `x`: ``` run(f"SELECT id, x, y, atan2(y, x), degrees(atan2(y, x)) FROM {TABLE} ORDER BY id LIMIT 10") ``` ``` [(1, 1.0, 1.0, 0.7853981633974483, 45.0), (2, -1.0, 1.0, 2.356194490192345, 135.0), (3, -1.0, -1.0, -2.356194490192345, -135.0), (4, 1.0, -1.0, -0.7853981633974483, -45.0), (5, 0.0, 2.0, 1.5707963267948966, 90.0), (6, 0.0, 0.0, 0.0, 0.0), (7, None, 1.0, None, None)] ``` Keep only the points more than 90 degrees counterclockwise from the positive x axis: ``` run(f"SELECT id, x, y FROM {TABLE} WHERE atan2(y, x) > pi() / 2 ORDER BY id LIMIT 10") ``` ``` [(2, -1.0, 1.0)] ``` ## How it runs in VAST The Query Engine runs on the cluster's CNodes, and a query on a table starts with a scan in VAST DataBase (`VAST_SCAN`). VAST DataBase can evaluate a comparison of a column with a constant, but not a function of a column, so `atan2()` is always computed by the Query Engine: - **In the `SELECT` list,** the scan reads both columns and the Query Engine computes `atan2()` for each row it returns. - **In `WHERE`,** the scan sends both columns for every row, and a `FILTER` step in the Query Engine computes `atan2()` and keeps the rows that match. No rows are skipped in storage. The plan of the `WHERE` example shows the `FILTER` step above the scan: ``` plan(f"SELECT id FROM {TABLE} WHERE atan2(y, x) > pi() / 2") ``` ``` ┌───────────────────────────┐ │ PROJECTION │ │ ──────────────────── │ │ #2 │ │ │ └─────────────┬─────────────┘ ┌─────────────┴─────────────┐ │ FILTER │ │ ──────────────────── │ │ (atan2(y, x) > 1 │ │ .5707963267948966) │ │ │ └─────────────┬─────────────┘ ┌─────────────┴─────────────┐ │ VAST_SCAN │ │ ──────────────────── │ │ Function: VAST_SCAN │ │ │ │ Projections: │ │ y │ │ x │ │ id │ │ │ └───────────────────────────┘ ``` ## Make it faster - **Select a quadrant with the signs of the coordinates.** An angle strictly between 0 and pi/2 is the same as `x > 0 AND y > 0`, and each of those is a comparison of a column with a constant, which is pushed down to VAST DataBase: ``` plan(f"SELECT id FROM {TABLE} WHERE x > 0 AND y > 0") run(f"SELECT id, x, y FROM {TABLE} WHERE x > 0 AND y > 0 ORDER BY id LIMIT 10") ``` ``` ┌───────────────────────────┐ │ VAST_SCAN │ │ ──────────────────── │ │ Function: VAST_SCAN │ │ Projections: id │ │ │ └───────────────────────────┘ [(1, 1.0, 1.0)] ``` - **Store the angle if you filter on it often.** Compute it when you write the rows and keep it in its own column: a condition on that column is pushed down, a condition on `atan2()` isn't. ## Limitations and errors - **Two arguments, `y` first.** `atan2(1)` fails with `No function matches the given name and argument types 'atan2(INTEGER_LITERAL)'`; the error lists the one form `atan2` has, `atan2(DOUBLE, DOUBLE) -> DOUBLE`. Swapping the arguments gives a different angle and raises no error. - **Numbers only.** A `BLOB`, a date, a boolean, a list or an interval fails with `No function matches the given name and argument types`. A string literal is converted to `DOUBLE` if it holds a number, and otherwise fails with `Could not convert string 'abc' to DOUBLE`. - **No degrees variant.** `atan2d` fails with `Scalar Function with name atan2d does not exist!`. Use `degrees(atan2(y, x))`: ``` run("SELECT atan2d(1, 1)") run("SELECT degrees(atan2(1, 1))") ``` ``` InternalError: Catalog Error: Scalar Function with name atan2d does not exist! [(45.0,)] ``` ## Similar functions | Function | Returns | For the point (-1, -1) | | --- | --- | --- | | `atan2(y, x)` | the angle of the point (x, y), from -pi to pi | `atan2(-1, -1)`: `-2.356194490192345` | | [atan](/develop/docs/dev-database-reference-sql-functions-numeric-atan) | the angle whose tangent is a ratio, from -pi/2 to pi/2: no quadrant | `atan(-1 / -1)`: `0.7853981633974483` | | [degrees](/develop/docs/dev-database-reference-sql-functions-numeric-degrees) | radians converted to degrees | `degrees(atan2(-1, -1))`: `-135.0` | ``` run("SELECT atan2(-1, -1), atan(-1 / -1), degrees(atan2(-1, -1))") ``` ``` [(-2.356194490192345, 0.7853981633974483, -135.0)] ``` Clean up: ``` run(f"DROP TABLE IF EXISTS {TABLE}") run(f"DROP SCHEMA IF EXISTS {SCHEMA}") conn.close() ``` ``` [] [] ``` ## See also - [Numeric and math functions](/develop/docs/dev-database-reference-sql-functions-numeric): all the numeric functions. - [Where filters run](/develop/docs/dev-database-reference-sql-select#where-filters-run) and [pushdowns](/develop/docs/dev-database-reference-pushdowns). - [EXPLAIN](/develop/docs/dev-database-reference-sql-explain): how to read a plan.