--- title: "degrees" slug: "dev-database-reference-sql-functions-numeric-degrees" updated: 2026-10-30T18:18:51Z published: 2026-10-30T18:18:51Z canonical: "docs.vastdata.com/dev-database-reference-sql-functions-numeric-degrees" --- > ## 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. # degrees *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) › Angles and constants.* Converts an angle from radians to degrees: `degrees(x)` is `x * 180 / pi()`. [radians](/develop/docs/dev-database-reference-sql-functions-numeric-radians) does the opposite. ## Syntax ``` degrees(x) ``` | Argument | Type | Description | | --- | --- | --- | | `x` | `DOUBLE` (any number) | An angle in radians. Integers, `DECIMAL` and `FLOAT` values are converted to `DOUBLE`. | **Returns:** `DOUBLE`. ## 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_degrees`. 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 five headings in radians. Row 3 has no heading: ``` 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_degrees"' 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}.headings" run(f"CREATE SCHEMA IF NOT EXISTS {SCHEMA}") run(f"CREATE TABLE IF NOT EXISTS {TABLE} (id BIGINT, rad DOUBLE)") run(f"INSERT INTO {TABLE} VALUES (1, 2.5), (2, -1.25), (3, NULL), (4, 0.0), (5, 1.0)") ``` ``` [] [] [(5,)] ``` ## What it does `degrees(x)` multiplies an angle in radians by 180/π. It doesn't wrap the result into a range: `degrees(-pi())` is `-180.0`. Use it to show the result of the inverse trigonometric functions, such as [asin](/develop/docs/dev-database-reference-sql-functions-numeric-asin) or [atan2](/develop/docs/dev-database-reference-sql-functions-numeric-atan2), in degrees. The result is rounded to the nearest `DOUBLE`, so it can be off in the last digit: `degrees(asin(0.5))` is `30.000000000000004`, not `30.0`. Round it if you display it. ## NULLs and edge cases | Input | Result | | --- | --- | | `NULL` | `NULL` | | `pi()`, `pi() / 2`, `-pi()` | `180.0`, `90.0`, `-180.0` | | `1` | `57.29577951308232` | | `radians(45)` | `45.0` | | `-0.0::DOUBLE` | `-0.0` | | `5e-324::DOUBLE` (the smallest `DOUBLE` above 0) | `2.8e-322` | | `1e308` | `inf`: the result is too large for a `DOUBLE`, and there's no error | | `'inf'::DOUBLE`, `'-inf'::DOUBLE`, `'nan'::DOUBLE` | `inf`, `-inf`, `nan` | | `'12'` (a string) | Converted to `DOUBLE`: `687.5493541569879` | | `'abc'` | 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 `'degrees(DATE)'` | | An `INTEGER`, `FLOAT` or `DECIMAL` value | Converted; the result is `DOUBLE` | The same cases, as the cluster returns them. They use the table and helpers from [Set up the examples](/develop/docs/dev-database-reference-sql-functions-numeric-degrees#set-up-the-examples): ``` run("SELECT degrees(NULL), degrees(pi()), degrees(pi() / 2), degrees(-pi()), degrees(1), degrees(radians(45))") run("SELECT degrees(-0.0::DOUBLE), degrees(5e-324::DOUBLE), degrees(1e308)") run("SELECT degrees('inf'::DOUBLE), degrees('-inf'::DOUBLE), degrees('nan'::DOUBLE), degrees('12')") run("SELECT typeof(degrees(1::INTEGER)), typeof(degrees(0.5::FLOAT)), typeof(degrees(0.5))") run("SELECT degrees('abc')") run("SELECT degrees(DATE '2026-10-16')") ``` ``` [(None, 180.0, 90.0, -180.0, 57.29577951308232, 45.0)] [(-0.0, 2.8e-322, inf)] [(inf, -inf, nan, 687.5493541569879)] [('DOUBLE', 'DOUBLE', 'DOUBLE')] OSError: Could not convert string 'abc' to DOUBLE InternalError: Binder Error: No function matches the given name and argument types 'degrees(DATE)'. You might need to add explicit type casts. ``` ## Examples Each heading in degrees, and rounded to one decimal place: ``` run(f"SELECT id, rad, degrees(rad), round(degrees(rad), 1) FROM {TABLE} ORDER BY id LIMIT 10") ``` ``` [(1, 2.5, 143.2394487827058, 143.2), (2, -1.25, -71.6197243913529, -71.6), (3, None, None, None), (4, 0.0, 0.0, 0.0), (5, 1.0, 57.29577951308232, 57.3)] ``` Keep the headings of more than 90 degrees: ``` run(f"SELECT id FROM {TABLE} WHERE degrees(rad) > 90 ORDER BY id LIMIT 10") ``` ``` [(1,)] ``` ## 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 `degrees()` of a column is always computed by the Query Engine: - **In the `SELECT` list,** the scan reads the column and the Query Engine computes `degrees()` for each row it returns. - **In `WHERE`,** the scan sends the column for every row, and a `FILTER` step in the Query Engine computes `degrees()` and keeps the rows that match. The plan of the `WHERE` example shows the `FILTER` step above the scan: ``` plan(f"SELECT id FROM {TABLE} WHERE degrees(rad) > 90") ``` ``` ┌───────────────────────────┐ │ PROJECTION │ │ ──────────────────── │ │ #1 │ │ │ └─────────────┬─────────────┘ ┌─────────────┴─────────────┐ │ FILTER │ │ ──────────────────── │ │ (degrees(rad) > 90.0) │ │ │ └─────────────┬─────────────┘ ┌─────────────┴─────────────┐ │ VAST_SCAN │ │ ──────────────────── │ │ Function: VAST_SCAN │ │ │ │ Projections: │ │ rad │ │ id │ │ │ └───────────────────────────┘ ``` ## Make it faster - **Convert the constant, not the column.** `rad > radians(90)` keeps the same rows as `degrees(rad) > 90`. `radians(90)` is computed once, before the scan, so the condition is pushed down to VAST DataBase and the plan has no `FILTER` step: ``` plan(f"SELECT id FROM {TABLE} WHERE rad > radians(90)") run(f"SELECT id FROM {TABLE} WHERE rad > radians(90) ORDER BY id LIMIT 10") ``` ``` ┌───────────────────────────┐ │ VAST_SCAN │ │ ──────────────────── │ │ Function: VAST_SCAN │ │ Projections: id │ │ │ └───────────────────────────┘ [(1,)] ``` - **Store angles in the unit you filter by.** If you query in degrees most of the time, store degrees and convert in the `SELECT` list. ## Limitations and errors - **No range check.** A result too large for a `DOUBLE` is `inf`, with no error. Infinity and NaN pass through unchanged. - **One argument, numbers only.** A second argument, a date, a boolean, a `BLOB`, a list or an interval fails with `No function matches the given name and argument types`. A string is converted to `DOUBLE` first, and fails with `Could not convert string ... to DOUBLE` if it isn't a number. - **Rounding.** Results are `DOUBLE` values, so conversions such as `degrees(asin(0.5))` can be off in the last digit. Use [round](/develop/docs/dev-database-reference-sql-functions-numeric-round) to display them. ## Similar functions | Function | Converts | Result for its argument | | --- | --- | --- | | `degrees(x)` | radians to degrees | `degrees(pi())` is `180.0` | | [radians](/develop/docs/dev-database-reference-sql-functions-numeric-radians)`(x)` | degrees to radians | `radians(180)` is `3.141592653589793` | | `x * 180 / pi()` | the same formula as `degrees`, written out | | | [atan2](/develop/docs/dev-database-reference-sql-functions-numeric-atan2)`(y, x)` | a point to its angle in radians; wrap it in `degrees()` for degrees | | ``` run("SELECT degrees(pi()), radians(180), 1 * 180 / pi(), degrees(1), radians(degrees(1)), degrees(atan2(1, 1))") ``` ``` [(180.0, 3.141592653589793, 57.29577951308232, 57.29577951308232, 1.0, 45.0)] ``` 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#angles-and-constants): pi, degrees and radians. - [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.