---
title: "pi"
slug: "dev-database-reference-sql-functions-numeric-pi"
updated: 2026-10-30T18:18:51Z
published: 2026-10-30T18:18:51Z
canonical: "docs.vastdata.com/dev-database-reference-sql-functions-numeric-pi"
---

> ## 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.

# pi

*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.* Returns the constant π, `3.141592653589793`, as a `DOUBLE`. It takes no arguments.

## Syntax

```
pi()
```

**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_pi`. 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 four circles with their radius in metres. Row 3 has no radius:

```
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_pi"'

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, "<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}.circles"
run(f"CREATE SCHEMA IF NOT EXISTS {SCHEMA}")
run(f"CREATE TABLE IF NOT EXISTS {TABLE} (id BIGINT, radius DOUBLE)")
run(f"INSERT INTO {TABLE} VALUES (1, 1.0), (2, 2.5), (3, NULL), (4, 0.0)")
```

```
[]
[]
[(4,)]
```

## What it does

`pi()` returns π rounded to the nearest `DOUBLE`, `3.141592653589793`. It's the same value as `acos(-1)` and `4 * atan(1)`. Use it in formulas such as `pi() * radius * radius` (the area of a circle), or to convert angles; [radians](/develop/docs/dev-database-reference-sql-functions-numeric-radians) and [degrees](/develop/docs/dev-database-reference-sql-functions-numeric-degrees) do that for you.

## NULLs and edge cases

| Input | Result |
| --- | --- |
| `pi()` | `3.141592653589793`, a `DOUBLE` |
| `pi()` on a row whose columns are NULL | `3.141592653589793`: it doesn't depend on the row |
| `2 * pi()` | `6.283185307179586` |
| `pi() = acos(-1)`, `pi() = 4 * atan(1)` | `true` |
| `pi(1)` | Error: `No function matches the given name and argument types &apos;pi(INTEGER_LITERAL)&apos;` |
| `pi` without parentheses | Error: `Referenced column &quot;pi&quot; not found in FROM clause!` |

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-pi#set-up-the-examples):

```
run("SELECT pi(), typeof(pi()), 2 * pi(), pi() = acos(-1), pi() = 4 * atan(1)")
run(f"SELECT id, radius, pi() FROM {TABLE} WHERE id = 3")
run("SELECT pi(1)")
run("SELECT pi")
```

```
[(3.141592653589793, 'DOUBLE', 6.283185307179586, True, True)]
[(3, None, 3.141592653589793)]
InternalError: Binder Error: No function matches the given name and argument types 'pi(INTEGER_LITERAL)'. You might need to add explicit type casts.
InternalError: Binder Error: Referenced column "pi" not found in FROM clause!
```

## Examples

The area and circumference of each circle. Row 3 has no radius, so both are NULL:

```
run(f"SELECT id, pi() * radius * radius, 2 * pi() * radius FROM {TABLE} ORDER BY id LIMIT 10")
```

```
[(1, 3.141592653589793, 6.283185307179586), (2, 19.634954084936208, 15.707963267948966), (3, None, None), (4, 0.0, 0.0)]
```

Keep the circles whose radius is more than π/2:

```
run(f"SELECT id, radius FROM {TABLE} WHERE radius > pi() / 2 ORDER BY id LIMIT 10")
```

```
[(2, 2.5)]
```

## 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`). `pi()` is a constant, so the Query Engine computes it once, before the scan:

- **Compared with a column,** as in `radius &gt; pi() / 2`, the whole right-hand side is a constant. The condition is pushed down to VAST DataBase, and the plan has no `FILTER` step.
- **In arithmetic on a column,** as in `pi() * radius * radius`, the Query Engine computes the expression for each row: in a `PROJECTION` step in the `SELECT` list, or in a `FILTER` step in `WHERE`.

The plan of the `WHERE` example has no `FILTER` step:

```
plan(f"SELECT id FROM {TABLE} WHERE radius > pi() / 2")
```

```
┌───────────────────────────┐
│         VAST_SCAN         │
│    ────────────────────   │
│    Function: VAST_SCAN    │
│      Projections: id      │
│                           │
└───────────────────────────┘
```

## Make it faster

- **Keep the column alone on one side of a comparison.** `pi() * radius * radius &gt; 5` makes the Query Engine compute the area for every row, in a `FILTER` step. `radius &gt; sqrt(5 / pi())` keeps the same rows, and the scan in VAST DataBase can evaluate it, because the right-hand side is a constant:

```
plan(f"SELECT id FROM {TABLE} WHERE pi() * radius * radius > 5")
plan(f"SELECT id FROM {TABLE} WHERE radius > sqrt(5 / pi())")
```

```
┌───────────────────────────┐
│         PROJECTION        │
│    ────────────────────   │
│             #1            │
│                           │
└─────────────┬─────────────┘
┌─────────────┴─────────────┐
│           FILTER          │
│    ────────────────────   │
│   (((3.141592653589793 *  │
│  radius) * radius) > 5.0) │
│                           │
└─────────────┬─────────────┘
┌─────────────┴─────────────┐
│         VAST_SCAN         │
│    ────────────────────   │
│    Function: VAST_SCAN    │
│                           │
│        Projections:       │
│           radius          │
│             id            │
│                           │
└───────────────────────────┘
┌───────────────────────────┐
│         VAST_SCAN         │
│    ────────────────────   │
│    Function: VAST_SCAN    │
│      Projections: id      │
│                           │
└───────────────────────────┘
```

## Limitations and errors

- **Parentheses are required.** `pi` alone is read as a column name and fails with `Referenced column &quot;pi&quot; not found in FROM clause!`.
- **No arguments.** `pi(1)` fails with `No function matches the given name and argument types &apos;pi(INTEGER_LITERAL)&apos;`.
- **There's no `e()` constant.** It fails with `Scalar Function with name e does not exist!`; use `exp(1)`:

```
run("SELECT e()")
run("SELECT exp(1)")
```

```
InternalError: Catalog Error: Scalar Function with name e does not exist!
[(2.718281828459045,)]
```

## Similar functions

| Expression | Result | Notes |
| --- | --- | --- |
| `acos(-1)`, `4 * atan(1)` | equal to `pi()` | the same value, computed |
| [radians](/develop/docs/dev-database-reference-sql-functions-numeric-radians)`(180)` | `3.141592653589793` | converts degrees to radians: `x * pi() / 180` |
| [degrees](/develop/docs/dev-database-reference-sql-functions-numeric-degrees)`(pi())` | `180.0` | converts radians to degrees |
| [exp](/develop/docs/dev-database-reference-sql-functions-numeric-exp)`(1)` | `2.718281828459045` | Euler's number; there's no `e()` |

```
run("SELECT acos(-1) = pi(), 4 * atan(1) = pi(), radians(180), degrees(pi()), exp(1)")
```

```
[(True, True, 3.141592653589793, 180.0, 2.718281828459045)]
```

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.