# Mathematical User-Defined Functions

Introduction

Mathematical UDFs

• Factorial

• PercentFrom

• PercentValue

• Degree

• Allocation

• Combination

• ## Introduction

I would like to write the series of articles about useful User-Defined
Functions grouped by the following categories:

• Date and Time User-Defined Functions

• Mathematical User-Defined Functions

• Security User-Defined Functions

• String User-Defined Functions

• System User-Defined Functions

• Text and Image User-Defined Functions
Functions.

## Mathematical UDFs

```
These scalar User-Defined Functions perform a calculation, usually
based on input values provided as arguments, and return a numeric
value.
```

## Factorial

```
Returns the factorial value of the given number.
Syntax
Factorial ( number )
Arguments
number
Is the integer value.
Return Types
bigint
The function’s text:

CREATE FUNCTION Factorial
( @number int )
RETURNS bigint
AS
BEGIN
DECLARE @i int, @factorial bigint
IF @number > 20 RETURN 0
SET @i = 1
SET @factorial = 1
WHILE @i <= @number
BEGIN
SET @factorial = @factorial * @i
SET @i = @i + 1
END
RETURN @factorial
END
GO

Examples
This example returns the factorial value of the number 5:

SELECT dbo.Factorial(5)
GO

Here is the result set:
——————–
120
(1 row(s) affected)
```

## PercentFrom

```
Returns the percent of the expression1 in the expression2.
Syntax
PercentFrom ( expression1, expression2 )
Arguments
expression1
Is an expression of the exact numeric or approximate numeric
data type category.
expression2
Is an expression of the exact numeric or approximate numeric
data type category.
Return Types
float
The function’s text:

CREATE FUNCTION PercentFrom
( @expression1 SQL_VARIANT,
@expression2 SQL_VARIANT )
RETURNS float
AS
BEGIN
RETURN (CAST(@expression1 AS FLOAT)/CAST(@expression2 AS FLOAT)*100)
END
GO

Examples
This example returns the percent of the 137 in the 273:

SELECT dbo.PercentFrom(137, 273)
GO

Here is the result set:
—————————————————–
50.183150183150182
(1 row(s) affected)
```

## PercentValue

```
Returns the percent’s value from the given expression for the
given percent.
Syntax
PercentValue ( expression, percent )
Arguments
expression
Is an expression of the exact numeric or approximate numeric
data type category.
percent
Is the integer value.
Return Types
float
The function’s text:

CREATE FUNCTION PercentValue
( @expression SQL_VARIANT,
@percent int )
RETURNS float
AS
BEGIN
RETURN ( CAST(@expression AS FLOAT) / 100 * @percent )
END
GO

Examples
Returns the percent’s value from the number 137 for the percent 11:

SELECT dbo.PercentValue (137, 11)
GO

Here is the result set:
—————————————————–
15.07
(1 row(s) affected)
```

## Degree

```
Returns the degree for the given number and degree value.
Syntax
Degree ( number, degree )
Arguments
number
Is an expression of the exact numeric or approximate numeric
data type category.
degree
Is the integer value.
Return Types
float
The function’s text:

CREATE FUNCTION Degree
( @number SQL_VARIANT,
@degree int )
RETURNS float
AS
BEGIN
DECLARE @i int, @res float
SET @i = 1
SET @res = 1
WHILE @i <= @degree
BEGIN
SET @res = CAST(@number AS FLOAT) * @res
SET @i = @i + 1
END
RETURN @res
END
GO

Examples
Returns the degree 4 for the number 3:

SELECT dbo.Degree(3, 4)
GO

Here is the result set:
—————————————————–
81.0
(1 row(s) affected)
```

## Allocation

```
Returns the allocation from the m by n.
Syntax
Allocation ( m, n )
Arguments
m
Is the integer value.
n
Is the integer value.
Return Types
int
The function’s text:

CREATE FUNCTION Allocation
( @m int,
@n int )
RETURNS int
AS
BEGIN
RETURN (dbo.Factorial(@m)/dbo.Factorial(@[email protected]))
END
GO

Examples
Returns the allocation from the 5 by 3:

SELECT dbo.Allocation(5,3)
GO

Here is the result set:
———–
60
(1 row(s) affected)
```

## Combination

```
Returns the combination from the m by n.
Syntax
Combination ( m, n )
Arguments
m
Is the integer value.
n
Is the integer value.
Return Types
int
The function’s text:

CREATE FUNCTION Combination
( @m int,
@n int )
RETURNS int
AS
BEGIN
RETURN (dbo.Factorial(@m)/(dbo.Factorial(@[email protected])*dbo.Factorial(@n)))
END
GO

Examples
Returns the combination from the 5 by 3:

SELECT dbo.Combination(5,3)
GO

Here is the result set:
———–
10
(1 row(s) affected)
``` Alexander Chigrik
I am the owner of MSSQLCity.Com - a site dedicated to providing useful information for IT professionals using Microsoft SQL Server. This site contains SQL Server Articles, FAQs, Scripts, Tips and Test Exams.