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Arithmetic and Numerical Functions

Written by Andy Brown

In this tutorial

Mathematical Symbols (Adding, Subtracting, Multiplying and Dividing)
Order of Symbols - BODMAS
The % Modulus Operator
Built-in Mathematical Functions
The Importance of Converting Numbers

This part of my tutorial on calculated columns in T-SQL looks at numerical formulae and expressions.

Mathematical Symbols (Adding, Subtracting, Multiplying and Dividing)

The main symbols that you can use in SQL are the standard ones:

Symbol	What it does
+	Addition
-	Subtraction
*	Multiplication
/	Division

Thus the following SQL would show for each film in a database the difference between the number of Oscar nominations and the number of Oscars won:

SELECT

FilmName,

FilmOscarWins AS Wins,

FilmOscarNominations AS Nominations,

-- calculate the difference

FilmOscarNominations - FilmOscarWins AS 'Oscar shortfall'

FROM

tblFilm

ORDER BY

'Oscar shortfall' DESC

In the standard Wise Owl database, Gangs of New York tops this list, with 10 nominations and no wins. At the other end of the scale, kudos to The Matrix for winning 4 out of the 4 Oscars for which it was nominated.

Order of Symbols - BODMAS

As in most arithmetic, the order of operations in SQL is:

Brackets / Of
Division / Multiplication
Addition / Subtraction

This is sometimes remembered by its acronym BODMAS. The difference is shown by the following example:

-- this query shows the difference

SELECT

2 + 3 * 5 as 'Without brackets',

(2 + 3) * 5 as 'With brackets'

Here is what you'd get if you ran this query:

Without brackets, the multiplication is done before the addtion.

The % Modulus Operator

If you want to find out the remainder when you divide one integer by another use the modulus operator, or %. The following query, for example, would show how long each film lasted in hours and minutes:

-- show film duration as hours and minutes

SELECT

FilmName,

FilmRunTimeMinutes AS Length,

(FilmRunTimeMinutes - FilmRunTimeMinutes % 60)/60 AS Hrs,

FilmRunTimeMinutes % 60 AS Mins

FROM

tblFilm

Here is what this query would show:

Film length, including hours and minutes

The results of running this query. For each film we see the whole number of hours, plus remaining minutes.

For example, Jurassic Park lasts 127 minutes. The remainder when 127 is divided by 60 is 7, which gives the Mins column, from which the Hrs column follows.

Built-in Mathematical Functions

Excel has various trigonometric functions (to calculate sines, cosines, tangents, etc.), but this blog will restrict itself to non-specialist mathematical functions. These are shown in the following SQL example:

-- show results of various functions

SELECT

Abs(-3.7) AS 'Absolute value',

Ceiling (3.7) AS 'Upper limit',

Floor(3.7) AS 'Lower limit',

Power(2,3) AS 'Power eg',

Round(3.14159,2) AS 'Rounding',

Sign(-3.7) AS 'Sign eg',

SqRt(2) AS 'Square root',

Square(2) AS 'Square eg'

Here's the output from running this query:

The results from running the query above.

The functions used are as follows:

Function	What it does
Abs	Takes the absolute value of a number (its positive amount).
Ceiling, Floor	Shows the next highest or lowest integer for a number.
Power	Raises one number to the power of another.
Round	Rounds a number to a number of decimal places.
Sign	Returns -1 if a number is negative, 0 (if zero) or +1 (if positive).
SqRt, Square	Takes the square root of a number or squares it.

If you're wondering what happens if you take the square root of a negative number, you get the error message An invalid floating point operation occurred - a typically user-friendly SQL Server message!

The Importance of Converting Numbers

SQL is nothing if not fussy about its data types. Consider the following query:

SELECT

FilmName,

FilmRunTimeMinutes,

-- show length of film in hours

FilmRunTimeMinutes / 60 AS Hours

FROM

tblFilm

What would you expect this to show for the hours? If a film lasted 75 minutes, will you see 1 or 1.25 hours? The answer is that because the FilmRunTimeMinutes column is an integer, so will the answer be:

The hours shown are all integers (whole numbers).

One way round this would be to convert the input values into float data types (ie non-integers); the answer will then automatically be returned as the same data type:

SELECT

FilmName,

FilmRunTimeMinutes,

-- show length of film in hours

CAST(FilmRunTimeMinutes AS float)/ 60 AS Hours

FROM

tblFilm

The answer is now accurate:

The data type of the answer is now float, not int.

You'll frequently find yourself having to cast integers as floating point numbers before using them in operations involving division, such as averaging.

So much for numbers - let's now look at text.

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WHERE criteria (version B)

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Formulae, Expressions and Calculations in SQL

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Online tutorials

Tutorials on SQL

Calculations and Expressions

Arithmetic and Numerical Functions

Mathematical Symbols (Adding, Subtracting, Multiplying and Dividing)

Order of Symbols - BODMAS

The % Modulus Operator

Built-in Mathematical Functions

The Importance of Converting Numbers

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