# How does SQL Server determine precision / scale?

I'm running SQL Server 2012

SELECT
0.15 * 30 / 360,
0.15 / 360 * 30


Results:

 0.012500,
0.012480


This one is even mor confusing to me:

DECLARE @N INT = 360
DECLARE @I DECIMAL(38,26) = 0.15 * 30 / 360
DECLARE @C DECIMAL(38,26) = 1000000

SELECT @C *  @I *  POWER(1 + @I, @N)  / ( POWER(1 + @I, @N) - 1 )
SELECT @C * (@I *  POWER(1 + @I, @N)  / ( POWER(1 + @I, @N) - 1 ) )


The first select gives me the correct result: 12644.44022 The second one truncates the result: 12644.00000

Determining precision and scale resulting from expressions is a rat's nest and I don't think anyone understands the exact rules in every scenario, especially when mixing decimal (or float!) and int. See this answer by gbn.

You can of course tailor the expressions to give you what you want by making much more verbose explicit conversions. This is probably overkill but:

SELECT
CONVERT(DECIMAL(15,6), CONVERT(DECIMAL(15,6), 0.15)
* CONVERT(DECIMAL(15,6), 30)
/ CONVERT(DECIMAL(15,6), 360)),
CONVERT(DECIMAL(15,6), CONVERT(DECIMAL(15,6), 0.15)
/ CONVERT(DECIMAL(15,6), 360)
* CONVERT(DECIMAL(15,6), 30));


Neither result is rounded wrongly due to broken floating point math or wildly wrong precision/scale.

0.012500    0.012500


As Aaron Bertrand mentioned, expressions are very tricky to predict.

If you dare go there, you could try to gain some insight using the following snippet:

DECLARE @number SQL_VARIANT
SELECT @number = 0.15 / 360
SELECT @number
SELECT
SQL_VARIANT_PROPERTY(@number, 'BaseType') BaseType,
SQL_VARIANT_PROPERTY(@number, 'MaxLength') MaxLength,
SQL_VARIANT_PROPERTY(@number, 'Precision') Precision


This is the result:

------------
0.000416

(1 row(s) affected)

BaseType     MaxLength    Precision
------------ ------------ ----------
numeric      5            6

(1 row(s) affected)


Notwithstanding the excellent answers already added to this question, there is an explicitly defined order of precedence for conversion of data types in SQL Server.

When an operator combines two expressions of different data types, the rules for data type precedence specify that the data type with the lower precedence is converted to the data type with the higher precedence. If the conversion is not a supported implicit conversion, an error is returned. When both operand expressions have the same data type, the result of the operation has that data type.

SQL Server uses the following precedence order for data types:

user-defined data types (highest)
sql_variant
xml
datetimeoffset
datetime2
datetime
smalldatetime
date
time
float
real
decimal
money
smallmoney
bigint
int
smallint
tinyint
bit
ntext
text
image
timestamp
uniqueidentifier
nvarchar (including nvarchar(max) )
nchar
varchar (including varchar(max) )
char
varbinary (including varbinary(max) )
binary (lowest)


So, for instance, if you SELECT 0.5 * 1 (multiplying a decimal by an int) you get a result that is converted to a decimal value, since decimal is higher precedence than the int data type.

See http://msdn.microsoft.com/en-us/library/ms190309.aspx for further details.

Having said all that, SELECT @C * (@I * POWER(1 + @I, @N) / (POWER(1 + @I, @N) - 1 ));  should probably return a decimal value, since practically all of the inputs are decimal. Interestingly, you can force a correct-ish result by modifying that SELECT to:

DECLARE @N INT = 360;
DECLARE @I DECIMAL(38,26) = 0.15 * 30 / 360;
DECLARE @C DECIMAL(38,26) = 1000000;

SELECT @C *  @I *  POWER(1 + @I, @N)  / (POWER(1 + @I, @N) - 1);
SELECT @C * (@I *  POWER(1 + @I, @N)  / (POWER(1E0 + @I, @N) - 1));


This returns: I am at a loss to explain how that makes any difference, although clearly it does. My guess is the 1E0 (an explicit float) in the POWER( function forces SQL Server to make a different choice on output types for the POWER function. If my supposition is correct, that would indicate a possible bug in the POWER function, since the documentation states the first input to POWER() is a float, or a number that can be implicitly converted to a float.

Are you familiar with the SELECT .. INTO syntax? It's a useful trick for deconstructing situations like this because it creates a table on the fly with just the right data types for the given SELECT list.

You can break up your calculation into its constituent steps, applying SQL Servers' precedence rules as you go, to see how the definition changes. Here's how your first example would look:

use tempdb;

SELECT
0.15             as a,
0.15 * 30        as b,
0.15 * 30 / 360  as c
into #Step1;

select * from #Step1;

select
c.name,
t.name,
c.precision,
c.scale
from sys.columns as c
inner join sys.types as t
on t.system_type_id = c.system_type_id
where object_id = object_id('#Step1');

drop table #Step1;


This is the output:

name    name        precision   scale
a       numeric     2           2
b       numeric     5           2
c       numeric     9           6

• This doesn't always help though. Both (1+1) and 2 are of type int but this question has an example where they end up producing a differently typed result. – Martin Smith Sep 26 '14 at 7:34