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SQL Server Rounding Functions - Round, Ceiling and Floor

MSSQLTips author Jeremy Kadlec By:   |   Read Comments (15)   |   Related Tips: More > Functions - System
Problem

I saw your recent tip on Calculating Mathematical Values in SQL Server and have some related issues as I try to round values in my application. My users and me have a difference of opinion on some of the calculations in our reporting applications. All of the code is in T-SQL, but I think the reporting issues are related to data types and rounding down or rounding up rules. Do you have any insight into these issues? I would like to see some examples with a variety of coding options.

Solution

Rounding can become misunderstood if the underlying data types and rounding functions are not understood. Depending on the data type (integer, float, decimal, etc.) the rounded value can be different. In addition, depending on the SQL Server rounding function (ROUND(), CEILING(), FLOOR()) used in the calculation the values can differ as well. As such, it is important to find out the user rounding requirements then translate those requirements into the appropriate T-SQL command.

From a definition perspective, let's start here:

  • ROUND - Rounds a positive or negative value to a specific length and accepts three values:
    • Value to round
      • Positive or negative number
      • This data type can be an int (tiny, small, big), decimal, numeric, money or smallmoney
    • Precision when rounding
      • Positive number rounds on the right side of the decimal point
      • Negative number rounds on the left side of the decimal point
    • Truncation of the value to round occurs when this value is not 0 or not included
  • CEILING - Evaluates the value on the right side of the decimal and returns the smallest integer greater than, or equal to, the specified numeric expression and accepts one value:
    • Value to round
  • FLOOR - Evaluates the value on the right side of the decimal and returns the largest integer less than or equal to the specified numeric expression and accepts one value:
    • Value to round

Let's walk through each function with a few different data types to see the results.

SQL Server ROUND, CEILING and FLOOR Examples for Integer Data Types

Example 1a - In this first example let's just look at rounding a positive integer for the precision value of 1 yields all three rounding functions returning the same value. In this example we are using a variable with the functions and check out the result commented out on the right of the function.

DECLARE @value int
SET @value = 6

SELECT ROUND(@value, 1)  -- 6 - No rounding with no digits right of the decimal point
SELECT CEILING(@value)   -- 6 - Smallest integer value
SELECT FLOOR(@value)     -- 6 - Largest integer value 

Example 1b - Since the CEILING AND FLOOR functions do not have any optional values, let's test some options with the ROUND function. In this example, let's see the impacts of a negative number as the precision as well as the specifying additional positions that exceed the value to round. Check out these results with the result commented out on the right of the function.

DECLARE @value int
SET @value = 6

SELECT ROUND(@value, 1)  -- 6  - No rounding with no digits right of the decimal point
SELECT ROUND(@value, -1) -- 10 - Rounding up with digits on the left of the decimal point
SELECT ROUND(@value, 2)  -- 6  - No rounding with no digits right of the decimal point 
SELECT ROUND(@value, -2) -- 0  - Insufficient number of digits
SELECT ROUND(@value, 3)  -- 6  - No rounding with no digits right of the decimal point
SELECT ROUND(@value, -3) -- 0  - Insufficient number of digits

Example 1c - Let's expand the digits in this example with the ROUND function and see the impacts with the result commented out on the right of the function.

SELECT ROUND(444,  1) -- 444  - No rounding with no digits right of the decimal point
SELECT ROUND(444, -1) -- 440  - Rounding down
SELECT ROUND(444,  2) -- 444  - No rounding with no digits right of the decimal point
SELECT ROUND(444, -2) -- 400  - Rounding down
SELECT ROUND(444,  3) -- 444  - No rounding with no digits right of the decimal point
SELECT ROUND(444, -3) -- 0    - Insufficient number of digits
SELECT ROUND(444,  4) -- 444  - No rounding with no digits right of the decimal point
SELECT ROUND(444, -4) -- 0    - Insufficient number of digits

SELECT ROUND(555,  1) -- 555  - No rounding with no digits right of the decimal point
SELECT ROUND(555, -1) -- 560  - Rounding up
SELECT ROUND(555,  2) -- 555  - No rounding with no digits right of the decimal point
SELECT ROUND(555, -2) -- 600  - Rounding up
SELECT ROUND(555,  3) -- 555  - No rounding with no digits right of the decimal point
SELECT ROUND(555, -3) -- 1000 - Rounding up
SELECT ROUND(555,  4) -- 555  - No rounding with no digits right of the decimal point
SELECT ROUND(555, -4) -- 0    - Insufficient number of digits

SELECT ROUND(666,  1) -- 666  - No rounding with no digits right of the decimal point
SELECT ROUND(666, -1) -- 670  - Rounding up
SELECT ROUND(666,  2) -- 666  - No rounding with no digits right of the decimal point
SELECT ROUND(666, -2) -- 700  - Rounding up
SELECT ROUND(666,  3) -- 666  - No rounding with no digits right of the decimal point
SELECT ROUND(666, -3) -- 1000 - Rounding up
SELECT ROUND(666,  4) -- 666  - No rounding with no digits right of the decimal point
SELECT ROUND(666, -4) -- 0    - Insufficient number of digits

Example 1d - Let's round a negative integer and see the impacts with the result commented out on the right of the function.

SELECT ROUND(-444, -1) -- -440  - Rounding down
SELECT ROUND(-444, -2) -- -400  - Rounding down

SELECT ROUND(-555, -1) -- -560  - Rounding up
SELECT ROUND(-555, -2) -- -600  - Rounding up

SELECT ROUND(-666, -1) -- -670  - Rounding up
SELECT ROUND(-666, -2) -- -700  - Rounding up

Example 1e - In our last example of this section, do not get fooled by your data types and actual values. In this example, the @value parameter is declared as an INT, but the value passed looks more like a decimal. Under these circumstances, let's see how the values are evaluated.

DECLARE @value int
SET @value = 16.999999

SELECT ROUND(@value,  1) -- 16 - No rounding with no digits right of the decimal point i.e. int
SELECT ROUND(@value, -1) -- 20 - Round up
SELECT CEILING(@value)   -- 16 - Smallest integer value
SELECT FLOOR(@value)     -- 16 - Largest integer value 
SELECT @value            -- 16 - Shows how the @value is evaluated based on the int data type 

SQL Server ROUND, CEILING and FLOOR Examples for Decimal, Numeric and Float Data Types

Example 2a - With a decimal data type and the ROUND function with various length parameters (i.e. 1, 2 or 3) yields different final values in our example. The 5 in the second digit to the right of the decimal point is significant when the length parameter is 1 when rounding the value. In addition, with the decimal data type the CEILING and FLOOR functions take the decimal places into consideration for differing values as well.

DECLARE @value decimal(10,2)
SET @value = 11.05

SELECT ROUND(@value, 1)  -- 11.10
SELECT ROUND(@value, -1) -- 10.00 

SELECT ROUND(@value, 2)  -- 11.05 
SELECT ROUND(@value, -2) -- 0.00 

SELECT ROUND(@value, 3)  -- 11.05
SELECT ROUND(@value, -3) -- 0.00

SELECT CEILING(@value)   -- 12 
SELECT FLOOR(@value)     -- 11 
GO

Example 2b - Here is a quick example of using the numeric data type with the ROUND function. This follows much of the same behavior as the decimal data type.

DECLARE @value numeric(10,10)
SET @value = .5432167890
SELECT ROUND(@value, 1)  -- 0.5000000000 
SELECT ROUND(@value, 2)  -- 0.5400000000
SELECT ROUND(@value, 3)  -- 0.5430000000
SELECT ROUND(@value, 4)  -- 0.5432000000
SELECT ROUND(@value, 5)  -- 0.5432200000
SELECT ROUND(@value, 6)  -- 0.5432170000
SELECT ROUND(@value, 7)  -- 0.5432168000
SELECT ROUND(@value, 8)  -- 0.5432167900
SELECT ROUND(@value, 9)  -- 0.5432167890
SELECT ROUND(@value, 10) -- 0.5432167890
SELECT CEILING(@value)   -- 1
SELECT FLOOR(@value)     -- 0

Example 2c - In the final example, with a float data type you can see the same type of behavior as was the case with the decimal and numeric examples above with the ROUND, CEILING and FLOOR functions.

DECLARE @value float(10)
SET @value = .1234567890
SELECT ROUND(@value, 1)  -- 0.1
SELECT ROUND(@value, 2)  -- 0.12
SELECT ROUND(@value, 3)  -- 0.123
SELECT ROUND(@value, 4)  -- 0.1235
SELECT ROUND(@value, 5)  -- 0.12346
SELECT ROUND(@value, 6)  -- 0.123457
SELECT ROUND(@value, 7)  -- 0.1234568
SELECT ROUND(@value, 8)  -- 0.12345679
SELECT ROUND(@value, 9)  -- 0.123456791
SELECT ROUND(@value, 10) -- 0.123456791
SELECT CEILING(@value)   -- 1
SELECT FLOOR(@value)     -- 0
Next Steps


Last Update: 12/31/2013


About the author
MSSQLTips author Jeremy Kadlec
Jeremy Kadlec is the CTO @ Edgewood Solutions, co-founder of MSSQLTips.com, Baltimore SSUG co-leader and SQL Server MVP since 2009.

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Comments and Feedback:
Thursday, September 20, 2012 - 1:06:06 PM - Gene Wirchenko Read The Tip
Integers can be rounded. round() will take a negative second argument. e.g. declare @SomeInt int=65536 select ROUND(65536,-3) // Result is 66000.

Thursday, October 18, 2012 - 5:10:21 PM - Sandeep Read The Tip

Thank U.


Wednesday, November 14, 2012 - 1:43:12 AM - Sankar Read The Tip

We are using numeric datatype size as 29,9 In this I am facing problem in rounding off any body can help

Ex:

1.

declare @NumberToBeRounded numeric(29,9)
SET @NumberToBeRounded=182.354838456
select @NumberToBeRounded

Expected result: 182.360

getting output: 182.350 ( rounding to 0.01)

 


Wednesday, November 14, 2012 - 8:43:43 AM - Jeremy Kadlec Read The Tip

Sankar,

If I understand your question correctly, try this code:

declare @NumberToBeRounded numeric(29,3)
SET @NumberToBeRounded=182.354838456
-- select @NumberToBeRounded
SELECT ROUND(@NumberToBeRounded, 2)
 
-- Expected result: 182.360
 
-- getting output: 182.350 ( rounding to 0.01)

 

HTH.

Thank you,
Jeremy Kadlec


Thursday, November 15, 2012 - 1:01:59 AM - Sankar Read The Tip

Thanks Jeremy for your response i tried that and found to be working..


Thursday, November 15, 2012 - 1:07:48 AM - Sankar Read The Tip

Instead of using cursors is there any other medthod is available. becoz cursor taking more time to fecth records when huge data


Monday, December 31, 2012 - 6:55:32 PM - Jeremy Kadlec Read The Tip

Sankar,

Sorry for my delayed response.  Do you just need to write a SELECT or UPDATE statement?  What are you trying to do?

Have you checked out the following:

SELECT Tutorial - http://www.mssqltips.com/sqlservertutorial/10/select-command-for-sql-server/

HTH.

Thank you,
Jeremy Kadlec
Community Co-Leader


Monday, December 31, 2012 - 6:56:38 PM - Jeremy Kadlec Read The Tip

Everyone,

This tip has been updated with additional examples and explanations.

Thank you,
Jeremy Kadlec


Monday, February 04, 2013 - 11:45:05 AM - ClaudioRound Read The Tip

why this rounding does not work?

DECLARE @value float

SET @value = 172.765

SELECT ROUND(@value, 2) 

 

 


Thursday, February 07, 2013 - 10:46:14 PM - Jeremy Kadlec Read The Tip

ClaudioRound,

FLOAT and REAL data types are approximate values.  I would move to a decimal data type based on the example you provided:

DECLARE @value decimal(38,2)
 
SET @value = 172.765
 
SELECT ROUND(@value, 2)
-- Result - 172.77

HTH.

Thank you,
Jeremy Kadlec
Community Co-Leader


Friday, May 24, 2013 - 2:22:50 AM - shri Read The Tip

Hello everyone

How to get last digit to the left of decimal point in sql query?

 


Tuesday, May 28, 2013 - 10:25:06 PM - Jeremy Kadlec Read The Tip

Shri,

Can you post some sample data and the expected results?

Thank you,
Jeremy Kadlec
Community Co-Leader


Wednesday, June 12, 2013 - 1:56:53 PM - Dave Read The Tip

In Numerical Control programming this is done all the time by using scaling and scaling factors. The scaling factor in this case is 10.

DECLARE @TestFloat FLOAT
SET @TestFloat = 123.456
SELECT @TestFloat, FLOOR(@TestFloat), FLOOR(@TestFloat) - (FLOOR(@TestFloat / 10.) * 10)

 


Monday, August 12, 2013 - 5:00:56 PM - Scott Coleman Read The Tip

In answer to ClaudioRound's question "why this rounding does not work" (for 172.765).

The code "DECLARE @value FLOAT = 172.765" stores the binary number 10101100.110000111101011100001010001111010111000010100,  which is about 172.764999999999986.  172.76 is the correct rounded value for something less than 172.765.

Subtracting 128 from this value drops the two leftmost bits, so it gains two more fractional bits resulting in 101100.11000011110101110000101000111101011100001010010.  (The mantissa is always 53 bits long in a float.)  This is about 44.76500000000000057, so even though it has the same fractional digits the value of "ROUND(44.765, 2)" is 44.77.

Another fun fact is that "ROUND(CAST(172.7650000000000160090000000000000099 AS FLOAT), 2)" returns 172.76, but if you add a trailing 0 then "ROUND(CAST(172.76500000000001600900000000000000990 AS FLOAT), 2)" returns 172.77.  Don't ask me why.

The moral of the story is that if you really care about exact fractional values then don't use FLOAT or REAL.  Even casting it to DECIMAL before ROUNDING may help.

DECLARE @value FLOAT = 172.765
PRINT ROUND(CAST(@value AS DECIMAL(10,4)), 2) 
172.77

Monday, November 04, 2013 - 5:27:02 PM - Gadi Read The Tip

Technically, there aren't an "insufficient number of digits" from example 1b.  When rounding to the nearest 100 (or 1,000), 6 is just closer to zero.  Same thing in 1c; 444 is closer to zero than to 1,000 or 10,000.

Good tip and explanation.  This is pretty logical overall, but sometimes you really need to stop and think it through.  These examples are a great help with that.



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