SQL Server Rounding Functions - Round, Ceiling and Floor

By: Jeremy Kadlec   |   Read Comments (13)   |   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

• Rounding values can cause confusion with various data types, so be sure to understand the user requirements then translate them to the correct data types and rounding functions.
• Check out these related tips on MSSQLTips:
  • Calculating Mathematical Values in SQL Server
  • SQL Server Text Data Manipulation
  • Date/Time Conversions Using SQL Server
  • SQL Server T-SQL Aggregate Functions
  • Daylight Savings Time Functions in SQL Server
  • SQL Server System Function Tips
  • SQL Server User Defined Function Tips

About the author

Jeremy is the CTO @ Edgewood Solutions, co-founder of MSSQLTips.com and SQL Server MVP since 2009.

View all my tips

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Comments and Feedback:

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

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