SQL Server's "Wrong" Math

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A couple of weeks ago I decided to rebuild my recording studio by getting rid of my fabric backdrop and replacing it with a true wall instead. Doing this would allow me more flexibility when shooting, further improving my filming process efficiency.

To determine how much lumber I would need for building the new walls, I decided to write a SQL query to help with my framing calculations. I was building a 6 foot wall and wanted to put a stud every 16 inches. Easy enough to do the math on this:

SELECT (6*12)/16


The output of the query above was 4, indicating the number of studs I would need for one wall section.

What's interesting is that if we do this same equation in a calculator, we get a slightly different answer: 4.5.


And while I didn't end up framing my walls incorrectly, if I trusted the output of my query I would have had some incorrectly sized walls.

Is SQL Server Bad At Simple Math?

What happened? Well it all has to do with how SQL Server handles calculations.

While tweeting about my studio rebuild processKenneth Fisher from SQL Studies tweeted about what I would learn about SQL Server from rebuilding the studio.


Jokingly, I tweeted back the above SELECT (6*12)/16 example because it is funny (scary?) how SQL Server chops off the .5 if you don't understand what's going on.

When you perform calculations in SQL Server, it converts any expressions to the datatype that has the highest precedence. In the above example, since all of the numbers we are dealing with are integers, SQL Server keeps the final answer as an integer, apparently not caring what should have come after the decimal.

The quick and dirty way to solve this is to include a datatype in the equation that allows for decimals and has a higher precedence than integer. Basically, convert one of the integers to a numeric by adding .0 to any of the values:

SELECT (6*12)/16.0


This will then return the expected result.

Following up on Twitter, Andy Mallon mentions that you don't even need the 0, simply adding . will suffice:


SELECT * (6*12)/16.

Pat Phelan then took it a step further, saying you can use the e syntax if you want to get the same successful result but confuse your users:


SELECT * (6*12)/16e0

Out of all of these methods, I prefer adding the .0 because it is the least ambiguous. For calculations that matter however, I also like to throw a CAST around individual values or the entire equation to be certain that I am getting a result with the precision and scale that I expect instead of letting SQL Server automatically guess for me:

SELECT CAST((6*12)/16.0 AS NUMERIC (2,1))

Yes, it's a few extra characters, but the intent is clear.

Why Does All of This Matter?

Implicit conversions and datatype precedence are something that most people starting with SQL Server are not aware of until they discover that their results are "wrong". If your queries require precise answers, then you have to be precise and explicit in how you handle the data (otherwise you might build a studio wall incorrectly!)

For more information about all these types of conversions, check out Andy's post on the subject which has even more fun examples.

Data Type Precedence and Implicit Conversions

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SQL Server needs to make sure data types match when performing operations that involve multiple pieces of data.

When the data types do not match, SQL Server has to implicitly convert the data before performing any operations.

While most of the time these implicit conversions go unnoticed, they are important to understand since they can lead to unexpected results.

When 4.4/.44 Doesn't Equal 10

Let's start with this example:


Ignoring for a moment that our denominator is of type VARCHAR, if we do some quick mental math or use a calculator, we can see that the answer should be 10:


However, if we look at the result SQL Server returns, it's strangely 11:


To understand why this happens, we need to understand SQL Server's data type precedence logic.

Data Type Precedence

If we start with a simpler version of this example, we'll see SQL Server does in fact know how to perform math and return an answer of 10:

SELECT 4.4/.44


We can use the SQL_VARIANT_PROPERTY() function to see what data types SQL Server is assuming we are using in our calculation:



In this case, since the data types of both components are numeric, SQL Server doesn't have to break a sweat making any drastic conversions to give us our expected answer. If we instead give it something a little more challenging:



Here we still return the result of 10, however SQL Server had to do a little more work. We know from the previous example that 4.4 on its own is of type numeric, and in this example we are explicitly casting .44 to a float. SQL Server isn't able to perform the division operation directly on two different data types, so it refers to its data type precedence table to decide which value to convert to a matching datatype.

In the linked table above, the float data type appears higher on the list than numeric (synonym: decimal) data type. This causes SQL Server to convert our numeric 4.4 to a float before dividing.

While SQL Server is doing extra work behind the scenes that we didn't explicitly request, we can't be too angry with it since it still is giving us the "correct" answer.

"Incorrect" Conversions

Let's look at something a little more dastardly:


You might think this should also return 10 based on the previous example, but in fact it returns 9.090909:


While we are still witnessing implicit conversion here (the numeric gets converted to a float in order to allow SQL Server to perform the division), we are also experiencing a case of default data type precision and scale. If we use the SQL_VARIANT_PROPERTY() function again to not only reveal base type but also precision and scale, we'll notice that when we let SQL Server "guess" the scale, it correctly chooses 1 decimal place, while when we use the default scale associated with numeric we get 0:




What this really means is that the decimal portion of 4.4 is getting chopped off, leaving us with an equation of 4 / .44 = 11.

Putting Everything Together

So back to our original example that returns 11:


What exactly is going on here? Well for starters, data type precedence is forcing SQL Server to convert the VARCHAR .44 to a numeric. But a numeric with what precision and scale?



Since SQL Server determines that our numerator is NUMERIC(2,1), it converts the denominator to a NUMERIC(2,1) as well. This means instead of dividing by .44, we end up dividing by .4 which results in 11:

-- An explicit version of the same calculation


SQL Server Isn't Wrong

While it's easy to blame SQL Server for not knowing how to perform simple mathematical operations, it's us the developers who are to blame. SQL Server is a piece of software following rules for how to handle unclear situations that we input into it.

Having SQL Server throw an error instead of assuming data types and implicitly converting data on our behalf would make things less ambiguous, but it would also make simple operations a lot more tedious (looking at you SSIS).

In reality, the best solution is to accurately define data types from initial creation and to always be explicit with data types when the value of your computations matters.