How to Use the ERF Function in Google Sheets

The ERF function in Google Sheets calculates for the Gauss error function of a value or an interval of values.

In other words, it returns the error function integrated between lower and upper limits or even just a lower limit. It’s a statistical tool that you encounter when integrating the normal distribution. The number generated represents how well your model fits the data. A lower number means you have less error. 

ERF is defined as follows:

ERF Formula

For a random variable normally distributed with a mean of 0 and a variance of 1/√2, ERF(x) describes the probability of the variable falling in the given range.

This is helpful for various complex problem-solving scenarios like determining how much of a nominal 100g is an outlier. In particular, if you’re selling milk with 100g per container and you know that the standard deviation is 1, you should be able to find out how many of the items are [99g, 101g].

Now, let’s learn how to write the ERF function in Google Sheets.



The Anatomy of the ERF Function in Google Sheets

The syntax (the way we write) of the ERF function goes as follows:

=ERF(lower_bound, [upper_bound])

Let’s dissect this thing and understand what each of these terms means:

  • = the equal sign is just how we start any function in Google Sheets.
  • ERF () is our Gauss error function.
  • lower_bound is the lower boundary for the integral.
  • [upper_bound] is the upper boundary for the integral. Note that you can omit this parameter from the function. This would assume that the integration is between 0 and the lower_bound.

Note that you will get the #VALUE! error value if your lower_bound and upper_bound are non-numeric.



Real Example of Using the ERF Function in Google Sheets

Take a look at some numbers I’m presenting to see how an ERT function will look like in Google Sheets. 

ERF Function in Google Sheets Table

In the first table, we see that only the lower limit is used in the ERF function. As mentioned, this assumes 0 as its pair. Meanwhile, in the second table, the upper limit is given.

Besides the negative and positive signs, the result should be the same for (-1,0) and (0,1) since their distance on a distribution table is the same.

You can make a copy of the spreadsheet I made using the link attached below:



At this point, I’ll show you how you can do this yourself with comprehensive steps.



How to Use the ERF Function in Google Sheets 

1. First, select the cell where you wish to put the result of your ERF function. In this case, that’s C3.

Select Cell

2. Next, enter the equal sign ‘=’ to begin the function. Then, follow it with the name of the function, which is ‘ERF’ (or ‘ERF’, both should work). An auto-suggest box should appear. There, you can click on the ERT option or type an open parenthesis ‘(‘.  You can read the pop-out with more information about the function.

ERF Function in Google Sheets

3. Now, enter the number that serves as your lower_bound. In this case, we select the cell where the data is entered prior, which is A3

Select Lower Limit

4. At this point, we can either select an upper limit or leave none to use the default pair of 0. To do the latter, simply enter a close parenthesis ‘)’ and select Enter on your keyboard. 

ERF Function in Google Sheets No Upper Limit

5. To add an upper limit, separate the parameter with a comma (,). Then, enter the number you intend. In this case, select the cell where the data is entered prior, which is B3. Finally, close the function with a close parenthesis ‘)’ and select Enter on your keyboard. 

ERF Function in Google Sheets with Upper Limit

That’s it! You’ve just learned how to use the ERF function in Google Sheets.


Frequently Asked Questions

What is ERFC?

ERFC stands for ‘complementary error function’ and gives out the value of 1.0 -erf(x). Its syntax is “ERFC(x)” where x is the number to calculate the complementary Gauss error function. For larger values of x, it is useful in place of the ERF function.

How do I use ERF in Excel?

ERF is used the same in Google Sheets and Excel. With that, simply follow the instructions in this article to use ERF in Excel. Note that in Excel 2007, you will get the #NUM! error value if you enter a negative value in the parameters. Calculating this function for both positive and negative ranges has been possible since Excel 2010. 

What is ERF in Heat Transfer?

The ERF function is commonly used in engineering, particularly in heat conduction problems. The formula is as follows:

ERF Formula

Here, erf(x) is the Gauss error function, t is time, and x is a complex number.


Make sure to explore the other Google Sheets functions available that can help you with mathematics and data manipulation. Also, comment down below if you have any more inquiries and if you’d like to give suggestions on what topic we should write about next. Make sure to subscribe to stay updated!

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