ERFC
TheERFC
function calculates the complementary error function of a given value, which is defined as 1 minus the error function. The error function represents the probability of a value being within a certain range of a normally distributed random variable. The complementary error function is often used in statistics and engineering applications to model random variables and calculate probabilities.
 How to use
ERFC
formula?  Examples of using
ERFC
formula ERFC
formula not working? Similar formulas to
ERFC
Usage
Use the ERFC
formula with the syntax shown below, it has 1 required parameter:
 z (required):
The value at which to evaluate the complementary error function. Must be a numeric value or a reference to a cell containing a numeric value.
Examples
Here are a few example use cases that explain how to use theERFC
formula in Google Sheets.
Calculate probability of a normally distributed variable
By using ERFC
, you can calculate the probability of a normally distributed variable being greater than a certain value or within a certain range. For example, you can use this function to calculate the probability of a stock price being above a certain threshold or between two values.
Calculate signaltonoise ratio in communication systems
In communication systems, the complementary error function is used to calculate the signaltonoise ratio (SNR) of a received signal. The SNR is a measure of the quality of a signal and is defined as the ratio of the signal power to the noise power. By using ERFC
, you can calculate the probability of a received signal being corrupted by noise and use this information to estimate the SNR.
Calculate probability of error in digital communication systems
In digital communication systems, the complementary error function is used to calculate the probability of error in the transmission of data over a noisy channel. By using ERFC
, you can estimate the probability of a bit error occurring in a digital communication system and use this information to optimize the system parameters.
Common Mistakes
ERFC
not working? Here are some common mistakes people make when using the ERFC
Google Sheets Formula:
Incorrect argument type
One common mistake is providing an argument that is not a number or a range of numbers. This will result in an error. Make sure to provide a valid numerical argument.
Incorrect number of arguments
Another common mistake is providing too many or too few arguments. ERFC requires only one argument, so make sure to provide exactly one argument.
Incorrect range reference
If you are providing a range of numbers as an argument, make sure to reference the correct range. An incorrect range reference will result in an error.
Incorrect function name
Make sure to spell the function name correctly. Misspelling the function name will result in an error.
Undefined function
If you are receiving an 'Unknown function' error, make sure that the ERFC function is available in your version of Google Sheets.
Related Formulas
The following functions are similar to ERFC
or are often used with it in a formula:

ERF
The
ERF
function calculates the error function of a given value. The error function returns the probability of a normal variable with a mean of zero and a standard deviation of one falling between two values. This function is commonly used in statistics and engineering applications. 
NORMSDIST
The
NORMSDIST
function returns the area under a normal distribution curve to the left of a specified value. This function is commonly used in statistics to calculate probabilities. 
NORMSINV
The
NORMSINV
function calculates the inverse of the standard normal cumulative distribution for a specified value of x. It is commonly used in statistical analysis to transform data from a normal distribution to a standard normal distribution with a mean of 0 and a standard deviation of 1.
Learn More
You can learn more about the ERFC
Google Sheets function on Google Support.