# ERFC

The `ERFC` 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.

## Usage

Use the `ERFC` formula with the syntax shown below, it has 1 required parameter:

Parameters:
1. 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 the `ERFC` 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 signal-to-noise ratio in communication systems

In communication systems, the complementary error function is used to calculate the signal-to-noise 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.

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.

You can learn more about the `ERFC` Google Sheets function on Google Support.