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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:

=ERFC(z)
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.

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.