# 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.

## Usage

Use the `ERF` formula with the syntax shown below, it has 1 required parameter and 1 optional parameter:

Parameters:
1. lower_bound (required):
The lower bound of the integral used to calculate the error function.
2. upper_bound (optional):
The upper bound of the integral used to calculate the error function. If not provided, the upper bound is assumed to be infinity.

## Examples

Here are a few example use cases that explain how to use the `ERF` formula in Google Sheets.

### Calculating the probability of a normal variable falling between two values

By using the `ERF` function, you can calculate the probability of a normal variable with a mean of zero and a standard deviation of one falling between two values.

### Calculating the cumulative distribution function

The `ERF` function can be used to calculate the cumulative distribution function of a normal variable with a mean of zero and a standard deviation of one.

### Calculating the complementary error function

By subtracting the result of the `ERF` function from one, you can calculate the complementary error function.

## Common Mistakes

`ERF` not working? Here are some common mistakes people make when using the `ERF` Google Sheets Formula:

### Missing or incorrect lower bound

One common mistake when using the ERF formula is to either forget to include the lower bound or to include an incorrect value for the lower bound. This can result in an inaccurate or incorrect result. Make sure to double check that the lower bound is included and accurate.

### Missing or incorrect upper bound

Another common mistake when using the ERF formula is to either forget to include the upper bound or to include an incorrect value for the upper bound. This can result in an inaccurate or incorrect result. Make sure to double check that the upper bound is included and accurate.

### Incorrect order of bounds

It's important to make sure that the lower bound is listed before the upper bound in the formula. If the order of the bounds is reversed, the result will be inaccurate or incorrect.

### Incorrect data type

The ERF formula requires numeric input for both the lower and upper bounds. If non-numeric data is included, an error will occur. Make sure to include only numeric data.

### Missing or incorrect arguments

If the ERF formula is missing one or both of its required arguments, or if the argument syntax is incorrect, an error will occur. Double check the formula syntax and make sure that both the lower and upper bounds are included.

The following functions are similar to `ERF` or are often used with it in a formula:

• `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.

• `NORMDIST`

The `NORMDIST` function in Google Sheets calculates the normal distribution for a specified value, mean, and standard deviation. It returns the probability of a value occurring within a specified range of a normal distribution. It is commonly used in statistics, finance, and science to analyze data and make predictions.

• `NORMINV`

The `NORMINV` function returns the inverse of the normal cumulative distribution for a specified value, mean, and standard deviation. It is commonly used in statistics to find the value at which a given percentage of observations lie below that value.

• `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.

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