# ERF.PRECISE

The `ERF.PRECISE` function returns the error function integrated between the specified lower bound and upper bound.

The error function is used to calculate the probability of a value falling within a certain range of values.

## Usage

Use the `ERF.PRECISE` 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 integration. Must be a numeric value.
2. upper_bound (optional):
The upper bound of the integration. If omitted, the upper bound is assumed to be 0. Must be a numeric value.

## Examples

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

### Calculate probability of a value within a range

Using `ERF.PRECISE`, you can calculate the probability of a value falling within a certain range of values.

### Calculate standard normal distribution

`ERF.PRECISE` can be used to calculate the standard normal distribution, where the lower bound is -infinity and the upper bound is the z-score.

### Calculate complementary error function

By subtracting the `ERF.PRECISE` result from 1, you can calculate the complementary error function.

## Common Mistakes

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

### Using invalid arguments

Make sure the lower_bound is less than the upper_bound and that both arguments are numeric values.

### Omitting arguments

Both lower_bound and upper_bound are required arguments. Make sure to include them in the formula.

### Using non-numeric values

The arguments must be numeric values. Check that the cells or values being used are formatted as numbers.

### Incorrectly ordering arguments

The first argument should be the lower_bound and the second argument should be the upper_bound. Double check that the arguments are in the correct order.

### Confusing ERF with ERF.PRECISE

ERF is a similar function but it returns an approximate result. Make sure you're using ERF.PRECISE if you need an exact result.

The following functions are similar to `ERF.PRECISE` 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.

• `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.

• `NORM.S.DIST`

The NORM.S.DIST function returns the standard normal cumulative distribution function. It calculates the probability that a random variable with a standard normal distribution is less than or equal to x. This function is commonly used in statistical analysis and hypothesis testing.

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