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Excel ERF Function

Author: Zhoumandy Last Modified: 2022-05-30

The ERF function returns the error function integrated between lower_limit and upper_limit.

erf function 5


Syntax

=ERF (lower_limit, [upper_limit])


Arguments

  • Lower_limit (required): The lower limit of integration.
  • Upper_limit (optional): The upper limit of integration. If omitted, the integration between 0 and the lower_limit will be returned.

Return value

The ERF function returns a numeric value.


Function notes

  1. The ERF function has been improved in Excel 2010 so that it can calculate negative values.
    In Excel 2007, the ERF function only accepts positive values. If any of the supplied arguments are negative values, the ERF function will return the #NUM! error value.
  2. The #VALUE! error value occurs if any of the supplied arguments are non-numeric.
  3. When the upper_limit is omitted, ERF integrates between zero (as the lower_limit value) and the lower_limit (as the upper_limit value). Therefore, when the lower_limit is positive, ERF returns a positive result. Vice versa.
    What's more, when the lower_limit is greater than the upper_limit, ERF returns a negative result. Vice versa.
  4. The resulting range returned by the ERF function is between -1 and 1.
  5. The equation of the Error function is:

    erf function 2


Examples

Example One: Result Without Upper Limit

In this case, we want to calculate the Error Function when the upper_limit argument is omitted. That means the ERF function integrates between zero and the lower_limit. Please do as follows.

1. Please copy the formula below into cell E5, then press the Enter key to get the result.

=ERF (B5)

2.Select this result cell and drag its autofill handle down to get the rest of the results.

erf function 3

Notes:

  1. As the above screenshot shows, when the only argument lower_limit is negative, the returned result is also negative. Vice versa.
  2. When the only argument lower_limit is zero (0), ERF returns zero (0) as the result.
  3. The argument in each of the above formulas is supplied as a cell reference containing a numeric value.
  4. We can also directly input a value in the formula. For example, the formula in cell E5 can be changed to:

    =ERF (-1)

Example Two: Result with Upper Limit

In this case, we want to calculate the Error Function when both the lower_limit and the upper_limit arguments are provided. Please do as follows.

1. Please copy the formula below into cell F5, then press the Enter key to get the result.

=ERF (B5, C5)

2.Select this result cell and drag its autofill handle down to get the rest of the results.

erf function 4

Notes:

  1. As the above screenshot shows, when the upper_limit is greater than the lower_limit, ERF returns a positive result. Vice versa.
  2. The arguments in each of the above formulas are supplied as cell references containing numeric values.
  3. We can also directly input values in the formula. For example, the formula in cell F5 can be changed to:

    =ERF (-1, 0)

Relative Functions:

  • Excel EVEN Function
    The EVEN function rounds numbers away from zero to the nearest even integer.

  • Excel EXP Function
    The EXP function returns the result of the constant e raised to the nth power.


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