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ERFC Function

Excel 2007+

Summary

The ERFC function calculates the complementary error function, which represents the area under the Gaussian curve from a given value x to infinity. This statistical function is essential for probability calculations, confidence intervals, and advanced data analysis.

Syntax

ERFC(x)

Parameters

Parameter	Type	Required	Description
x	`Number`	Yes	The lower limit for the complementary error function integration

Using the ERFC Function

ERFC is primarily used in statistical applications requiring precise calculation of tail probabilities under the normal distribution. It's valuable for quality control, risk assessment, and scientific computing where complementary error probabilities are needed.

Common ERFC Examples

Basic ERFC Calculation

=ERFC(1)

Calculates the complementary error function for x=1, returning approximately 0.1573 which represents the tail probability beyond 1 standard deviation.

Statistical Application

=ERFC(1.96/2)

Calculates two-tailed probability for 95% confidence level (critical z-value), useful for hypothesis testing.

Frequently Asked Questions

ERFC(x) = 1 - ERF(x), where ERF is the error function representing area from 0 to x under the Gaussian curve.

Use ERFC when you need tail probabilities (from x to infinity) rather than cumulative probabilities (0 to x).

Common Errors and Solutions

#VALUE!

Cause: x argument is non-numeric

Solution: Ensure x contains a valid number

Notes

ERFC(x) approaches 0 as x increases (tail gets smaller)
ERFC(0) = 1 (entire area under curve)
Precision maintained for large x values
Related to Q-function in communications engineering

Compatibility

Available in: Excel 2007, Excel 2010, Excel 2013, Excel 2016, Excel 2019, Excel 2021, Microsoft 365

Not available in: Excel 2003 and earlier

Content last reviewed: December 9, 2025
Update frequency: As needed
Excel versions tested: Excel 2007+