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ERF Function
Summary
The Excel ERF function calculates the error function, which is the integral of the Gaussian distribution between specified limits. This statistical function is essential for probability calculations, confidence intervals, and scientific computations involving normal distributions.
Syntax
ERF(lower_limit,[upper_limit])Parameters
| Parameter | Type | Required | Description |
|---|---|---|---|
| lower_limit | Number |
Yes | Required lower bound for ERF integration |
| upper_limit | Number |
No | Optional upper bound. Omits to integrate from 0 |
Using the ERF Function
ERF is a key statistical function for calculating areas under the normal distribution curve between two points. Use it for probability density calculations, statistical modeling, quality control analysis, and scientific research involving Gaussian processes.
Common ERF Examples
Single Limit Integration
=ERF(0.745)Calculates error function from 0 to 0.745, returning approximately 0.7079 - represents area under Gaussian curve.
Two Limit Integration
=ERF(1,0.5)Calculates error function integral between 0.5 and 1.
Standard Normal Probability
=ERF(1.96/1.414213562)Calculates probability for 95% confidence interval (two-tailed).
Frequently Asked Questions
Common Errors and Solutions
#VALUE!
Cause: lower_limit or upper_limit contains non-numeric values
Solution: Ensure both arguments are valid numbers
#NUM!
Cause: Arguments exceed calculation limits
Solution: Use values within ERF's computational range (±5 is typically safe)
Notes
- ERF approaches 1 as lower_limit approaches infinity
- ERF(0) always equals 0
- Use ERFC for complementary error function (1-ERF)
- Available since Excel 2007
- Essential for normal distribution CDF calculations
Compatibility
Available in: Excel 2007, Excel 2010, Excel 2013, Excel 2016, Excel 2019, Excel 2021, Excel 365, Excel for Mac, Excel Online
Not available in: Excel 2003, Excel XP, Excel 2000
Content last reviewed: December 9, 2025
Update frequency: As needed
Excel versions tested: Excel 2007+