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ERF Function (LibreOffice Calc)

Statistical Intermediate LibreOffice Calc Introduction not established

The ERF function returns the Gaussian error function, used in probability, statistics, and engineering for modeling normal distributions and cumulative error.

Verification status: Consult the documentation, examples and any stated test scope below. How formula examples are checked

Availability and version history

  • Introduced: Documented by LibreOffice 26.8.1.1; original introduction not established.
  • Availability: Supported in LibreOffice 26.8.1.1, verified against its function registry. This identifies a supported release, not a final working version.
  • Scope: Desktop Calc, using the English function name. Availability in other spreadsheet applications is separate.
  • Checked: 2026-10-14 — function reference; versioned support. Documentation/source check; not a new native test. Existing example-specific test claims below retain their stated scope.
The **ERF** function returns the **Gaussian error function**, a key mathematical function used in probability, statistics, engineering, and diffusion modeling. It represents the integral of the normal distribution curve.

What the ERF Function Does

  • Computes the error function
  • Used in normal distribution, probability, and signal processing
  • Supports single‑limit and two‑limit forms
  • Useful in diffusion equations, heat transfer, and cumulative probability models

Syntax

ERF(lower_limit; [upper_limit])

Arguments

  • lower_limit:
    The lower bound of the integration.

  • upper_limit (optional):
    The upper bound.
    If omitted, ERF(lower_limit) is computed from 0 → lower_limit.

Mathematical Definition

[ \text{ERF}(x) = \frac{2}{\sqrt{\pi}} \int_0^x e^{-t^2} , dt ]

Two‑limit form:

[ \text{ERF}(a, b) = \text{ERF}(b) - \text{ERF}(a) ]

Basic Examples

Standard error function

=ERF(1)
→ 0.84270079

Negative input

=ERF(-1)
→ -0.84270079

Two‑limit form

=ERF(1; 2)
→ ERF(2) - ERF(1)

Zero input

=ERF(0)
→ 0

Advanced Examples

Convert ERF to normal CDF

=0.5 * (1 + ERF(x / SQRT(2)))

Compute probability between two z‑scores

=0.5 * (ERF(b / SQRT(2)) - ERF(a / SQRT(2)))

Use ERF in diffusion/heat‑transfer modeling

=ERF(x / (2 * SQRT(D * t)))

Use ERF for smoothing functions

=0.5 * (1 + ERF((A1 - threshold) / width))

Two‑limit integration for probability density

=ERF(A1; A2)

Approximate tail probability

=1 - 0.5 * (1 + ERF(x / SQRT(2)))

Edge Cases and Behavior Details

ERF returns a number between –1 and 1

Behavior details

  • ERF(∞) → 1
  • ERF(–∞) → –1
  • ERF is odd: ERF(–x) = –ERF(x)
  • Two‑limit form is simply ERF(upper) – ERF(lower)
  • Inputs can be any real number

Invalid input → Err:502

Common Errors and Fixes

Err:502 — Invalid argument

Cause:

  • Non‑numeric input
  • Invalid references

Fix:

  • Wrap with VALUE()
  • Validate numeric ranges

Unexpected negative values

Cause:

  • Negative input produces negative ERF

Fix:

  • Confirm sign of input

Best Practices

  • Use ERF for Gaussian‑based modeling
  • Use ERFC for complementary probability
  • Convert ERF to normal CDF using 0.5*(1+ERF(x/SQRT(2)))
  • Use two‑limit form for interval probabilities
  • Document units when used in engineering models
ERF is the backbone of Gaussian probability and diffusion modeling — mastering it unlocks advanced statistical and engineering workflows.
  • ERFC — complementary error function
  • NORMDIST / NORMSDIST — normal distribution functions
  • EXP — exponential function
  • SQRT / PI — supporting math functions
  • Custom integrals — advanced modeling

By mastering ERF, you can build precise statistical, probabilistic, and engineering models in LibreOffice Calc.