ERF Function (LibreOffice Calc)

• 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

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.

[ \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) ]

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

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)))

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

• 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

• 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.