ERFC Function (LibreOffice Calc)

• Computes the complementary error function
• Represents the upper tail of the Gaussian distribution
• Useful in probability, statistics, and engineering
• Handles any real input value

ERFC(x)

Arguments

• x:
  The value at which to evaluate the complementary error function.

[ \text{ERFC}(x) = 1 - \text{ERF}(x) ]

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

Standard complementary error function

=ERFC(1)
→ 0.15729921

Negative input

=ERFC(-1)
→ 1.84270079

Zero input

=ERFC(0)
→ 1

Large positive input

=ERFC(5)
→ very small number (close to 0)

Convert ERFC to normal distribution tail probability

=0.5 * ERFC(x / SQRT(2))

Compute probability between two z‑scores

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

Use ERFC in diffusion/heat‑transfer modeling

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

Use ERFC for smoothing/activation functions

=0.5 * ERFC((threshold - A1) / width)

Approximate survival probability in Gaussian models

=ERFC(z / SQRT(2)) / 2

ERFC returns a number between 0 and 2

Behavior details

• ERFC(∞) → 0
• ERFC(–∞) → 2
• ERFC is monotonic decreasing
• ERFC(x) = 1 – ERF(x)
• Inputs can be any real number

Invalid input → Err:502

• Use ERFC for Gaussian tail probabilities
• Use ERF for central cumulative probabilities
• Convert ERFC to normal CDF with 0.5 * ERFC(x/SQRT(2))
• Use ERFC in diffusion and heat‑transfer equations
• Document units and scaling in engineering models

• ERF — central error function
• NORMDIST / NORMSDIST — normal distribution functions
• EXP — exponential
• SQRT / PI — supporting math
• Custom integrals — advanced modeling

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