Calculadora da Função de Erro (erf)
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
Formula
erf(x) = (2/√π) ∫₀ˣ e^(−t²) dt
About this calculator
The Error Function Calculator (erf) approximates erf(x) for any real number x using the Abramowitz-Stegun formula, which provides an approximation with a maximum error of 1.5×10⁻⁷, ensuring high precision for scientific and engineering applications. The error function is defined as the integral from 0 to x of e^(−t²) dt, multiplied by 2/√π. It is widely used in statistics, probability theory, signal processing, and differential equations.
To use the calculator, simply enter the value of x in the input field. The result is displayed immediately, without needing to click any buttons, thanks to real-time calculation. The tool also shows the complementary function erfc(x) = 1 - erf(x), useful for tail probability problems. The calculation is done via JavaScript in the browser, with no data sent to servers.
Common use cases include: calculating probabilities in normal distributions (erf is related to the cumulative distribution function), modeling diffusion processes in physics, and solving heat or wave problems. Caution: the Abramowitz-Stegun formula is valid for all real x, but for very large values (|x| > 6) the result may be 1 or -1 with limited precision. Always verify that the approximation meets the required accuracy for your application.
Frequently asked questions
What is the precision of the calculator?
The precision is approximately 1.5×10⁻⁷ for all x values, according to the Abramowitz-Stegun formula.
Can I use the calculator for negative x?
Yes, the error function is odd: erf(-x) = -erf(x). Just enter the negative value.
What is erfc?
erfc(x) is the complementary error function, defined as 1 - erf(x). It is useful for tail probability calculations.
Does the calculator work offline?
Yes, after the page loads, the calculation is done locally in your browser, no internet needed.
What is the error function used for in practice?
It is used in statistics (normal distribution), physics (diffusion, heat), and engineering (signal processing).