Error Function Calculator (erf, erfc, Inverse)

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Forward mode: enter x, get erf(x) and erfc(x). Inverse mode: enter a probability p, get the x for which erf(x) = p.
The argument of the error function. Any real number.
erf(x)
0.842701

Probability that a standard normal variable lies within [-x, x] (scaled by 2/sqrt(pi))

erfc(x)0.157299
erfcx(x)0.427584
0.84270180.0% below · x

erf(1) = 0.842701, erfc(1) = 0.157299

  • erf(1) = 0.842701: approximately 84.27% of the standard normal distribution's probability mass lies within the symmetric interval [-|x|, |x|] times sqrt(2).
  • erfc(1) = 0.157299: this is the probability remaining in the two tails beyond that interval.

Next stepIn statistics, erf(x / sqrt(2)) equals the probability that a standard normal variable falls in the interval [-x, x]. At x = 1, that probability is 68.27%.

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