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Complementary Error Function Calculator

Compute erfc(x) = 1 − erf(x) to high precision, accurate even far in the tail.

Related tools

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Error Function CalculatorEvaluate erf(x), erfc(x) and their inverses erf⁻¹ and erfc⁻¹ to high precision.Beta Function CalculatorCompute the Euler Beta function B(x, y) = Γ(x)·Γ(y) / Γ(x+y) via a stable log-gamma.Function Composition CalculatorEvaluate and graph (f∘g)(x) and (g∘f)(x) for any two functions, with a value table and point evaluation.Function GrapherPlot up to three functions f, g and h over a custom x- and y-range on an interactive canvas.Function Odd Even Neither CheckerCheck whether a function is even, odd or neither by testing f(−x) against ±f(x).Inverse Function CalculatorSolve f(x) = y numerically for x and see the inverse as the mirror of f across the line y = x.Gamma function calculator Γ(x)Evaluate the gamma function Γ(x), the continuous extension of the factorial with Γ(n) = (n−1)! for positive integers. It uses the Lanczos approximation and Euler's reflection formula to handle negative arguments, and flags the poles at 0, −1, −2, … where Γ blows up. For whole numbers it also shows the exact factorial (x−1)!. Γ appears throughout probability, combinatorics and the analysis of special functions.Möbius function calculator μ(n)The Möbius function μ(n) is 0 if n has a squared prime factor, otherwise +1 or −1 for an even or odd number of distinct prime factors. Enter n and get μ(n) with its prime factorisation and whether n is squarefree.

Complementary Error Function Calculator is free to use as often as you like, directly from this page. It sits under Algebra & equations in our catalogue, alongside Error Function Calculator and Beta Function Calculator.

How to use it

  1. Open the tool — no signup or install needed.
  2. Enter your input or adjust the available options.
  3. Get your result instantly, then copy or download it.

Frequently asked questions

What does Complementary Error Function Calculator do?

Compute erfc(x) = 1 − erf(x) to high precision, accurate even far in the tail.

When would I actually use this?

Getting through a problem set: solving for the unknown, factoring an expression, and — more usefully — seeing the steps that got there.

What is the most common mistake?

Losing a solution when both sides are squared or divided by an expression. Squaring can add roots that do not satisfy the original equation, and dividing can remove one — check every answer back in the original.

How is Complementary Error Function Calculator different from Error Function Calculator?

They sit next to each other but answer different questions: Error Function Calculator is the one to open when you need it to evaluate erf(x), erfc(x) and their inverses erf⁻¹ and erfc⁻¹ to high precision. Pick whichever matches what you're starting from — both are free.

Is there a tool for the next step?

Beta Function Calculator is the closest one after this: Compute the Euler Beta function B(x, y) = Γ(x)·Γ(y) / Γ(x+y) via a stable log-gamma.

What else is worth having open alongside it?

Function Composition Calculator and Function Grapher — they come up in the same task often enough to be worth a second tab.

Where do the figures come from?

The algebra is symbolic where the expression allows it and numeric otherwise, and the tool says which it used. Exact results are given as fractions or radicals rather than rounded decimals.

Further reading

All guides →
How-toHow to Use the Quadratic Formula: Solving ax² + bx + c = 0Solve any quadratic equation with x = (−b ± √(b² − 4ac)) / 2a, and read the discriminant to know how many real solutions to expect.How-toHow to Find a Cube Root by HandA step-by-step guide to finding a cube root by estimation and refinement — plus how it differs from a square root and when a value stays irrational.ExplainerHow Exponents Work: Powers and the Laws of ExponentsAn exponent is repeated multiplication. Learn the laws of exponents, what negative and fractional powers mean, and why anything to the zero is one.How-toHow to Calculate Percent Error: The Accuracy Formula for SciencePercent error tells you how close a measurement is to the true value. Learn the formula, work through an example, and see how scientists use it to judge accuracy.ExplainerPercentage Difference vs. Percentage Change vs. Percentage ErrorThree percentages that look alike but answer different questions. Learn the formula for each, when to use it, and why they give different numbers.ExplainerThe Flat Pattern of a Cone Is a Sector, Not a CircleRoll a 50 mm cone 80 mm tall and its pattern is a 190.8° slice of a 94 mm circle. Flatten a nearly cylindrical lampshade and the pattern radius runs to 839 mm — the shallower the taper, the further away the apex.