How this calculation works
Recover the real number whose hyperbolic tangent equals a selected value.
THE FORMULA
artanh x = [ln(1+x)−ln(1−x)]/2A worked example
artanh 0.6 = ln(4)/2 = ln 2.
Good to know
The real inverse requires |x|<1.
Reference: OpenStax Algebra and Trigonometry (opens in a new tab) ↗
Read the result
Recover the real number whose hyperbolic tangent equals a selected value.
The primary result is labeled “Inverse hyperbolic tangent”. Keep the input definitions in view when comparing this result with another method.
Try a related calculation
The real inverse requires |x|<1.
For a related exercise, try the quadratic equation solver.
A few questions, answered
How can I check the default inputs by hand?
artanh 0.6 = ln(4)/2 = ln 2.
Which rule does this calculator apply?
artanh x = [ln(1+x)−ln(1−x)]/2