ATANH Function (LibreOffice Calc)

• Computes the inverse hyperbolic tangent
• Returns an angle in radians
• Accepts values strictly between –1 and 1
• Useful in scientific, engineering, and computational mathematics

ATANH(number)

Arguments

• number:
  A numeric value strictly between –1 and 1.

Inverse hyperbolic tangent of a value

=ATANH(0)
→ 0

=ATANH(0.5)
→ 0.549306144

Convert result to degrees

=DEGREES(ATANH(0.5))

Using a cell reference

=ATANH(A1)

Compute ATANH using its logarithmic identity

=0.5 * LN((1 + A1) / (1 - A1))

Normalize input to avoid domain errors

=ATANH(MAX(-0.999999; MIN(0.999999; A1)))

Hyperbolic geometry modeling

=ATANH(TANH(A1) * COSH(A2))

Engineering formula example

=ATANH((V - I) / (V + I))

Use with EXP and LN for analytic transformations

=ATANH((EXP(A1) - EXP(-A1)) / (EXP(A1) + EXP(-A1)))

ATANH returns a numeric value (radians)

Accepts:

• Numbers strictly between –1 and 1
• Expressions that evaluate to numbers

Behavior details

• Domain is (–1, 1)
• Output is in radians
• ATANH is undefined at –1 and 1
• Use DEGREES() to convert the result

Invalid input → Err:502

ATANH of an error → error propagates

• Always validate that |number| < 1
• Convert to degrees when presenting angles
• Use ATANH with ASINH and ACOSH for full hyperbolic workflows
• Combine with LN and EXP for scientific modeling
• Normalize floating‑point inputs to avoid domain errors

• Use TANH for forward hyperbolic tangent
• Use ACOTH for inverse hyperbolic cotangent
• Use DEGREES and RADIANS for angle conversion
• Use LN and EXP for analytic transformations

By mastering ATANH and its companion functions, you can build precise, reliable hyperbolic and scientific models in LibreOffice Calc.