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ATANH Function (LibreOffice Calc)

Mathematical Intermediate LibreOffice Calc LibreOffice 3.0

The ATANH function returns the inverse hyperbolic tangent of a number. The result is expressed in radians and is used in advanced mathematics, engineering, and scientific modeling.

Verification status: Consult the documentation and examples below. Native application testing has not been documented for this guide. How formula examples are checked

The **ATANH** function returns the **inverse hyperbolic tangent** of a number. The result is an angle in **radians**, and the function is widely used in engineering, physics, and advanced mathematical modeling involving hyperbolic functions.

What the ATANH Function Does

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

Syntax

ATANH(number)

Arguments

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

Basic Examples

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)

Advanced Examples

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)))

Edge Cases and Behavior Details

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

Common Errors and Fixes

Err:502 — Invalid argument

Cause:

  • Input ≤ –1 or ≥ 1
  • Input is text

Fix:

  • Clamp values using MAX/MIN
  • Convert text to number with VALUE

Unexpected result

Cause:

  • Forgetting ATANH returns radians
  • Using values extremely close to ±1 (results approach ±∞)

Fix:

  • Wrap with DEGREES
  • Validate numeric stability

Best Practices

  • 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
ATANH is your inverse‑hyperbolic‑tangent tool — essential for engineering, physics, and advanced mathematical modeling.
  • 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.

Reproducible example (tested in LibreOffice Calc)

This standalone example was calculated in LibreOffice Calc 25.2.3.2 and matched the expected value. It is a practical cross-check of one usage, not proof that every example elsewhere on this page is correct.

=ATANH(0)

Expected result: 0.

Calculate the inverse hyperbolic tangent of zero.

If the result differs, check the referenced cells, argument separators and number formatting. For more information, consult the LibreOffice Calc official help.