ATANH in Collabora Office: Invert Values Strictly Between Minus One and One

• Introduced: original Collabora release and launch date are not established by the sources reviewed.
• Availability: documented in Collabora Office 26.04 help, scoped to the desktop-help release.
• Platform scope: support in every online or mobile deployment is not inferred from desktop documentation.
• Checked: October 14, 2026. Direct function-specific documentation and independent numerical examples; no native Collabora test was performed.

=ATANH(number)

Collabora documents the condition -1<number<1. Both inequalities are strict. Exactly −1 and 1 are outside the real finite-input rule, unlike a function whose domain includes its endpoints.

The corresponding forward function is TANH. ATANH is not ATAN, which inverts the circular tangent and returns an angle. Do not apply a degree/radian conversion to a dimensionless ATANH input merely because the names look similar.

Examples use English function names. Their rounded decimal results are independent mathematical expectations, not native application observations.

Enter −0.9, −0.5, 0, 0.5, 0.9 in A2:A6. In B2 enter and fill down:

=ATANH(A2)

Expected B2:B6, approximately: −1.472219490, −0.549306144, 0, 0.549306144, 1.472219490. Equal opposite inputs produce equal opposite outputs.

The output is not restricted to the same −1 to 1 interval. The first and last examples already have magnitudes greater than 1. The domain constrains the input, not the size of every valid result.

=TANH(ATANH(0.6))
=ATANH(TANH(-1))

Expected results, within numerical precision: 0.6 and −1. ATANH(0.6) itself is approximately 0.693147181.

Use unrounded formula results for the inverse check. Re-entering a shortened displayed decimal introduces a separate rounding step and can explain a small reconstruction difference.

=ATANH(0.9)
=ATANH(0.99)

Expected results: approximately 1.472219490 and 2.646652412. As valid inputs approach 1 from below, the result grows rather than settling at a finite endpoint value.

This does not authorize replacing 1 with 0.99 just to avoid a domain failure. Such a change alters the input and requires a justified rule outside the function itself. The same caution applies near −1.

Suppose a constructed model defines a dimensionless ratio r=(a-b)/(a+b) for positive a and b. For a=4 and b=1, the ratio is 0.6. Use:

=ATANH((4-1)/(4+1))

Expected result: approximately 0.693147181. Reversing a and b gives a ratio of −0.6 and an output of approximately −0.693147181.

The positivity assumptions keep the denominator nonzero and the ratio strictly inside the domain. If you allow zero or signed inputs, those conclusions must be checked again. The formula is an algebraic demonstration, not a universal validation rule for arbitrary data.

Keep the intermediate ratio in a helper column when adapting the example. It makes an out-of-domain result easier to diagnose than a single long nested expression.

For valid real x, the identity is:

=0.5*LN((1+A2)/(1-A2))

At A2=0.6, the internal ratio is 4 and half its natural logarithm is approximately 0.693147181. At A2=−0.6, the ratio is 0.25 and the result is its negative counterpart.

LN explains the natural-logarithm operation. This identity is useful for checking the intended mathematics, but a hand-built expression can lose precision near the boundaries and is not an all-purpose replacement for the dedicated function.

TANH approaches −1 and 1 mathematically. In a finite-precision calculation, a sufficiently large input to TANH can produce a stored endpoint value after rounding. Passing that stored value into ATANH may then violate its documented strict domain, even though the symbolic composition looks reversible.

Do not infer an unlimited native round-trip guarantee from small successful examples. This article has not tested extreme inputs, text coercion or every product error display. For values near the boundary, inspect the actual stored number and choose a tolerance policy appropriate to the model.

Confirm that the input is the bounded ratio intended by the task, rather than a percentage entered as 50 instead of 0.5. Keep units and scale explicit. A percentage display format does not automatically repair a number stored on the wrong scale.

Test zero, a positive value, its negative and values near both endpoints. Those controls expose sign and scaling mistakes while respecting the real domain.

• Collabora Office 26.04: ATANH.
• Editorial testing standards.

The official section supplies the product-specific definition and documented domain or angle branch. Original worked values were independently calculated. Native execution, extreme-value benchmarks and broader client compatibility remain unverified.