TANH in Collabora Office: Use a Bounded Hyperbolic Transformation

• Introduced: documented in Collabora Office 26.04 Help; the original introduction version is not established by the reviewed history.
• Availability: the official TANH reference documents support in Calc’s 26.04 desktop manual.
• Scope: this evidence does not establish identical behavior in Collabora Online, mobile clients or older releases.
• Checked: October 14, 2026 against the captured 26.04 manual. Examples were calculated independently; no native Collabora execution was performed.

=TANH(number)

Hyperbolic tangent is related to the exponential function by:

tanh(x) = (exp(2*x)-1)/(exp(2*x)+1)

It also equals sinh(x)/cosh(x). These identities explain the expected values; they are not promises that expanded formulas have the same numerical stability as a dedicated TANH implementation at every magnitude.

TANH is different from TAN. Its argument is not automatically an angle in degrees, it is not periodic and it has no finite-real singularities like tangent’s odd quarter-turns.

Enter −2, −1, 0, 1, 2 in A2:A6. In B2 enter and fill down:

=TANH(A2)

Expected B2:B6: approximately −0.964027580, −0.761594156, 0, 0.761594156, 0.964027580.

The sign changes with the input, and the function is odd: tanh(−x) = −tanh(x). The change from one to two produces a smaller output increment than the change from zero to one, illustrating saturation toward the limits.

Put 1 in D2 and compare:

=TANH(D2)
=(EXP(2*D2)-1)/(EXP(2*D2)+1)

Expected result for both: approximately 0.761594156. At this moderate input the exponential terms are manageable, making the identity a transparent arithmetic check.

For very large positive values, EXP(2*x) can overflow even though the true hyperbolic tangent is bounded. That is a limitation of the expanded computation, not a reason to replace the dedicated function with it indiscriminately.

=TANH(LN(2))

Expected result: approximately 0.6. Since exp(2×ln 2) = 4, the definition gives (4−1)/(4+1) = 3/5.

The same result follows from the independently checked values sinh(ln 2) = 0.75 and cosh(ln 2) = 1.25. Dividing 0.75 by 1.25 gives 0.6. See SINH and COSH for those companion examples.

Suppose a constructed display rule maps a numeric input x to:

=100*TANH(A2/2)

For inputs −4, −2, 0, 2, 4, expected outputs are approximately −96.402758008, −76.159415596, 0, 76.159415596, 96.402758008.

The factor 100 sets the mathematical outer limits at ±100, while dividing the input by two controls how quickly the curve approaches them. This is an illustrative transformation, not a validated scoring or decision system.

It preserves order for real inputs but compresses differences at the extremes. Values far apart in the source can become visually similar after rounding. Retain the original values whenever the differences matter.

For a desired output of 0.5, the identity x = ln((1+y)/(1−y))/2 gives:

=LN((1+0.5)/(1-0.5))/2

Expected input: approximately 0.549306144. Applying TANH to that result is expected to give approximately 0.5.

This inverse expression requires −1 < y < 1. Endpoints ±1 are limiting values, not outputs with a finite real inverse input. Do not use it with an arbitrary percentage without checking the stored number and the intended scale.

A spreadsheet may display, or numerically round to, exactly 1 or −1 for sufficiently large finite inputs. That does not contradict the strict mathematical bound; it reflects finite representation and display precision. Avoid a workflow that assumes a rounded saturated output can reconstruct the original large input.

Do not label TANH as a probability without defining an additional mapping and validating the model. Its raw values can be negative. A transformation’s neat range is not evidence that it fits an application’s data or decision rules.

Check zero, one positive input and its negative, then compare a larger magnitude to observe saturation. Use a suitable tolerance for the independently calculated decimals, and keep model inputs, scaling constants and display rounding separate.

• Collabora Office 26.04 Help: TANH — direct product-specific definition and syntax.
• Editorial testing standards.

The examples use semicolon argument separators. Displayed decimals are rounded expected values, not exact native outputs. Mathematical identities are explanatory calculations; product support is limited to the cited documentation scope.