ATANH in SoftMaker PlanMaker 2026: inverse hyperbolic tangent, syntax and examples

The hyperbolic tangent maps any finite real number to a value in the open interval (−1,1). ATANH(x) recovers the original input whose hyperbolic tangent equals x: ATANH(TANH(y))=y mathematically, subject to rounding. Unlike ATAN, this is not the ordinary inverse tangent used to find angles in radians. SoftMaker explicitly identifies TANH as its inverse and demonstrates ATANH(TANH(0.1234)) returning 0.1234. See also the separately documented ATAN.

The mathematical identity ATANH(x) = LN((1+x)/(1-x))/2 is useful for independent cross-checks where −1 < x < 1; it does not imply that PlanMaker internally implements ATANH using this formula. The separately documented PlanMaker LN returns a natural logarithm.

=ATANH(Number)

There is exactly one required numeric argument, no second argument, no optional argument and no default. The English 2026 SoftMaker manual writes ATANH(Number) and documents both bounds explicitly. For the English manual, ATANH is the canonical name; no separate English alias is indicated on its reference page. The PlanMaker 2021 ATANH reference independently shows the same name, argument and bounds. This establishes documentation in these editions, not the first software version containing it.

PlanMaker requires an = at the beginning of manually entered formulas. The examples here assume English function names and decimal periods. The Edit-tab settings allow system or custom decimal/thousands separators, and SoftMaker discusses translated function names. Because ATANH has one argument, a formula list separator does not arise in its own invocation; combined formulas may use a locale-specific separator. No translated-language or locale-specific execution was conducted.

Open a blank worksheet; enter Input in A1 and Inverse hyperbolic tangent in B1. Type the numbers below as numeric values in A2:A11. In B2 enter =ATANH(A2) and fill down through B11. Display ten decimals if desired (number formatting does not change the underlying result).

As the input approaches +1 from below, the result grows without bound; approaching −1 from above, it decreases without bound. ATANH(-x) = -ATANH(x) mathematically. These statements describe the mathematical function, not measurements of PlanMaker floating-point precision. The vendor reference supplies the permitted input interval. SoftMaker ATANH.

Quick independent formula checks

• =ATANH(0) → 0.
• =ATANH(0.5) → approximately 0.5493061443, in agreement with SoftMaker’s 0.54931 rounded example.
• =ATANH(-0.5) → approximately −0.5493061443.
• =ATANH(TANH(0.1234)) → approximately 0.1234; this is also a vendor-published example.
• =LN((1+0.6)/(1-0.6))/2 → approximately 0.6931471806, independently equal to =ATANH(0.6) within ordinary floating-point rounding. Parentheses around both 1±0.6 terms are essential.

For correlation coefficients strictly between −1 and +1, the Fisher z-transformation is mathematically z = ATANH(r). In A15 type Correlation, B15 type Fisher z, then A16=0.6 and B16:

=ATANH(A16)

Independently expected B16: approximately 0.6931471806. The transformation is useful for statistical inference when its assumptions are met, but the function alone does not establish sample adequacy, confidence intervals, independence, or statistical significance. To convert the transformed result back to an r-like coefficient, C16 can contain =TANH(B16); independently expected 0.6. This is an illustrative mathematical use, not a claim that SoftMaker publishes a statistical Fisher-workflow tutorial. ATANH; TANH.

Suppose an analytical model uses response = TANH(stimulus/3) and you need the stimulus from a measured normalized response. In A20 enter 0.8. Enter this in B20:

=3*ATANH(A20)

Independently expected B20: approximately 3.2958368660. Cross-check by entering =TANH(B20/3) in C20; independently expected 0.8. This inversion assumes the normalized response lies strictly between −1 and 1 and that the model really follows the specified form. For measured endpoints ±1, do not silently clamp them to nearby numbers; that changes the mathematical model. Vendor inverse-function relationship.

If p is a proportion strictly between 0 and 1, the identity log(p/(1-p)) = 2*ATANH(2*p-1) holds mathematically. In A24 type 0.8, then enter:

=2*ATANH(2*A24-1)

Independently expected result: 1.3862943611. For comparison, =LN(A24/(1-A24)) gives the same mathematical result. This is a general mathematics example, not evidence that a statistical package’s fitting methods are built into PlanMaker. Avoid p=0 or p=1: those map to excluded ATANH endpoints, and the log-odds become unbounded. PlanMaker domain rule; PlanMaker LN.

Versions, platforms, locales and Excel comparison

PlanMaker 2026 (English reference): ATANH(Number), strict (−1,1) domain, TANH inverse relationship and vendor examples are documented. PlanMaker 2021 (English reference): the same syntax and domain are independently documented. The PlanMaker 2024 ATANH reference could not be independently opened this run, so this guide does not assert a 2024 documentation comparison. Neither manual proves feature identity across specific Windows/macOS/Linux builds, older perpetual editions, NX subscriptions or mobile versions; no native installation was tested. 2026 documentation; 2021 documentation.

Locale: The examples use English function naming and decimal periods. SoftMaker’s function-language help and Edit settings make it unsafe to promise identical formula text for all UI languages or number formats. No locale-specific names were guessed or tested.

Microsoft Excel: Microsoft’s ATANH documentation independently documents the name, one-number syntax and allowable range. This is documentation-level mathematical/syntactic alignment; no actual Excel calculation, .xlsx round trip, error-code match or implementation parity test was performed.

Related official references (all checked October 13, 2026)

• SoftMaker PlanMaker 2026 — ATANH: syntax, bounds, examples and TANH relationship.
• SoftMaker PlanMaker 2021 — ATANH: older vendor documentation, not a feature-introduction date.
• SoftMaker PlanMaker 2026 — TANH and ATAN: similar names, different mathematical operations.
• SoftMaker PlanMaker 2026 — LN: logarithm used for the independent algebraic identity.
• SoftMaker formula entry, regional numeric separators and function-name localization guidance.
• Microsoft Excel — ATANH: separate-application comparison only.

Documentation examined: 2026-10-13, PlanMaker 2026 and historical PlanMaker 2021 manuals, Microsoft Excel documentation and vendor input/locale guidance. Native PlanMaker execution: zero; native Excel execution: zero; native screenshots: zero; import/export tests: zero. Tabulated numerical results are independent mathematical predictions, not verified PlanMaker outputs.