Use =ATANH(0.8) to get the independently calculated 1.09861229 (shown to eight decimal places). ATANH finds the finite real number t whose hyperbolic tangent equals x. The finite real-number domain is strictly −1 < x < 1. At ±1, the mathematical inverse diverges; outside, no real result exists. The output shown here is a mathematically expected value, not an actual Calligra Sheets execution result.

=ATANH(number)

The KDE handbook and the tagged Calligra 26.08.2 trig.xml declare ATANH(Float) and show the expected =ATANH(0.8) example. The associated trig.cpp registers ATANH and calls calc->atgh(args[0]). This checks the one-argument implementation’s documented intent; it is not a test of a packaged Calligra binary. The 26.08.2 KDE Gear release was dated October 8, 2026 (announcement); sources were accessed 2026-10-11. A function’s presence in the handbook and source registry does not guarantee that a particular installed package enables the function or reproduces the same display formatting.

Domain and inverse-function distinction

The finite real-number domain is strictly −1 < x < 1. At ±1, the mathematical inverse diverges; outside, no real result exists. The inverse hyperbolic function is not the ordinary inverse trigonometric function (for example, ATAN). Despite a generic “Angle (radians)” parameter label inherited from the older KDE handbook, the input is normally a dimensionless real number; the output is not an ordinary angle that should be converted to degrees. Do not insert RADIANS or DEGREES automatically.

Formula entry and locale details

Enter =ATANH(A2) in the formula bar. Numbers such as 0.8 are written with a decimal point in this English-language example; your regional numeric conventions may require a comma. The KDE English function examples use semicolons between arguments for multi-argument functions, but this function has exactly one argument, so no separator is needed. If your installation localizes function names, use the function chooser; no native localized system or conversion was tested.

1. In a blank sheet, enter Numeric x into A1 and ATANH(x) into B1.
2. Type the six numeric inputs into A2:A7, in the exact order below; these are numeric values, not quoted strings.
3. In B2, enter =ATANH(A2) and fill/copy the formula through B7. The relative A2 reference must increment to A3, A4, etc.
4. Format column B to eight decimal places and compare within a small tolerance (for example 0.00000001 plus a sensible floating-point margin).

All displayed outputs were independently calculated using Python math.atanh and then rounded for presentation on 2026-10-11. They were not observed by running Calligra or importing a workbook. Hand-calculated identities and independently evaluated numerical examples complement documentation checking; they do not replace real spreadsheet validation. Displaying eight decimals does not alter underlying floating-point precision.

Cross-check with its paired hyperbolic function

The mathematical inverse relationship is TANH(ATANH(x)) = x for |x| < 1. =ATANH(TANH(1)) should return 1 within numeric precision. ATANH(-x)=-ATANH(x) for all |x|<1. The algebraic identity =LN((1+A2)/(1-A2))/2 matches mathematical ATANH(A2) inside the domain, but becomes numerically delicate as x approaches ±1 and depends on correct parentheses; the direct function is preferred.

For a real-valued sample correlation r strictly between -1 and 1, Fisher’s z-transform is z=ATANH(r). Put 0.8 in E2, and enter =ATANH(E2) in F2: the expected z-value is 1.09861229. In G2, enter =TANH(F2) to invert it; independently expect approximately 0.8. This transformation is often used for statistical work with correlations, but it does not itself compute confidence intervals, check independence, or verify statistical assumptions. Correlations exactly -1 or 1 are outside the transform’s finite real domain.

• Inputs at -1 or +1. The finite inverse does not exist at either boundary: the mathematical result diverges. The KDE handbook mentions invalid/NaN for absolute inputs greater than one but does not specify the precise cell error at equal to one. No native version was run, so do not infer an observed result or code.
• Outside (-1,1). No real answer for x<-1 or x>1. Check calculations producing values slightly outside the allowed interval, including rounded correlations.
• Values very near ±1. The result grows in magnitude without bound as x approaches an endpoint and is sensitive to numerical precision. Inputs formatted as 1.00 can still store e.g. 0.9999; inspect actual stored values.
• Ordinary tangent confusion. ATAN and ATAN2 are circular inverse functions; ATANH is hyperbolic. Do not use a degree conversion on the result unless a different model explicitly requires it.
• Unrecognized formula: Verify the function spelling, leading =, and that your installed package includes the trigonometry function module. A release registration is not proof of behavior in a particular installation.
• Text versus numeric data: Imported strings, numbers stored as text, and units such as "2 units" are not documented floating-point numeric arguments. Native coercion rules and resulting error strings have not been checked.
• Rounding and display: Check actual stored input cells and show more decimal places before assuming the function result is wrong. Round-trip identities should be compared with tolerance, not strict equality in every case.
• Regional settings: If the example formula appears as text or parses unexpectedly, check cell format, decimal conventions and localized formula entry. No locale-specific native test was run.

Excel’s ATANH(number) requires -1 < number < 1, consistent with the finite real domain here; Calc also documents the inverse hyperbolic tangent. Cross-spreadsheet parity is documentation-level only; cell error codes, near-boundary precision, localized decimal marks and file conversions were not tested.

The comparison uses the official Microsoft Excel ATANH help and LibreOffice Calc mathematical functions, accessed 2026-10-11; neither application was executed. Mathematical agreement does not establish identical parsing, coercion, domain errors, decimal formatting or workbook compatibility.

• Official TANH function reference — paired hyperbolic function, for checking the inverse identity.
• Official ATANH function reference — exact signature and built-in examples.
• KDE Calligra 26.08.2 trigonometry descriptions and registered C++ implementation — released code, not native test output.
• KDE Gear 26.08.2 release and Calligra downloads — release/platform scope; Linux packages and Flatpak are recommended, while Windows support is listed as in progress.

These are checked official external documentation/source destinations. The proposed future internal tutorial slug is /calligra/functions/atanh/, but it has not been published or verified as a live page; do not assume the links are working internal pages.

• Calligra Sheets — function documentation
• 26.08.2 trig.xml
• KDE tagged trig.cpp
• announcement
• LibreOffice Calc mathematical functions
• Official TANH function reference

Verification status: Official documentation checked; example outcomes were independently reasoned or arithmetically checked where applicable. Not executed in Calligra Sheets.

• No genuine Calligra Sheets screenshots are included; this guide does not use mock application images.