ACOTH Function in ONLYOFFICE Spreadsheet Editor: Syntax, Examples and Compatibility

The named function and the syntax below are in the current, unversioned English ONLYOFFICE Docs Spreadsheet Editor documentation reviewed on 13 October 2026 (UTC). This is documentary support for the current reference, not a successful execution test in ONLYOFFICE Docs/web or Desktop Editors, and it is not a claim of support in all earlier versions, hosting editions, mobile apps, or imported Excel workbooks. The Docs changelog lists version 10.0.0 dated 10 October 2026; that changelog does not identify these particular functions as newly introduced in 10.0. Desktop release history is maintained separately, and no first-supported Desktop/web version has been established for this function.

Verification labels used in this guide: vendor documented = stated in a linked ONLYOFFICE source; independently calculated expectation = calculated outside ONLYOFFICE using mathematics/Python; native result = none obtained. Illustrations/screenshots were not fabricated or substituted for actual tests.

=ACOTH(number)

• number (required, numeric): One required numeric value, x < −1 or x > 1. There are no optional arguments and no default. The strict inequality is explicit in the vendor reference.
• Argument order: one positional numeric argument only. Optional arguments/defaults: none.
• Return type: numeric real value for an in-domain mathematical input; the exact cell display can vary with number format.
• Mathematical domain: Strictly ABS(number)>1. Inputs −1, 0, +1, and every point between −1 and +1 are outside the real domain.
• Principal range / behaviour: Mathematically, the real output is nonzero; positive input >1 gives a positive result, and input <−1 gives a negative result. The value approaches zero as the input magnitude increases.
• Units: The mathematical output is a dimensionless hyperbolic parameter, not degrees. Do not use DEGREES unless your calculation specifically requires an unrelated unit transformation.

Mathematical interpretation: For real |x|>1: acoth(x) = ½·ln((x+1)/(x−1)) = atanh(1/x). These are independent mathematical identities, not claims that ONLYOFFICE internally evaluates one function through another.

1. Create an empty spreadsheet in the ONLYOFFICE Spreadsheet Editor, using its English formula language for the formulas shown.
2. Enter the numbers exactly as shown in the Input in A column below, beginning in A2 and going down one row per example; do not include the units, symbols, or quotation marks as part of the values.
3. In B2, enter =ACOTH(A2), press Enter, and fill the formula down the column. Numeric cells can be formatted to show ten decimal places.
4. Compare your result to the independently calculated expectation, allowing for display rounding and floating-point arithmetic. This guide does not claim that steps 1–3 were executed in either ONLYOFFICE product.

Interpreting the table: values are independent mathematical expectations rounded for readability, not screenshots or verified calculations performed in ONLYOFFICE. Values at very small magnitude may display in scientific notation when the worksheet format changes.

1. Independently check the logarithm identity

Set up: Enter D2 = 2, then =ACOTH(D2) in E2 and =0.5*LN((D2+1)/(D2-1)) in F2.

Expected output: Both ≈ 0.5493061443 (independently calculated, not native-tested).

Why it works: The mathematical identity supplies a second calculation path. It is useful for auditing a worksheet; it is not a claim that either formula has been executed in ONLYOFFICE.

2. Inverse relation with COTH

Set up: Enter =COTH(ACOTH(2)) in F3.

Expected output: 2 within floating-point precision (independently calculated, not native-tested).

Why it works: The pair should return the starting value over the real ACOTH domain. Near boundary conditions, finite precision can cause small differences.

3. Prevent invalid real inputs

Set up: Set D4 = 1.5, and enter =IF(ABS(D4)>1,ACOTH(D4),"Outside real domain") in F4.

Expected output: ≈ 0.8047189562 (independently calculated, not native-tested).

Why it works: The IF condition implements the exact strict domain. Change D4 to 1 to verify the intended text branch when testing natively.

4. Equivalent expression using ATANH

Set up: Enter D5 = -2, =ACOTH(D5) in E5, and =ATANH(1/D5) in F5.

Expected output: Both ≈ −0.5493061443 (independently calculated, not native-tested).

Why it works: Both formulas are mathematically equivalent for |D5|>1. The ATANH reference independently specifies its own valid interval (−1,1).

5. Approach the domain boundary

Set up: Enter D6 = 1.001 and =ACOTH(D6) in E6.

Expected output: ≈ 3.8007011673 (independently calculated, not native-tested).

Why it works: As x approaches 1 from above, the inverse grows without bound. Do not replace the strict >1 requirement with ≥1.

Error-code caution: ONLYOFFICE documentation for this function does not establish exact error strings for every invalid input, coercion, overflow, or version. Thus this guide does not assert #NUM!, #DIV/0!, or other codes as observed in ONLYOFFICE. Record actual native outputs and version/edition before relying on undocumented error behavior.

The examples use English function names, decimal points and (where needed) comma-separated arguments. The official Insert Function guide explains that manual formulas begin with = and that arguments are separated by commas in its English instructions. The Advanced Settings page documents configurable formula language and regional decimal/thousands separators. Neither source establishes how this exact function was spelled or evaluated for every locale. Do not rewrite formulas using a different locale based only on habits from another spreadsheet program.

The vendor distinguishes the web/Docs editor from Desktop Editors and maintains separate release changelogs. The current function page does not state a first-supported version or guarantee parity across historical installations. Version-sensitive behaviour, real error results, large-value precision, workbook imports, mobile editions, and localized syntax therefore require native verification. A release-note mention of a related Spreadsheet Editor improvement must not be mistaken for a function introduction.

• COTH function — vendor function reference.
• LN function — vendor function reference.
• ATANH function — vendor function reference.
• IF function — vendor function reference.
• ABS function — vendor function reference.
• Insert functions in ONLYOFFICE Spreadsheet Editor — function-selection, autocomplete and entry workflow.
• Spreadsheet Editor advanced settings — formula language, regions, and separators.

What values can ACOTH accept?

Only numeric values strictly below −1 or strictly above 1 according to its official reference.

Is ACOTH the inverse of COT?

No. ACOTH is inverse hyperbolic cotangent; the ordinary inverse cotangent is ACOT.

What does ACOTH(2) return?

The independently calculated expectation is about 0.5493061443. It has not been measured in ONLYOFFICE Desktop or web editors.

Verification limitations: Native Docs/web and Desktop execution, localized parsing, extreme-value precision, historical editions and runtime error behavior were not tested.