ACOTH Function (OpenOffice Calc)

Use ACOTH to obtain the inverse hyperbolic cotangent of a number. For real-valued results, the input must be greater than 1 or less than −1. Apache’s Calc 4.1 guide documents the function as ACOTH(number) and describes the returned value using the radian convention [S1].

=ACOTH(2)

Independently calculated expected result: 0.549306144334055 (rounded). ACOTH is not the same function as the ordinary inverse cotangent, ACOT [S1, S2].

=ACOTH(number)

• number — required: one real numeric value or a reference/formula returning a numeric value. There are no optional arguments and no default. The real-number domain is ABS(number)>1; −1, 0, 1, and numbers between −1 and 1 are outside that domain [S1, S3, M1].
• Result: one numerical value, described in Apache OpenOffice Calc’s 4.1 function appendix as the inverse hyperbolic cotangent expressed in radians [S1].
• Version evidence: the function appears in the official Apache OpenOffice 4.1 guide published August 25, 2025. The released application version checked for the saved research was 4.1.16 (November 10, 2025), but its runtime was not installed or tested during preparation [S1, S4].
• Locale: ACOTH accepts only one argument, so there is no multi-argument delimiter to enter. The examples use an English-style decimal point (1.5). For a locale using a decimal comma, enter the equivalent locale-specific numeric literal or, preferably, refer to a numeric cell. Function-name localization and the exact UI error label have not been tested [S1, V1].

Unlike ordinary ACOT, ACOTH is a hyperbolic inverse function; interpreting its output as a geographic or circular angle is usually inappropriate. For a circular inverse cotangent, use ACOT instead [S1, S2].

Enter the following numeric values into column A (do not type the word number in a value cell):

On a narrow screen, scroll this table sideways to see every column.

In B2, enter =ACOTH(A2) and fill down through B5. The displayed number of decimal places depends on cell formatting. Negative inputs less than −1 yield negative results; positive inputs greater than 1 yield positive results [M1]. These values have not been observed in native Calc.

Check one answer without trusting a prewritten value

For A2 = 2, calculate the equivalent natural-log expression in C2:

=LN((A2+1)/(A2-1))/2

Mathematically expected: 0.549306144334055, matching ACOTH(A2) to rounding. This checks the real-valued identity independently of Calc’s implementation [M1]. LN here means natural logarithm, not base-10 logarithm.

An input of 1, 0, or −1 is not a valid real-number argument. To show explanatory text rather than intentionally entering a domain-invalid function, place test inputs in A2:A6 and use:

=IF(ABS(A2)>1;ACOTH(A2);"Outside real domain")

The added fifth test input A6 = 0 should produce the text Outside real domain under the documented IF/ABS logic; the first four rows should produce their numerical results [S1, M1, V1]. This example uses the standard semicolon argument separators shown in Apache Calc documentation; locale and application settings may affect formula entry. Native error-avoidance behaviour remains untested [V1].

Use the guard only when a cell is already known to contain a number; unexpected text, blank cells, or pre-existing spreadsheet errors should be investigated rather than assumed to be handled identically.

Reverse-check with the hyperbolic cotangent

=ACOTH(COTH(0.5))

Mathematically expected: approximately 0.5. The intermediate COTH(0.5) is approximately 2.163953413738653, inside the valid real domain for ACOTH [S2, M1]. This is a consistency check, not a native execution record.

Equivalent alternative with ATANH

For any real number x with ABS(x)>1, the identity ACOTH(x)=ATANH(1/x) holds [S5, M1]. If A2 contains 2:

=ATANH(1/A2)

Mathematically expected: approximately 0.549306144334055. Apache’s spreadsheet-function implementation notes discuss an ATANH(1/x) translation for interoperability [S5]. That historical discussion is not proof of the current Excel import/export implementation and should not be treated as a tested conversion procedure.

On a narrow screen, scroll this table sideways to see every column.

The real-valued inverse is defined by:

ACOTH(x) = 0.5 * LN((x+1)/(x-1))       when ABS(x)>1

As x approaches 1 from above, the value grows without bound; as it approaches −1 from below, it decreases without bound. Ordinary floating-point rounding may affect values close to the boundary. This is a mathematical and numerical caveat, not a documented exact Apache error threshold [M1].

The function reports an error: First confirm that the input is numeric and lies outside the closed interval [-1,1]. To avoid misdiagnosing a locale problem, test =ACOTH(2) before using decimal literals or referenced data. The precise Apache OpenOffice 4.1.16 error token has not been observed [S1, S3, V1].

The result looks surprising: Remember that the function is hyperbolic; =ACOT(2) is a different operation. Verify a known example against the natural-log formula above [S1, S2, M1].

The last decimals do not match: Compare rounded results with =ROUND(ACOTH(2);6); expected 0.549306. Check number formatting and calculation precision before assuming the formula is incorrect [M1, V1].

A downloaded Excel workbook changes behaviour: Test both ACOTH and the fallback ATANH(1/x) on real inputs. Documentation describes these mathematical relationships but does not establish every import/export conversion or error message for the particular versions in use [S5, S6, V1].

The Apache OpenOffice 4.1 function appendix and Microsoft’s Excel documentation both name ACOTH(number) as the inverse hyperbolic cotangent [S1, S6]. Microsoft’s documentation also specifies ABS(number)>1 and provides the result ACOTH(6)≈0.168 [S6]. This supports a mathematical cross-application comparison, not a claim that all error messages, file conversions, or localized formula syntax match. Microsoft lists Excel 2016 and newer named releases on that support page; older Excel versions were not verified in this review.

LibreOffice’s formulas were not used as evidence that the corresponding function is supported by Apache OpenOffice.

• ACOT — ordinary inverse cotangent
• COTH — hyperbolic cotangent
• ATANH — inverse hyperbolic tangent
• ACOSH — inverse hyperbolic cosine
• ABS — absolute value
• IF — conditional result
• LN — natural logarithm

Accessed 2026-10-12. Source tags below correspond to claim-level evidence in the accompanying calculation record; the full official source addresses are supplied here as source references.

• [S1] Apache OpenOffice 4.1 Calc Guide, Appendix B — Description of Functions, published August 25, 2025, pp. 4–5 (PDF page indices 3–4): ACOTH(number) returns inverse hyperbolic cotangent in radians. https://wiki.openoffice.org/w/images/d/d0/AOO41CG16-CalcFunctions.pdf
• [S2] Apache OpenOffice Wiki, Mathematical Functions — identifies ACOTH among the hyperbolic functions and distinguishes ACOT among ordinary inverse trigonometric functions. https://wiki.openoffice.org/wiki/Documentation/How_Tos/Calc:_Mathematical_functions
• [S3] Apache OpenOffice Wiki, French ACOTH reference — documents ACOTH(nombre) and an error in the closed interval [-1,1]; the translation and its age are explicitly noted. https://wiki.openoffice.org/wiki/Documentation/FR/Calc:_fonction_ACOTH
• [S4] Apache OpenOffice downloads — released 4.1.16 on November 10, 2025; 4.1.17 was still described as in preparation on the September 26, 2026 project update. https://openoffice.apache.org/downloads.html and https://openoffice.apache.org/blog/what-is-going-on-in-Apache-OpenOffice-development.html
• [S5] Apache OpenOffice Wiki, spreadsheet function implementation — historical discussion uses the ACOTH(x) = ATANH(1/x) identity for Excel-file interoperability. https://wiki.openoffice.org/wiki/Calc/Implementation/Spreadsheet_Functions
• [S6] Microsoft Support, ACOTH function — independent Excel reference for syntax, domain and an example; not proof of Apache support. https://support.microsoft.com/en-us/excel/functions/acoth-function
• [M1] Independent calculation — math.atanh(1/x) compared with 0.5*log((x+1)/(x-1)) for test inputs, within floating-point rounding; see calculation record for actual calculation inputs and values.
• [V1] Native verification — not performed in Apache OpenOffice 4.1.16. All worksheet outputs above are expected, not observed application results.

The syntax and behaviour are based on the Apache OpenOffice Calc references cited above. The sample calculations were independently checked; they are expected results, not outputs observed in Apache OpenOffice Calc. Test locale-sensitive text conversion and imported files in your own installation. View the example-check record.

Official ACOTH reference · Editorial standards