ACOSH Function in ONLYOFFICE Spreadsheet Editor: Inverse Hyperbolic Cosine, Domain Limits and Examples

ACOSH returns the nonnegative inverse hyperbolic cosine of an input. Its real-valued domain begins at 1, and the principal output is nonnegative. COSH(t) is even: COSH(t) = COSH(-t). ACOSH selects the nonnegative principal value, so it cannot retrieve the sign of an original COSH input.

The defining mathematical identity is acosh(x) = ln(x + √(x - 1) · √(x + 1)) for x ≥ 1. This is a mathematical equation, not a claim about the vendor’s internal implementation or floating-point algorithm. This guide is about a real-number mathematical function, not formatting, a formula-name alias, or an add-on.

=ACOSH(number)

Documented input requirement: ONLYOFFICE explicitly requires number >= 1. For real arithmetic, a value below 1 has no real ACOSH result. No optional argument or second parameter appears in ONLYOFFICE’s official ACOSH entry, accessed 2026-10-13. The function name is uppercase in English; a formula begins with = when typed into a worksheet. This syntax and the number of arguments are vendor-documented; the numerical examples below are separate mathematical calculations.

The official Insert Functions guide explains that users can enter the formula manually, search for a function under Formulas/Math and Trigonometry, or open the Insert Function dialog (including Shift+F3). Its generic examples describe argument separators as commas, but ACOSH has only one argument, so no separator appears in this guide’s primary formulas.

1. Open a blank spreadsheet and, for reproducibility, use English formula language and a decimal-point regional setting. This page does not assume a user has any existing data.
2. In A1 enter Input; in B1 enter ACOSH output; in C1 enter Independent expected output.
3. Enter the numeric A2:A13 values exactly as shown in the following table (not text strings). All twelve are within the function’s documented real-number input domain.
4. In B2 enter =ACOSH(A2) and press Enter, then fill/copy B2 down to B13. Each relative A-reference should follow its corresponding input row.
5. The values in the last column were precomputed mathematically. Use them to compare results after you open the workbook in your own Desktop or web editor. Different display formats and floating-point rounding may change visible final digits. This five-step procedure is a reproducible manual test plan, not a test reported as executed here.

The expected values use the mathematical function acosh from Python’s standard library, rounded for display to at most ten decimals; equality at more decimals and vendor-specific handling have not been measured. To confirm the copied range refers to the correct row, change A3 temporarily to another valid number, observe B3 in a native test, then restore it.

• =ACOSH(1) → 0 (independent mathematical expectation; not observed in ONLYOFFICE).
• =ACOSH(1.25) → 0.6931471806 (independent mathematical expectation; not observed in ONLYOFFICE).
• =ACOSH(2.5) → 1.566799237 (independent mathematical expectation; not observed in ONLYOFFICE).
• =ACOSH(5) → 2.2924316696 (independent mathematical expectation; not observed in ONLYOFFICE).

When entering a numeric literal, use parentheses and the leading =. In =ACOSH(A2), A2 is a cell reference; number in the vendor syntax is a placeholder, not the word to type into a formula.

For an idealized catenary with normalized height ratio y/a = cosh(x/a), ACOSH(y/a) gives the nonnegative dimensionless |x|/a. In this use case A2 stores a height ratio, not a distance. Do not use the function as a general-purpose geometric solver without the model assumptions.

Procedure: Put the relevant inputs in A2:A13, enter =ACOSH(A2) in B2 and copy down. Keep the original inputs intact for auditing; use a separate output column. Change only the business meaning of the inputs, not the mathematical domain or syntax. The expected results remain those independently computed in the worksheet table.

1. A safe input-domain gate

Place a ratio 0.9 in A2. =IF(A2>=1,ACOSH(A2),"Outside real domain") is proposed to return the explanatory text mathematically. IF is an officially documented function, but this exact nested expression was not executed; verify evaluation and locale.

2. Principal inverse of a positive input

For t=2 in A2, =ACOSH(COSH(A2)) is mathematically 2. For t=-2 it is also 2, demonstrating loss of the sign when inverting the even COSH function.

3. Recover catenary distance magnitude

Put a positive scale a=3 in D2 and y/a=2 in A2. =$D$2*ACOSH(A2) mathematically gives about 3.95087369. It is the nonnegative distance magnitude under the stated model.

4. Independent logarithmic check

For x=2 in A2, =LN(A2+SQRT(A2-1)*SQRT(A2+1)) should mathematically give about 1.31695790. This formula is an independent identity, not a substitute for native ONLYOFFICE testing.

5. Round only at output

For x=10, =ROUND(ACOSH(A2),3) should be about 2.993. Keep the unrounded cell result for subsequent calculations.

For nested examples, refer to the relevant source cells stated in each example. Arithmetic equalities are mathematical expectations, and should be tested in the user’s particular ONLYOFFICE edition before relying on edition-specific output.

Missing arguments: =ACOSH() omits the only required argument. Do not assume a specific error label from Excel or another spreadsheet: the short ONLYOFFICE reference identifies the required argument but does not enumerate exact product error messages across releases. For domain-invalid inputs, the mathematical result is not a finite real number; the precise editor response requires a native test. No screenshots were captured.

• Vendor-confirmed syntax: the function name, number argument, documented domain, and category come from the official ACOSH reference reviewed on 2026-10-13.
• Locale: ONLYOFFICE’s Advanced Settings specifies a configurable Formula Language and configurable regional decimal and thousands separators. Choose English if using the exact formulas in this tutorial. A German, French, or other localized function spelling and decimal-input syntax are not independently tested.
• Formula entry: the Insert Functions guide documents entering = and a named function, as well as the Insert Function wizard. The particular shortcuts or visual placement can vary by edition.
• Web and Desktop: the vendor maintains a unified, unversioned function page; existence of the reference establishes documentation for ONLYOFFICE Spreadsheet Editor but does not establish first-supported Desktop/web versions, rollout order, platform parity or exact historical behavior. The Docs 10.0 announcement dated October 2026 does not independently prove this function was newly added then.
• Compatibility with other spreadsheets: no Excel, Google Sheets or LibreOffice workbook execution or file interchange test was performed. The formulas follow standard mathematics, but vendor behavior, error codes, names and localized separators must not be inferred from other products.
• Verification levels: source syntax/domain = official documentation check; displayed numeric values and identities = independent mathematical calculations, not observations; native ONLYOFFICE execution, screenshot evidence, exact error codes, localized behavior and cross-product output = not performed.

• COSH function — related vendor reference, checked 2026-10-13.
• LN function — related vendor reference, checked 2026-10-13.
• SQRT function — related vendor reference, checked 2026-10-13.
• ROUND function — related vendor reference, checked 2026-10-13.
• ONLYOFFICE Insert Functions — vendor instructions for function search and entering formulas (checked 2026-10-13).
• ONLYOFFICE Advanced Settings — Formula Language, region, and separators (checked 2026-10-13).

Reference access date: 2026-10-13. Source-page version: unversioned ONLYOFFICE Help Center pages (the vendor pages do not provide a first-support release). Do not claim that a particular historical release provides identical evaluation until native version-by-version tests exist.