COSH in Calligra Sheets: Hyperbolic Cosine with Examples

Use =COSH(0.8) for an independently expected 1.33743495 (eight decimal places), or =COSH(0) for 1. Hyperbolic cosine acts on a real numeric argument; it is not the ordinary cosine of a degree angle.

These values and examples are expected from independent mathematical calculation. They are not observed results from the Calligra Sheets application.

=COSH(number)

• number (required): A single real numeric value, calculation or reference to one numeric cell. In the KDE handbook, the signature is COSH(Float) and the parameter type is floating point; the older handbook labels it an angle in radians, but hyperbolic calculations usually treat the input as dimensionless. No optional argument, extra argument or default is documented.
• Returns: A floating-point numerical value representing the mathematical hyperbolic cosine. Values in this guide are displayed to eight decimals, not promised exact native formatting.
• Definition: COSH(x) = (EXP(x) + EXP(-x)) / 2. This is a mathematical identity, independently checked by numeric evaluation; it is not a second Calligra-native test.
• Release scope: The stable KF6 Calligra Sheets function handbook documents the one-argument syntax and a numeric example. The tagged KDE Calligra 26.08.2 trigonometry source separately registers the function and invokes calc->cosh(args[0]) in its implementation. Calligra 26.08.2 was dated October 8, 2026. Sources checked October 11, 2026. Presence in official documentation and tagged source is evidence of intended support, not proof of successful execution in every packaged installation.
• Platform: Calligra’s official download guidance emphasizes Linux distribution packages and Flatpak; Windows support is in progress. Exact installed version, available function modules and user-interface language can differ. See Calligra downloads.

Important distinction from ordinary trigonometric functions

A hyperbolic function is defined through exponentials, not through the sine/cosine/tangent of an angle on a circle. For an ordinary degree angle you would use SIN(RADIANS(degrees)), COS(RADIANS(degrees)), or TAN(RADIANS(degrees)) instead. Do not convert your numeric x using RADIANS merely because the old handbook says “Angle (radians).” Conversion is appropriate only if the specific mathematical model provides an angle input that requires it. Here COSH(x) takes the numeric x directly.

Locale and formula entry

Enter =COSH(A2) in the formula cell (the equals sign is important). In these English examples, 0.8 is a numeric decimal; locales using a decimal comma may require different input notation. The KDE English guide often writes semicolons between parameters of multi-argument functions, but COSH takes only one, so this guide needs no parameter separator. Use the installed function picker when entering localized workbooks; no localized Calligra binary was tested.

1. In a blank sheet, type Input x into A1 and COSH(x) into B1.
2. Enter the six numeric values shown below in A2:A7, one per cell. Do not type quotes around numeric entries.
3. Enter =COSH(A2) in B2; fill down through B7 so the references advance. These formulas refer only to the inputs in column A.
4. Display B2:B7 to eight decimal places for comparison. The expected numbers below were computed with Python’s math.cosh as a separate numerical cross-check on October 11, 2026; no Calligra runtime was used.

Interpretation: Hyperbolic cosine is even: COSH(-2) and COSH(2) are equal. For real inputs, the exact result is at least 1, with its minimum at x = 0. These are rounded expected values, not native program screenshots or measured spreadsheet outputs.

A second check without using COSH directly

COSH(x) may also be checked algebraically as (EXP(x)+EXP(-x))/2. The identity COSH(-x)=COSH(x) and the lower bound COSH(x)≥1 are exact for real x. Any near-equality comparisons after spreadsheet execution should allow floating-point tolerance.

A simplified mathematical catenary-style profile relative to its lowest point is y = a × (COSH(x/a) − 1), where a > 0 is a scale parameter and x is horizontal displacement from the centre. In E2 enter 10 (scale a). Put x = 0, 5, and 10 in F2:F4. In G2 enter:

=$E$2*(COSH(F2/$E$2)-1)

Copy G2 down through G4. Mathematically expected y values are 0.000000, 1.276260, 5.430806. The $E$2 absolute reference keeps the scale constant when copying. If you use a localized formula parser, the usual sheet reference convention should be verified in that installation.

This is a mathematical illustration, not a structural-engineering model. A real cable or chain calculation needs physical assumptions, forces and boundary conditions not established here. An independent check at a = 1, x = LN(2) is =COSH(LN(2)) → 1.25, since (2+1/2)/2=1.25.

• Confusing with ordinary COS: COS is circular and oscillatory. COSH is hyperbolic and for real inputs is never less than 1. Using degree conversion on this mathematical numeric parameter usually changes the intended problem.

• Symmetry misunderstanding: COSH(-x) = COSH(x); negative input does not imply negative output.

• Large inputs: The underlying exponentials grow quickly and can overflow a finite floating-point representation. Native overflow messages and limits in the shipped Calligra build are unverified.

• Inverse-domain traps: ACOSH is a separate inverse function and, for real arithmetic, requires input ≥1. It is not the same as ordinary ACOS. ACOSH(COSH(-2)) yields the principal nonnegative magnitude 2, rather than −2.

• Cancelling close values: For very small x, COSH(x)-1 is near zero and floating-point subtraction can lose relative precision. Format carefully and use domain-specific tolerance tests.

• Formula entered as text or with an unexpected value: Start a numeric formula with = and reference numeric cells. Values imported with units such as "2 units" are text, not documented numeric parameters; coercion and exact error codes can depend on locale and software version.

• Unexpected parsing or localized decimal marks: These examples use the English-language dot decimal mark and Calligra’s English documentation. In a locale with decimal commas, type inputs using the installed numeric convention. The official English examples separate arguments with semicolons where applicable; these three functions each accept exactly one argument, so no separator is required in their immediate calls.

• Result looks rounded, truncated, or stale: Increase column width, apply suitable numeric precision, and check the spreadsheet’s recalculation setting. Formatting does not change the mathematical definition. Do not assume a particular error dialog or return code without running the installed version.

• Floating-point differences: Expect small machine-precision discrepancies versus the rounded examples, especially after chaining multiple functions. These example values are for numerical verification within a sensible tolerance, not exact string equality.

Microsoft Excel and LibreOffice Calc also document this same one-argument hyperbolic function, so the fundamental real-number mathematical definition is compatible. A formula entered as =COSH(A2) is conceptually portable, with ordinary caveats for localized decimal marks, workbook import/export, text-to-number coercion, finite precision and application-specific error handling. No workbook was opened or evaluated in either other spreadsheet program; compatibility here is documentation-checked, not integration-tested.

The corresponding official references are Microsoft Excel COSH and LibreOffice Calc mathematical functions. On another system, review the version-specific function list rather than assuming numerical formatting or import behavior matches exactly.

• ACOSH, the corresponding inverse hyperbolic function. ACOSH is the principal inverse on inputs ≥ 1; because COSH is even, ACOSH(COSH(x)) = ABS(x) for real x, not necessarily x.
• SINH, COSH, TANH: related mathematical functions. These are official documentation links, not claims that corresponding tutorials are published on Spreadsheet-Tutorials.com.
• KDE Calligra Sheets formula-entry chapter for using formulas and the function picker.
• Calligra source, tagged release 26.08.2 and KDE 26.08.2 announcement for supported-source/version evidence.
• Excel COSH documentation and LibreOffice Calc mathematical functions for cross-spreadsheet documentation comparison.

These official references were accessed 2026-10-11. Related links were checked as documentation references; internal proposed URL /calligra/functions/cosh/ is not live or link-verified. No new page has been approved or published.

• Calligra Sheets — function documentation
• tagged KDE Calligra 26.08.2 trigonometry source
• LibreOffice Calc mathematical functions
• ACOSH
• SINH
• TANH
• KDE Calligra Sheets formula-entry chapter

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.