CSCH in Calligra Sheets: Syntax, Examples and Zero-Input Limits

• Introduced: Documented by 26.08.2; original introduction not established.
• Availability: Supported in Calligra Sheets 26.08.2, based on the function-specific registration.
• Scope: The official application listing provides Linux installation; other packaged builds are unverified here.
• Checked: October 14, 2026. Documentation/source check; no new native test in Calligra Sheets 26.08.2.

Use CSCH for the hyperbolic cosecant of a real number: the reciprocal of SINH. For example, =CSCH(1) has an independently calculated expected result of approximately 0.8509181282. The pinned source calls calc->sinh and divides 1 by it; this establishes the intended operation, not an observed application result. [E1, E2, E3]

The defining operation is 1/sinh(x). The hyperbolic sine/cosine function is not the same as ordinary circular sine/cosine. The numerical expectations below were independently calculated with Python’s mathematical standard library; no formula has been run in a native Calligra Sheets installation. The function’s presence in the KDE handbook and 26.08.2 source proves documentation/registration, not installed-package availability. [E1, E2]

=CSCH(number)

KDE’s shipped function-description XML gives the literal syntax CSCH(Float), with one <Parameter> of type Float and a floating-point return type. The sole required argument is a real numeric value or cell reference containing a number. No second argument, mode switch or default is declared. The source wrapper reads args[0] and forwards it into the corresponding hyperbolic calculation (SINH). The definition is 1/sinh(x). [E1, E2]

Mathematical domain: All finite real inputs except zero in the mathematical definition. For x=0, sinh(0)=0, so the reciprocal is undefined. Exact Calligra display/error labels have not been measured. [E2, E3]

Radian and locale notation: KDE’s XML calls the argument an “Angle (radians).” The trigonometric-family nomenclature should not be mistaken for ordinary periodic sine and cosine: SINH/COSH define hyperbolic functions. For any workflow that explicitly starts from degrees, convert the intended angle with RADIANS first; in many exponential/hyperbolic models the input is simply a dimensionless number x. The one-argument formulas do not require an argument separator; multi-argument examples here use semicolons as in KDE’s English handbook (=ROUND(CSCH(1);6)). A localized installation may require different decimal/list separators; check the formula editor in that specific installation. [E1, E5]

Version and platform: This guide is scoped to Calligra 26.08.2 (KDE Gear release 2026-10-08), source commit 72123cc643f6625351139e7df294544255a1056f. Official docs and source checked 2026-10-13 UTC. KDE distributes Calligra across packages that may differ by operating system or release; no Linux Flatpak, distribution-package, or Windows execution was performed. The catalogued function is not independently runtime-certified by this manuscript. [E1, E2, E4]

1. In a blank worksheet, enter Input x in A1 and CSCH(x) in B1. Optionally enter Reciprocal reference in C1.
2. Enter the nine numeric values shown in column A, one per cell A2:A10. Enter them as numbers without quotes and use the locale’s decimal syntax.
3. Enter =CSCH(A2) in B2 and fill/copy down to B10. In C2 enter =1/SINH(A2) and fill down if you want a second spreadsheet expression to compare. It relies on the same underlying family of calculations; this is not an independent native cross-platform test.
4. Format B (and C, if used) to roughly ten decimal places. Compare with the expected results below, which are independent mathematical calculations. A blank cell, text, error or unusual locale may behave differently; those cases were not native-tested.

Calculation method: for CSCH, Python 3 calculates 1/math.sinh(x) using the exact x-values above, before formatting the decimal output to ten places. For example, the pinned KDE XML example CSCH(PI()/2) reports approximately 0.434537208. Independently calculating 1/math.sinh(math.pi/2) reproduces that value (up to rounding). [E1, E2, E3]

A calculated value is not a statement that a native Calligra sheet was executed. Slightly different trailing digits can occur from floating-point rounding. The source proof and calculated expectations are kept separate in this guide. [E2, E3]

• Odd symmetry: mathematically, CSCH(-x)=-CSCH(x) for every valid x. [E3]
• Do not substitute an ordinary function: CSCH is not the same as CSC. A hyperbolic function is based on exponential identities, unlike the ordinary reciprocal sine function. [E2, E3]
• KDE handbook cross-check: The pinned KDE XML example CSCH(PI()/2) reports approximately 0.434537208. Independently calculating 1/math.sinh(math.pi/2) reproduces that value (up to rounding). [E1, E3]
• Important edge: =CSCH(0) is undefined mathematically; the pinned wrapper performs division through Calligra’s calculation engine without a locally explicit zero guard. Do not promise the exact displayed error without a native Calligra test. [E2, E3]

To audit a positive or negative nonzero input in D2, enter 1 in E1 as a reminder of the reciprocal operation, and compare =CSCH(D2) in E2 with =1/SINH(D2) in F2. Set D2 = 2: both expressions have the independently calculated expectation 0.2757205648. The source implementation is itself a reciprocal-SINH calculation, so these two spreadsheet formulas are not independent implementation tests; agreement only checks formula wiring and rounding. A separate Python standard-library math.sinh evaluation was used to calculate the table.

For a numerical identity test on a nonzero input, enter =ROUND(SINH(D2)*CSCH(D2);9) into G2; the expected result is 1.000000000. This is a derived mathematical consistency check, not a native result and not a vendor-provided example. At D2 = 0 the identity is invalid because CSCH is undefined. Very large magnitudes can overflow/underflow intermediate computations; compare moderately sized inputs first. [E2, E3]

When x approaches zero, sinh(x) approaches x and CSCH(x) grows in magnitude like 1/x. Put 0.1, 0.01, and 0.001 in H2:H4, and place =CSCH(H2) in I2 (copy down). Expected values are approximately 9.983352757, 99.998333353, and 999.999833333 respectively. They are expected mathematical values, not runtime observations. The large changes make this unsuitable as a stable substitute for a zero-input handler in models with noisy measurements. If zero is meaningful in your application, define an explicit business-rule outcome rather than silently substituting a tiny number. [E3]

The following table distinguishes mathematical limitations, source-inferred details, and untested native behavior. The exact displayed errors in a real 26.08.2 build are not confirmed by source registration alone. [E2, E3]

Numerical precautions

1. Prefer moderate finite inputs for cross-checking. The reciprocal calculation calls a hyperbolic function first; the result may be very small or involve a very large intermediate for extreme inputs. The exact precision, overflow and display behavior varies by platform and was not tested in Calligra. [E2, E3]
2. Check any source data for numbers stored as text, unexpected locale decimal punctuation and formulas that already contain errors. The XML’s Float type does not, on its own, establish all coercion rules. [E1, E5]
3. When comparing two systems, check meaningful sample values and edge cases. A mathematically equal positive number does not prove equivalent error handling, rounding or formatting. [E2, E6]

Microsoft’s official Excel CSCH reference documents the same named mathematical operation with one required numeric argument in radians. For ordinary finite numeric inputs, the source-described Calligra expression and Microsoft’s documented Excel function have the same mathematical definition; this is not a claim that importing a workbook has been tested in either program. [E2, E6]

Excel’s documentation imposes an absolute argument bound below 2^27 and specifies Excel #NUM! outside its constraints and Excel #VALUE! for nonnumeric input. Those are Excel-specific documented rules; the pinned Calligra wrapper has no identical explicit bound at its own call site, and the exact Calligra error display, numeric range, import handling and Excel parity remain unverified. Do not copy the Excel limits into a Calligra reference as if they had been natively established. [E2, E6]

Portability check: confirm the Calligra/Excel version, formula name, data types, decimal/list separators, zero and very large inputs, and calculated values. Other spreadsheet programs need their own official, version-specific evidence; this guide does not assert their runtime behavior.

Is CSCH the same as CSC? No. CSC(x)=1/SIN(x) is the ordinary cosecant; CSCH(x)=1/SINH(x) is the hyperbolic cosecant. The two functions generally return different values.

What is CSCH(0)? Mathematically undefined because the denominator is zero. The exact Calligra cell error has not been observed in a running instance.

Can the answer be negative? Yes: CSCH(-1) is expected to be approximately -0.8509181282; odd symmetry applies.

• SINH in Calligra Sheets.
• COSH in Calligra Sheets.
• PI in Calligra Sheets.
• RADIANS in Calligra Sheets.

For first-party instructions, see the KDE Calligra Sheets function handbook, pinned 26.08.2 XML, pinned C++ registration/implementation and formula editor help. Source links were checked 2026-10-13 UTC. [E1, E2, E5]

The numbered references support the claims above at the indicated scope. Access/verification date: 2026-10-13 UTC.

• [E1] KDE Sheets official handbook — CSCH and release-pinned trig.xml — registered user-facing syntax CSCH(Float), one Float parameter, floating return, handbook example. The HTML handbook is not a native release execution.
• [E2] Pinned trig.cpp registration and C++ wrapper — source-level registration and expression 1/sinh(x). The released wrapper calls calc->div(1,calc->sinh(args[0])); native display/error behavior was not observed.
• [E3] The displayed inputs and outputs were independently checked with Python standard-library hyperbolic functions and arithmetic; these are mathematical expectations, not Calligra executions.
• [E4] KDE Gear 26.08.2 release announcement, dated 2026-10-08, release-scope only; pinned source revision 72123cc643f6625351139e7df294544255a1056f.
• [E5] KDE Sheets formula editor — formula entry and locale considerations; not a native test of this page.
• [E6] Microsoft Excel official CSCH documentation — Excel one-argument syntax, 2^27 limit and Excel-specific errors, not Calligra proof.

Validation: Official documentation and pinned source reviewed; examples independently calculated. Native Calligra execution and screenshots were not performed.