CSCH Function (Gnumeric)

=CSCH(1) is expected to be approximately 0.85091813. Its result is negative for negative real inputs and the function is mathematically undefined at zero.

CSCH calculates the hyperbolic cosecant, the reciprocal of hyperbolic sine. It is useful when a model explicitly involves the reciprocal of SINH and the input cannot be zero.

CSCH(x)=1/SINH(x)=2/(EXP(x)-EXP(-x)) for nonzero real inputs within a numerical calculation range. CSCH(-x)=-CSCH(x) (odd symmetry). The function grows in magnitude without bound near zero; it decays toward zero for large positive and negative inputs.

=CSCH(x)

CSCH(x) — one required numeric argument x; no optional arguments or documented defaults. The Gnumeric manual describes x as a number. The hyperbolic input is not an ordinary geometric angle measured in degrees.

To read a source cell rather than a literal, use =CSCH(A2). Cell formulas begin with = in Gnumeric. A function with one argument has no multi-argument separator, so these examples avoid ambiguity between commas and semicolons. The tables use the English decimal-point convention, such as 0.5; Gnumeric’s local numeric format depends on locale and operating system. Check locale and spreadsheet parsing if your system expects a decimal comma. The identity statements below are mathematical deductions rather than quoted implementation promises. Formula-entry reference; Gnumeric locale reference.

The following table contains independently calculated mathematical expectations, not observed Gnumeric results. Expected numbers are rounded to eight decimal places for display; formulas may return additional digits. All examples use Gnumeric’s documented function syntax.

For a simple start, enter the first formula in any empty cell and verify that the result is plausible. Then copy a data-driven example into a column, replace constants with cell references and compare against an independent identity. If a near-singular formula gives a very large result, check the input’s domain before treating the cell as a measurement.

Worksheet table with values on both sides of zero

Enter the values -2, -1, -0.5, 0.5, 1, 2 in A2:A7, then use:

=CSCH(A2)

Copy down. Independently calculated expected results (to six decimals) are -0.275721, -0.850918, -1.919035, 1.919035, 0.850918, 0.275721. These exhibit the function’s odd symmetry. Do not include zero in an unrestricted denominator-based series.

Guard a zero input explicitly

When an input of zero is possible, a tutorial or dashboard may display a meaningful label instead of attempting an undefined calculation:

=IF(A2=0,"undefined",CSCH(A2))

This is a documentation-derived illustrative formula, not a Gnumeric-native execution result. Decide whether a text label, blank, or explicit error is appropriate for your downstream formulas. For high-sensitivity analyses, use a tolerance such as ABS(A2)<0.000001 if “near zero” should also be treated as unreliable—this is a modelling threshold, not a built-in domain rule.

Cross-check with SINH

For A2=1, compare =CSCH(A2) and =1/SINH(A2). Both independently calculated expected results are approximately 0.85091813. This relationship should be checked away from zero and away from machine-number extremes.

A reciprocal-response illustration

For a positive dimensionless input increasing from 0.5 to 3, CSCH decreases from approximately 1.91903475 to approximately 0.09982157. This is an illustrative mathematical response, not a validated physical or financial model.

• Zero is a singularity: SINH(0)=0, so CSCH(0) is mathematically undefined. The official Gnumeric paragraph does not specify the exact displayed error at zero; native observation is required before documenting it.
• Small nonzero values: Near zero, CSCH(x) is approximately 1/x and can be extremely large in magnitude. A tiny input error can have a huge effect.
• Do not confuse CSCH with CSC: CSC is 1/SIN(angle in radians) while CSCH is 1/SINH(x). The former is periodic; the latter is not.
• Cancellation/overflow: The alternate expansion 2/(EXP(x)-EXP(-x)) may lose accuracy near zero and overflow at large magnitudes. Prefer the named function for ordinary calculations; no native speed/precision claim is made.
• Numerical/coercion errors: Verify numeric data and check the exact Gnumeric error case natively; do not assume Excel’s #NUM! or #VALUE! behaviour applies identically.

How to diagnose a surprising value: inspect the underlying numeric cell, check units (radians versus dimensionless hyperbolic inputs), test a simple known case, compare with the identity only in a numerically safe range, and confirm the workbook’s locale. Record the application version and the exact error shown before adding specific product-error claims. The official short documentation does not fully specify behaviour for blanks, text values, machine overflow, or all singularities.

Gnumeric’s official manual currently calls CSCH not Excel compatible while also identifying it as OpenFormula compatible. Microsoft’s separate current documentation supports CSCH in Excel 2016, 2019, 2021, 2024 and Microsoft 365. The statements refer to different vendor documentation classifications and should not be collapsed into “absent from Excel.” Microsoft’s Excel documentation states |number| < 2^27 and named Excel error values; these are Excel rules only, not verified Gnumeric runtime rules. For older applications that lack CSCH, use 1/SINH(x) for x≠0, with attention to numeric range and error handling.

Compatibility may also depend on worksheet file format and the exact importer/exporter. Merely documenting a function in two programs does not prove bit-for-bit identical precision, error codes or conversion behaviour. See Gnumeric’s manual and Microsoft’s current CSCH documentation, accessed 2026-10-12.

Why is CSCH undefined at zero? Its denominator is SINH(0)=0.

Is CSCH a degree-based trig function? No. It takes a real numeric argument; do not apply ordinary degree-to-radian conversion automatically.

Is CSCH odd or even? It is odd: changing the input sign changes the output sign.

Can CSCH be computed without the named function? For a nonzero real input, calculate =1/SINH(A2) subject to the same mathematical singularity and numerical limitations.

SINH, COTH, SECH, CSC, IF.

The official Gnumeric reference establishes the function’s purpose and argument structure. The arguments and worked examples were editorially reviewed and the stated expected results were independently calculated.

Review date: 2026-10-12. No native application run: the worked outputs are documentation-based or independently calculated expectations, not measurements from installed Gnumeric. Ordinary numeric cases and the stated text-construction examples are checked; blank/text coercion, machine extremes and workbook round trips are not certified. The formula editor in your installed version is the authority for localized separators.

Example-check record · Editorial standards.