CSC Function (LibreOffice Calc)

• Introduced: LibreOffice 3.5.
• Availability: Supported in LibreOffice 26.8.1.1, verified against its function registry. This identifies a supported release, not a final working version.
• Scope: Desktop Calc, using the English function name. Availability in other spreadsheet applications is separate.
• Checked: 2026-10-14 — function reference; versioned support. Release availability is source-checked. The native examples below have their own named development-build scope.

Quick answer: =CSC(0.5) has mathematical value approximately 2.085829642933, matching the ordinary development-build example below.

CSC is the reciprocal of sine: CSC(x)=1/SIN(x). Its argument is an angle measured in radians. A valid finite result is a real number, with the same sign as sine and magnitude at least 1. The reciprocal is different from ASIN, which takes a sine value and returns an angle. Pinned LibreOffice evaluator.

=CSC(Number)

Supply one numeric argument. If your source measurement is in degrees, convert it with RADIANS before calling CSC; already-radian values need no conversion. A referenced empty cell is converted to zero in the tested call. The Boolean TRUE becomes 1. Those coercions are worksheet behavior, not a substitute for validating the angle data.

These formulas were recalculated through XLSX import in LibreOfficeDev 26.8.0.0.alpha0, build 2c87e51eeaa2b413ff4ae097b2705eea1995d8e5. Saved values agree with independent high-precision mathematics. Values below are rounded to twelve decimal places; scientific notation uses thirteen significant digits.

Make the angle units explicit

If A2 contains a 30-degree angle, enter =CSC(RADIANS(A2)) in B2. The ideal mathematical result is 2, and the corresponding literal formula was recalculated in the development-build checks below. If A2 instead stores radians, use =CSC(A2). Mixing the two conventions produces a plausible number for the wrong angle.

For an acute right triangle, cosecant is hypotenuse divided by opposite-side length. With an opposite side of 5 and angle 30 degrees, the hypotenuse is 5×2=10. The model requires the appropriate geometric angle and side definitions; a raw cosecant is a ratio, not a length.

Check reciprocal and symmetry identities

For x=0.5 radians, CSC(x) is approximately 2.085829642933 and CSC(x)×SIN(x) is mathematically 1. Negating x negates the result. Another identity is CSC(x)^2−COT(x)^2=1 away from the poles. These are useful moderate-input checks, not guarantees of exact floating-point cancellation.

Distinguish an exact pole from a rounded angle

Mathematically, sine is zero at integer multiples of π, and cosecant is undefined there. Calc’s PI() is a finite floating-point approximation. CSC(PI()) and CSC(2*PI()) therefore evaluate near the ideal poles and can return very large finite numbers. The native diagnostics retain what actually happened in the named build.

An equality guard such as IF(SIN(A2)=0;...;CSC(A2)) detects a computed zero denominator. It does not reliably identify angles intended to represent every exact multiple of π. If near-pole values are unsuitable for your model, specify a tolerance or minimum acceptable |SIN(A2)| based on the model’s accuracy needs. There is no universal cutoff suitable for all units and applications.

At exact numeric zero, the reciprocal is undefined. The table below records the native error display rather than assuming it must be the same error code as a separately entered division formula. Do not treat an ODS numeric cache of zero as a successful zero result when the cell has an error. Non-numeric text and an extra argument are separate invalid-input cases. Large finite near-pole outputs are mathematically sensitive, so more printed digits do not make them reliable.

Development-build diagnostics

In this run, zero and a blank reference produced #NUM!. The additional formulas use the same headless import path. H5 is an actually empty cell. The table uses saved numeric values or exact error displays; retained application display text can round a numeric value differently in its last printed place.

SIN, COT, ASIN, RADIANS, DEGREES.

The LibreOffice 26.8.1.1 source evaluates a reciprocal of the sine function. Native observations cover only the eight reference formulas and listed diagnostics in the named development build. A deliberately stale SUM cache changed from 999999 to 3 and an uncached SUM returned 7 after forced recalculation. Formula identities, error displays and blank input were checked. Other composite explanations are mathematical checks; no stable-release, GUI or exhaustive extreme-input behavior is inferred.