SEC in Calligra Sheets: Syntax, Radians, Examples and 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.

The SEC function returns the secant of an angle, mathematically 1 divided by the cosine. A quick reproducible example is =SEC(RADIANS(60)), whose independently calculated expected result is approximately 2. This result has not been observed by executing a formula in a native Calligra Sheets installation. [E1, E2, E3]

The rule is 1/cos(x). Any real angle in radians provided its cosine is nonzero. The pinned Calligra source, not merely a similar function in Excel, is the basis for the syntax and interpretation described here. [E1, E2]

=SEC(number)

• Required argument (one): Angle in radians (not degrees). The Calligra 26.08.2 XML has one <Parameter> of type Float; the function is registered without an extra optional argument or default. The official XML syntax is SEC(Float). [E1, E2]
• Return: a floating-point number. The XML return type is Float and the pinned implementation is a floating calculation. [E1, E2]
• Spreadsheet entry: type the initial = before the function. These examples use the English KDE documentation convention: decimal point and semicolon between arguments in multi-argument formulas (for example =ROUND(SEC(0);6)). Decimal and list separators can vary with operating locale; confirm them in the user’s installation rather than replacing commas or semicolons blindly. [E1]
• Verified scope: Calligra 26.08.2, released 2026-10-08, at pinned revision 72123cc643f6625351139e7df294544255a1056f; source/documentation accessed 2026-10-12. This proves registration and source semantics for that release, not actual behavior of an installed distribution package or particular OS. [E1, E2, E5]

Mathematical domain/limits: any real angle in radians provided its cosine is nonzero. The secant is undefined at 90°, 270° and every other angle of 90° + 180° × integer (π/2 + kπ radians). Native displayed error messages and package-specific numerical limits are not established by this guide. [E2, E3]

Put Degrees in A1, Secant in B1, and Formula in C1. Enter the listed degree values in A2:A7, type =SEC(RADIANS(A2)) in B2, then fill down through B7. Put the literal text =SEC(RADIANS(A2)) in C2 only as a label if you want a formula reference; do not type it as an evaluated formula there. [E1, E3]

How to check the results: For B2, the input 0° converts to 0 radians and cos(0)=1, so SEC(0)=1. At 60°, cos(π/3)=0.5, therefore the secant is 2 (rounding may display 2.0000000000000004). For 120°, cosine is −0.5, so secant is −2. All calculated results are expected approximate numbers based on Python’s independent standard-library trigonometric functions, not observations in Calligra. Differences of a few trailing digits are normal with floating-point evaluation. [E3]

Practical formula check

Check the cosine independently: In D2 enter =COS(RADIANS(A2)). Multiplying =B2*D2 should be approximately 1 for defined, well-conditioned inputs. That numerical identity is a cross-check rather than proof of how the application evaluated the formula. To display six decimals in an English-locale example, use =ROUND(SEC(RADIANS(60));6); decimal and argument separators can differ by locale. [E2, E3]

Suppose the adjacent side of a right triangle is 12 cm and its acute angle is 60°. Set E2=12 (adjacent length) and F2=60 (degrees). In G2 enter =E2*SEC(RADIANS(F2)). The independently calculated expected hypotenuse is 24 cm, since 12 × (1 / cos 60°) = 24. Use this geometry only for an acute right-triangle angle, where cosine and the measured lengths are positive. With F2 = 45°, G2 is approximately 16.9705627485 cm. When the angle nears 90°, the secant becomes extremely sensitive to the angle and tiny rounding differences. [E3]

• Undefined points: If the input is 90° or 270° (or another π/2 + kπ angle), the mathematical secant is undefined. The pinned function wrapper delegates division to the underlying calculation engine and does not guarantee a particular on-screen error. A formula using PI()/2 can also evaluate to a very large finite number because of floating-point approximation. Do not treat that as a meaningful secant. [E2, E3]
• Degrees entered as radians: =SEC(60) computes secant of 60 radians, not 60°. Use =SEC(RADIANS(60)) for degrees. [E2, E3]
• Poor numerical stability: Near an undefined angle, small rounding or measurement errors make very large changes in the result. Avoid using secants near 90° + 180° × k for engineering calculations without a numerical stability review. [E2, E3]
• Text and blank inputs: Official metadata expects one float. Locale-dependent text coercion, empty-cell treatment and displayed error strings were not tested in native Calligra. Use numeric references and investigate errors with a small reproducible sheet. [E2, E3]
• Large angles: Excel documents a 2^27 magnitude constraint for its SEC implementation; do not infer the same Calligra constraint from Excel documentation. Precision for large radian angles remains unbenchmarked here. [E2, E3]

Microsoft Excel documents SEC(number) with an input in radians and the same reciprocal-cosine mathematics on valid numeric examples. Excel additionally documents its own #NUM!/#VALUE! behavior and a magnitude constraint on the argument. No evidence in the pinned Calligra wrapper establishes the same Excel limit or on-screen errors. Do not automatically transplant these Excel diagnostics to Calligra. Other spreadsheet programs may support the same named function, but their availability and exact error semantics were not native-tested in this run. [E2, E4]

Portability checklist: make a local copy of your workbook; verify radians versus degrees; check decimal/list separators; compare a simple expected result; deliberately test boundary/error cases in the destination program before relying on a high-stakes numerical result. This guide does not claim an Excel or LibreOffice runtime test.

Can I use degrees directly? No. The pinned function expects radians; wrap degree numbers in RADIANS(...).

Is the result exact? No promise of bit-for-bit equality is made. These functions use floating point; table figures are rounded expected values. [E2, E3]

What happens at problematic values? The secant is undefined at 90°, 270° and every other angle of 90° + 180° × integer (π/2 + kπ radians). If a formula produces a surprising number or displayed error, confirm it on native Calligra and check the exact input units and numeric precision. The source wrapper is not a native screen test. [E2]

COS gives the denominator of SEC; RADIANS converts degrees to radians; DEGREES converts radian angles back to degrees; PI supplies π; CSC is the reciprocal of sine. These exist in the verified Calligra 26.08.2 function registry. The links below point to the official references. [E1, E2]

Read the official KDE Sheets function reference for current HTML help, the pinned Calligra 26.08.2 function definitions for declared syntax and the pinned implementation for source-level behavior. These are official external links, checked 2026-10-12. [E1, E2]

[E1] KDE official Sheets function handbook — SEC and the pinned 26.08.2 XML (function entry around L306-L319), accessed 2026-10-12; official one-argument syntax/type and supplied examples.

[E2] Pinned 26.08.2 C++ implementation and registration, verified 2026-10-12. Source-inferred behavior, not native execution. The official pinned XML labels the input as an angle in radians and gives SEC(0)=1. The pinned C++ source does calc->div(1, calc->cos(args[0])); the return/error handling of an exact zero denominator belongs to deeper engine logic and has not been executed here.

[E3] Independent calculations using Python 3 standard-library math with the exact input values shown above; expected numbers only.

[E4] Microsoft official Excel SEC documentation, accessed 2026-10-12, used for claims about Excel, not to infer Calligra error semantics.

[E5] KDE Gear 26.08.2 release announcement, dated 2026-10-08; pinned source revision 72123cc643f6625351139e7df294544255a1056f.

Validation: Official documentation and version-pinned source reviewed; examples independently calculated. No native Calligra execution was performed.