The TAN function returns the tangent of an input angle in radians. =TAN(0) is expected to return 0 and =TAN(RADIANS(45)) should be approximately 1. A typical use is converting an incline’s angle into a rise/run slope. Tangent becomes unbounded near 90° and 270°, so it needs special attention around vertical directions. These results are mathematical expectations, not observations from a Calligra installation.

=TAN(angle)

• angle: One required floating-point numeric value, expression or cell reference specifying an angle in radians. No documented optional arguments or defaults.
• Return: Floating-point tangent, conceptually SIN(angle)/COS(angle) for inputs where cosine is nonzero. Unlike sine and cosine, tangent has no finite universal magnitude bound.
• Evidence/version: The KDE official stable-KF6 function handbook documents TAN(Float), TAN(0) = 0 and TAN(0.7) about 0.84228838. The pinned 26.08.2 Calligra source registers TAN in its trig module; this is source evidence, not a native version test. Both sources checked 2026-10-11.

Start formula cells with =. The English handbook uses semicolons to separate parameters in multi-parameter functions; TAN itself has only one. Here decimal points and argument names follow English presentation; localized input conventions may differ. Use Insert → Function in the installed application to confirm formula conventions. Degrees must be converted with RADIANS(angle) or multiplied by PI()/180.

1. Enter the headings in A1:C1 and the numeric angles in B2:B6.
2. In C2 type =TAN(RADIANS(B2)), then copy down through C6.
3. Display six decimal places. The table avoids 90°, where mathematical tangent is undefined.

Interpretation: Positive/negative slopes come from the angle’s direction. Do not confuse TAN(45) (45 radians) with TAN(RADIANS(45)) (45 degrees).

Suppose the roof’s horizontal run is 10 metres and its inclination is 12 degrees. Enter E2 = 10, F2 = 12. In G2 enter:

=E2*TAN(RADIANS(F2))

Expected rise ≈ 2.125566 metres. If the goal is a percent grade, enter in H2:

=100*TAN(RADIANS(F2))

Expected grade ≈ 21.255656%. Note that if you format the H2 value as a percent instead, you should use =TAN(RADIANS(F2)) (expected 0.21255656 displayed as 21.255656%); multiplying by 100 and applying percentage formatting would incorrectly show about 2125.57%. These calculations are for illustrative geometry only, not building-code or engineering approval.

Handle nearly vertical angles before calculating

Tangent is undefined at 90° plus whole multiples of 180° in exact real arithmetic. An installed spreadsheet may return an enormous finite approximation instead of a clear numerical error when fed a floating-point representation of such an angle. For a threshold-based worksheet warning, try this proposed expression, placing a degree value in J2:

=IF(ABS(COS(RADIANS(J2)))<0.000000001;"Near vertical: do not use tangent";TAN(RADIANS(J2)))

Mathematically, the warning should appear for J2 = 90 and 270, and the tangent result should appear for J2 = 45. The exact IF evaluation behavior, localized decimal input, and value shown have not been tested in Calligra 26.08.2. Choose a tolerance suitable to the problem; this example uses 1e-9 for illustration, not as an accuracy guarantee. The site’s existing-source IF guide explains conditionals, but its live route was not reachable for verification.

• Degree/radian mismatch: Use RADIANS on degree values. This is by far the most common conceptual error.
• Vertical or nearly vertical line: The mathematical slope is undefined at odd multiples of 90°. Treat large numeric results near these angles as suspect, not measured slopes. Do not report a specific Calligra error code without native testing.
• Unexpected sign: Tangent is negative in quadrants II and IV and positive in I and III. Check angle conventions and the signed direction.
• Text masquerading as a number: Remove degree symbols or imported text formatting; enter a numeric cell value. A typed "12°" is not assumed to be a usable numeric argument.
• Formula parsing: Check leading =, parentheses, references and the function name. KDE documents #VALUE! as one symptom of an unrecognized expression; not every error is a syntax error.
• Narrow column or recalculation issue: KDE’s Simple Sums guide documents width warnings and manual Tools → Recalculate Sheet for sheets without automatic recalculation.

SIN, COS, RADIANS and ATAN are related documented Calligra functions, but these proposed guides are not yet claimed as live internal URLs. The existing-source IF guide is relevant to warning formulas; its presence in the owner’s snapshot is not publication proof. Calligra function index is a candidate navigation path that needs live checking before approval.

• KDE Calligra TAN entry, and RADIANS reference, stable KF6, accessed 2026-10-11.
• Pinned KDE Calligra trigonometric source, 26.08.2: registered name, not an execution test.
• KDE 26.08.2 announcement, release date 2026-10-08.
• KDE Simple Sums guide, input parsing and recalculation, checked 2026-10-11.
• LibreOffice Calc function documentation, and Microsoft’s RADIANS documentation, comparison sources checked 2026-10-11.

• Calligra Sheets — function documentation
• Simple Sums guide
• RADIANS reference
• Pinned KDE Calligra trigonometric source, 26.08.2
• KDE 26.08.2 announcement
• LibreOffice Calc function documentation

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.