ATAN: Find the principal inverse tangent (arctangent) of a numeric ratio or slope. The returned angle is in radians. For a first check, see the six-row worksheet below. All shown outputs are expected values independently calculated from the documented mathematical function; they have not been observed in native Calligra Sheets.

ATAN reverses the tangent function on its principal interval. It maps a rise/run ratio to a radian angle, e.g. a ratio of 1 maps to π/4 radians (45°).

The output is the principal arctangent. It does not retain all quadrant information from an x/y point.

=ATAN(value)

The official KDE Calligra Sheets function list displays ATAN(Float) and describes its return value as floating-point. In that notation Float denotes the required numeric input; it is not a keyword to type in a formula. The function takes one required argument, with no documented optional parameters or default values.

• Argument: value — required numeric tangent ratio (for example, vertical rise divided by horizontal run); it is not an angle in radians or degrees. The result is the principal angle in radians, approaching the limits −π/2 and +π/2 for very large negative/positive finite inputs.
• Mathematical rule: angle (radians) = arctan(value); for finite real inputs, −π/2 < angle < π/2.
• Documented reference example: The KDE handbook gives ATAN(0.8) ≈ 0.67474094 radians and ATAN(0) = 0.
• Version and scope: This function is listed in the online KDE stable-KF6 handbook (the longer handbook is older than the current application) and separately identified in the recorded Calligra 26.08.2 source registry as func_atan in the trig module. The 26.08.2 KDE Gear release is dated October 8, 2026. Registry presence is release-scoped evidence, not a claim that a particular installed binary has been executed. Platform builds may differ; the Calligra download page focuses on Linux distribution packages/Flatpak and describes Windows work as ongoing.

Formula entry and locale: A formula cell begins with =. The KDE formula editor instructions use a semicolon (;) between arguments of multi-argument functions; ATAN itself has one argument. This page uses an English-style period for decimal numbers (for example, 0.5). Regional numeric formats, separators and localized display strings can differ; use Insert → Function to inspect the function help in your installed language, and never blindly convert between comma-decimal locales and the examples here.

1. In a blank sheet enter Label, Input, Result in A1, B1 and C1.
2. For DEGREES, type each formula beginning with = into B2:B7; for the other four functions, type the numeric values in B2:B7. The B column must contain numbers after entry; the examples contain no angle symbols in numeric cells.
3. Enter =ATAN(B2) in C2; copy/fill it down to C7, allowing each row reference to update naturally.
4. Format C2:C7 to six decimals for comparison. The table’s six-digit figures are rounded expectations, not exact binary-floating-point checks.

Check: Compare the inputs row-by-row. If a result differs, verify the numeric cell values, function spelling, formula entry, chosen input units and decimal display precision before concluding the function is wrong. The table’s expected six-decimal values were generated using independent Python math calculations.

A ramp rises 3 metres over a horizontal run of 8 metres. Put run 8 in E2 and rise 3 in F2. First form the dimensionless tangent ratio F2/E2, then convert the resulting radian angle:

=DEGREES(ATAN(F2/E2))

The independently calculated angle is 20.556045° to six decimal places. This is not 37.5°: F2/E2*100 is the 37.5% grade, which is a different unit from the angle. For E2 = 0, ordinary division is invalid, and for a vector pointing into another quadrant the principal-angle result is insufficient. Consider ATAN2 only after checking the exact argument order and behavior supported by your installed Calligra version.

• ATAN expects a ratio: ATAN(45) is inverse tangent of 45, not a 45-degree input.
• Radians output: ATAN(1) should give about 0.785398 radians. DEGREES(ATAN(1)) should display 45 degrees.
• Quadrant loss: ATAN(y/x) cannot distinguish coordinates with identical ratios but opposite signs. Do not assume it reconstructs every compass bearing or vector direction.
• Run = 0: dividing by zero to calculate slope is undefined. Check the run before computing a ratio.
• Mathematical limit vs exact endpoint: finite inputs approach ±90°, but do not reach the endpoint in exact real arithmetic.
• Unrecognized input/locale: keep ratios numeric and ensure =/parentheses are correct. No universal runtime error label is asserted.

Excel, LibreOffice Calc and Calligra document ATAN(number) as returning a principal radian angle; DEGREES converts it to degrees. ATAN2 is a different function: documented argument order and zero-coordinate error behavior must be compared separately rather than assumed identical across spreadsheet applications.

The equivalent operation and examples are documented in Microsoft Excel help and LibreOffice Calc mathematical-function help. Those sources were checked on 2026-10-11. They establish comparable documented mathematics, not proof of identical parsing, precision, platform support or worksheet import behavior.

• KDE handbook: ATAN syntax, input and sample, accessed 2026-10-11; older handbook revision must not be misrepresented as a complete 26.08.2 inventory.
• Recorded Calligra 26.08.2 trig-module source registration, linked from the repository’s release-scoped official catalogue; revision 72123cc643f6625351139e7df294544255a1056f. This source location was taken from the already verified source inventory; no native execution was done.
• KDE Gear 26.08.2 release announcement, 2026-10-08, checked 2026-10-11.
• KDE formula editing and semicolon conventions, checked 2026-10-11.
• KDE formula errors and recalculation, checked 2026-10-11.
• Microsoft Excel ATAN reference and LibreOffice Calc function reference, checked 2026-10-11.

• Calligra Sheets — function documentation
• KDE formula editor instructions
• Simple Sums troubleshooting guide
• LibreOffice Calc mathematical-function help
• Recorded Calligra 26.08.2 trig-module source registration
• KDE Gear 26.08.2 release announcement

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.