ACOS: Find the principal inverse cosine (arccosine) of a cosine value between -1 and 1. The result is in radians from 0 through π. 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.

ACOS reverses the cosine function on its principal interval. A cosine ratio of 0.5 corresponds to a principal angle of π/3 radians. It takes a cosine ratio, not the angle in degrees.

The output is the principal arccosine in [0,π] radians. Input domain is [-1,1].

=ACOS(value)

The official KDE Calligra Sheets function list displays ACOS(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 cosine ratio in [-1, 1]. The return is a floating-point angle in radians on the principal interval 0 to π. The handbook’s generic input comment mentions radians, but the input is a dimensionless cosine value, not an angle.
• Mathematical rule: angle (radians) = arccos(value); −1 ≤ value ≤ 1.
• Documented reference example: The KDE handbook gives ACOS(0.8) ≈ 0.6435011 radians and ACOS(0) ≈ π/2.
• 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_acos 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; ACOS 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 =ACOS(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.

The law of cosines connects the three sides of a triangle with their included angle. Put side lengths 3 (E2), 4 (F2), and the opposite side 5 (G2) in metres. The angle between the sides of lengths 3 and 4 is:

=DEGREES(ACOS((E2^2+F2^2-G2^2)/(2*E2*F2)))

Expected result: 90° because the cosine ratio is (9+16−25)/24 = 0. For other dimensions, require E2 and F2 to be positive and the three lengths to satisfy triangle inequalities; division by zero or a cosine ratio outside [-1,1] indicates an invalid set of sides. Data rounded to a few digits may also nudge a borderline ratio outside its valid range; do not silently clamp an impossible triangle.

• Wrong input type: ACOS(60) is not “acos of sixty degrees.” ACOS expects a cosine ratio, never a degree measure.
• Input outside [-1,1]: ACOS(1.1) has no real-valued result; native Calligra error text was not checked.
• Radians vs degrees: ACOS(0.5) gives about 1.047198 radians; DEGREES(ACOS(0.5)) is 60 degrees.
• Principal branch: the returned angle is 0 to π only. Other geometrically equivalent rotations require contextual handling.
• Precision near ±1: inverse cosine is sensitive to small input changes near its endpoints. Avoid rounding measurement ratios before calculating if precision matters.
• Geometry data quality: validate units, triangle inequality and nonzero side lengths before using the law-of-cosines formula.

Excel, LibreOffice Calc and Calligra all document principal ACOS in radians, typically followed by DEGREES for a human-readable angle. Locale punctuation, numeric rounding and invalid-argument errors can differ; no cross-app execution was performed.

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: ACOS 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 ACOS 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.