POLR in Calligra Sheets: Find a Cartesian Point’s Radius

POLR converts a point’s Cartesian x and y components into its nonnegative distance from the origin: =POLR(X;Y). The official reference documents =POLR(12;0) → 12 and =POLR(12;12) → approximately 16.9705. The independent precise mathematical value of the second is 16.9705627485. Both parameters must be numeric components in x; y order. KDE function handbook; pinned source.

This is a source/documentation-verified numerical guide, not a claim of running the Calligra function in a live application.

For point (x,y), the polar radius is the Pythagorean length of its vector from (0,0):

r = √(x² + y²)

The 26.08.2 func_polr wrapper squares each parameter, adds the squares and calls the Calligra sqrt helper. The result has no direction information and is the same for (3,4), (−3,4), (3,−4) and (−3,−4). POLR is therefore suitable for lengths and radii, not headings or quadrants. Unlike POLA, the source does not divide by the radius, so a zero vector has an independent mathematical expected radius of 0. The actual UI has not been tested. Pinned code; official documented examples.

=POLR(X;Y)

Both are required, with no optional arguments/defaults in the official XML metadata and an explicit two-argument source registration. A numeric cell reference or numeric expression may be used. Input is x first, y second, not y;x, not an angle and radius pair. English examples use semicolons. Formula-entry instructions show how to use Insert → Function and may need localized decimal separators when installed elsewhere. KDE handbook; pinned metadata; pinned C++ registration; KDE function dialog.

Version scope: Documentation read alongside the official 26.08.2 source (released October 8, 2026). No native application, package, OS or locale was used to observe results. KDE release list.

1. Start a blank Calligra sheet. In row 1 put Point (A1), x (B1), y (C1), POLR (D1), and Companion value, independent model (E1).
2. Enter the numeric x and y components for rows 2 through 12 as listed. Use numbers (not quoted strings), including negative signs. The zero-vector case in row 11 is intentionally reserved for troubleshooting.
3. In D2 enter =POLR(B2;C2) and copy/fill down through D12. Format to nine decimal places to compare expectations. The companion values are independently calculated rather than native results.
4. For the zero vector, do not treat a purely mathematical expectation as evidence of Calligra’s UI error display. The table explicitly differentiates the pinned source-level outcome where relevant.

The values were calculated outside Calligra with Python math.hypot(x,y) for radius and math.acos(x/math.hypot(x,y)) for the inspected POLA algorithm when radius was nonzero. This is an independent numerical model following the pinned implementation, not a native function invocation. The expected values are rounded; output may differ in the least significant displayed decimal through floating-point conventions. [KDE XML metadata](https://github.com/KDE/calligra/blob/72123cc643f6625351139e7df294544255a1056f/sheets/functions/conversion.xml); pinned calculation code.

Suppose you record start coordinates (A2=2, B2=3) and destination (C2=5, D2=7). Compute deltas Δx=3, Δy=4 using:

=POLR(C2-A2;D2-B2)

Independently expected distance: 5 units. This is a straight-line planar distance, not road distance or geographic distance on a spherical Earth. If you are measuring geographical latitude/longitude, a different model is needed. The expression mirrors =SQRT((C2-A2)^2+(D2-B2)^2) mathematically for ordinary finite numeric values. POLR wrapper; KDE SQRT reference.

Put object x in B2, y in C2 and allowed distance from the origin 5 in D2:

=IF(POLR(B2;C2)<=D2;"Within radius";"Outside radius")

For (3,4), independently expected Within radius at a threshold of 5. For (6,8) independently expected Outside radius, because the radius is 10. The IF function is available as Calligra’s source-registered spreadsheet function, but this combined formula has not been executed natively. This is a useful geometric filter that keeps x/y signs intact even though POLR itself ignores sign in the result. POLR source.

If radius 10 and angle =PI()/6 produced coordinates through CARX and CARY, the reconstructed radius can be checked with:

=POLR(CARX(10;PI()/6);CARY(10;PI()/6))

Independently expected 10 within floating-point rounding. This identity is a consistency check; it cannot recover the original angle or quadrant. These companion names are independently registered functions in the source. KDE conversion-module source.

Error-message integrity: No source branch in func_polr explicitly returns a named error for (0,0). That does not authorize claiming all input types succeed or a particular error display. Pinned code.

The Pythagorean expression =SQRT(x^2+y^2) is a mathematical alternative for finite numeric inputs, using the KDE-documented SQRT function. In a Calligra worksheet, =POLR(B2;C2) can be compared with =SQRT(B2^2+C2^2). Calligra’s specific POLR name, internal overflow behavior and error coercions must not be assumed to exist identically in another spreadsheet. No Excel, Sheets or LibreOffice runtime tests were performed. KDE POLR; KDE SQRT.

Why not use POLA for distance?

POLA is an angle function, not a distance function. The pinned implementation of POLA calls POLR first, divides x by the resulting radius and takes inverse cosine. Its angle can lose the sign of y; the two functions are complementary for a specific source implementation but do not by themselves guarantee a full directional reconstruction. Source of both implementations.

Explore the related mathematical functions below:

• SIN in Calligra Sheets — sine of a radian angle.
• COS in Calligra Sheets — cosine of a radian angle.
• PI in Calligra Sheets — reference for π and the unit circle.
• RADIANS in Calligra Sheets — degrees to radians.
• DEGREES in Calligra Sheets — radians to degrees.
• SQRT in Calligra Sheets — square root; useful for vector length.
• ACOS in Calligra Sheets — inverse cosine; useful for understanding POLA’s implementation.

CARX and CARY calculate Cartesian components; POLR calculates length. POLA has a separate source-level quadrant limitation described above.

Evidence and dated verification

Research checked on 2026-10-13 UTC:

1. KDE Sheets function handbook — this function documents function name, syntax, argument labels, return type and examples. Its handbook text is not proof of runtime behavior on every version.
2. KDE Calligra 26.08.2 pinned conversion.xml specifies the two ordered Double parameters and related functions.
3. KDE Calligra 26.08.2 pinned conversion.cpp registers the function and reveals its implementation, including caveats the handbook omits.
4. KDE Sheets formula-entry instructions document Insert → Function, the = formula format and the semicolon between arguments in the English handbook.
5. KDE Calligra Sheets release list identifies 26.08.2 as released October 8, 2026.

What was and was not validated: Documentation inspection: yes. Version-pinned source review: yes. Mathematical outputs: independently calculated in Python’s standard math module. Native Calligra execution: no. No Linux, Windows, Flatpak or other platform build was run; no locale-specific execution or UI screenshots were captured.