SMALL in Calligra Sheets: Find the k-th Smallest Value

SMALL returns the numeric value at ascending position k. With k=1, it gives the minimum; with k=2, the second entry in sorted ascending order. Repeated values occupy separate positions. The KDE handbook documents SMALL(range; k) and its example SMALL(A1:A3;1) on values 3, 1 and 5 as 1. Official KDE function reference; 26.08.2 implementation.

=SMALL(A2:A9;2)

The independent expected result for the reproducible eight-score dataset is 7. This is a mathematical calculation, not a native Calligra test.

=SMALL(range; k)

• range (first, required): numeric cell range or array; XML documents a range of Double values and the registration enables array arguments.
• k (second, required): integer position from the smallest value, starting at 1. k=2 does not mean return the second distinct value.
• Return type: number (KDE’s XML calls it Float); values themselves rather than rank positions or addresses.
• Defaults/arity: the C++ registration specifies exactly two required arguments, and there is no documented default. The function converts k to integer internally; fractional/text conversion behavior should not be assumed without a native test. KDE SMALL XML; function registration; implementation.

1. Open a blank sheet in Calligra Sheets. Enter Score in A1.
2. Enter these eight numeric values, not quoted text, in the cells shown:

3. In an unused cell, type each formula below with the leading equals sign. For an ordinary English-language setup, use the semicolon argument separator documented by KDE. Press Enter to evaluate it in your own installed application.
4. For independent cross-checking, ascending order is 4, 7, 7, 12, 12, 15, 20, 30; descending order is 30, 20, 15, 12, 12, 7, 7, 4. The two 7s and two 12s are intentional and make ties observable.

All results below are independently derived mathematical expectations, not screenshots or observed outputs from a running copy of Calligra. The examples avoid blanks and text because the pinned implementation’s array helper converts entries to floating point values instead of visibly skipping every non-numeric type. Do not extrapolate Excel’s text/blank rules to this Calligra source.

COUNT(A2:A9) independently equals 8 for this all-numeric dataset. The combined COUNT/SMALL formula is a documentation-and-math expectation, not a tested Calligra composite. For a three-number sanity check, enter 3, 1 and 5 in A1:A3 of a separate sample sheet; KDE’s documented SMALL(A1:A3;1) should give 1. SMALL handbook; COUNT handbook.

Lowest-three cutoff: In B2, enter =A2<=SMALL($A$2:$A$9;3) and fill B2:B9. SMALL(...;3) is 7; the eight expected flags are FALSE, TRUE, FALSE, TRUE, FALSE, FALSE, FALSE, TRUE. This selects the three lowest entries 7, 7 and 4, not three distinct score values. The comparison result is a boolean, not a ranking position.

Lowest-five cutoff: =A2<=SMALL($A$2:$A$9;5) sets a threshold of 12. Because 12 is duplicated, it selects five entries in this dataset: 4, 7, 7, 12, 12. If you need exactly four lowest rows, SMALL(...;4) yields the same 12 threshold and a comparison <= would still select five. A tie-breaking rule must be chosen separately, not silently assumed.

Dynamic requested position: Put k values 1, 4, 8 in B2:B4. Set =SMALL($A$2:$A$9;B2) in C2 and copy it down. Independently expected C2:C4: 4, 12, 30. The $ fixes the range on copied formulas, as explained in KDE’s absolute reference guidance.

Comparing percentile-like positions: SMALL takes an integer order-statistic position; it does not interpolate between observations. Do not automatically substitute it for KDE’s separate PERCENTILE function, which has a different statistical meaning and implementation.

The inspected body begins its internal counter at 1 and increments it when collecting values. This counter is not a user-facing 0-based index; the return uses array.at(k-1). If your installed package differs, record its version and exact formula before concluding a documentation error. Helper implementation; SMALL body.

SMALL(A2:A9;1) gives the same independent result as MIN(A2:A9) (4) for clean numeric cells. SMALL(A2:A9;8) is 30, while LARGE(A2:A9;1) is 30. RANK(7;A2:A9;1) asks for the ascending rank of 7 rather than returning a value at a chosen position; that rank is 2, including the tied 7. PERCENTILE can interpolate and must not be treated as a synonym for SMALL.

1. KDE SMALL reference — purpose, arity, parameter types and example; checked 2026-10-13.
2. KDE 26.08.2 statistical XML — typed arguments and syntax; checked 2026-10-13.
3. Version-pinned registration — registration and two parameters, accepting arrays; checked 2026-10-13.
4. Version-pinned source body and array helper — sorting, index formula and error branches; checked 2026-10-13.
5. KDE formula entry/absolute references — =, semicolons, copy behavior; checked 2026-10-13.
6. Release notice, application listing, download guidance — date and platform; checked 2026-10-13.

This review is scoped to Calligra Sheets 26.08.2 from KDE Gear, officially dated 8 October 2026. The exact registered function and parameter counts were inspected in the KDE source at commit 72123cc643f6625351139e7df294544255a1056f and the official KDE XML function descriptions. KDE release notice; Calligra Sheets release listing; version-pinned function registry; XML descriptions. Registration and handbook presence demonstrate source/catalogue availability, not successful execution on a particular installed package.

KDE’s formulas guide says formulas begin with =; argument separators are semicolons in its examples; function names are case-insensitive; absolute references such as $A$2:$A$9 resist movement when filled. A locale or packaged build can behave differently: alternate decimal symbols, argument separators, language, and parsing were not tested. The review formulas use period decimals (where applicable), standard A1 references, and semicolons.

KDE’s download page documents Linux distribution installation and Flatpak and says Windows availability is still being worked on. Therefore Windows execution is not claimed. The Calligra source does not establish interoperability with Microsoft Excel, LibreOffice or Google Sheets, nor does it validate import/export of their workbooks. If transferring a workbook, re-test the formula, separators, sorting, ties and error cases in the target application rather than assuming identical results.

Related official references: LARGE, SMALL, RANK, MEDIAN, and COUNT all have official KDE function-reference entries.

Official handbook/XML/C++ source inspected: YES, on 2026-10-13. Numerical results independently calculated: YES. Native Calligra worksheet execution: NOT PERFORMED. Visual/UI errors, locales, platform-specific packages, XLSX round-trips, screenshots: NOT TESTED.