SUMSQ Function in Apple Numbers: Add Squares of Values and Ranges

=SUMSQ(num-value, num-value…)

Argument: First `num-value

Required?
Yes

Officially documented type
Number or collection of numeric values

What it contributes
One numeric value, cell, or range to square and include.

Argument: Each further `num-value…

Required?
Optional; repeatable

Officially documented type
Number or collection of numeric values

What it contributes
Adds each further value or range’s squared numbers.

Apple explicitly states the first argument is a number or a collection containing numbers and additional number values or collections are optional (official SUMSQ). For example, both =SUMSQ(3,4) and =SUMSQ(B2:D2) fit that signature. A range does not need to be expanded into individual comma-separated references. No numerical default for a missing required first argument is documented. The Apple entry does not set an explicit maximum argument count; do not import Excel’s separate 255-argument limit as an Apple rule.

The mathematical operation on a sequence of numeric values x₁, …, xₙ is:

SUMSQ(x₁, …, xₙ) = x₁² + … + xₙ²

Regional settings: In Apple’s English help, function arguments are separated by commas. When the user’s decimal separator is a comma, Apple says to type semicolons between separate arguments. Thus =SUMSQ(3,4) can require =SUMSQ(3;4) in such a locale; =SUMSQ(B2:D2) has one range argument and no separator to change (Apple syntax overview). Numeric text pasted from another country may need conversion to actual numbers; adjust table cell formatting rather than guessing automatic coercion.

Version and device qualification: The documentation edition reviewed here is Apple’s Formulas and Functions Help 15.4, not a claim about an app named Numbers 15.4. Apple describes an in-app function browser for Numbers on Mac, iPhone, iPad and iWork on iCloud.com (welcome). First support dates for SUMSQ and all-platform/edition edge-case equivalence were not established. Native testing remains necessary.

In Numbers make a single table named Vector Checks with exactly one header row. Put numeric inputs in B through D; columns E and F are formulas. Negative values are intentional: squaring them makes their contribution nonnegative.

Row: 2

A: Label
3-4 example

B: X
3

C: Y
4

D: Z
0

E: Expected SUMSQ
25

F: Expected length
5

Row: 3

A: Label
Signed 3D values

B: X
−3

C: Y
4

D: Z
12

E: Expected SUMSQ
169

F: Expected length
13

Row: 4

A: Label
Zero vector

B: X
0

C: Y
0

D: Z
0

E: Expected SUMSQ
0

F: Expected length
0

Row: 5

A: Label
Mixed directions

B: X
2

C: Y
−1

D: Z
2

E: Expected SUMSQ
9

F: Expected length
3

Row: 6

A: Label
Fractional readings

B: X
1.5

C: Y
−2

D: Z
0.5

E: Expected SUMSQ
6.5

F: Expected length
2.549510 (rounded)

In E2 enter:

=SUMSQ(B2:D2)

Copy E2 down through E6. For example, row 3’s expected value is (-3)^2+4^2+12^2 = 9+16+144 = 169, and row 6’s expected value is 1.5²+(-2)²+0.5² = 2.25+4+0.25 = 6.5.

To calculate the Euclidean length of the resulting vector, enter in F2:

=SQRT(E2)

Copy through F6. The 3–4–0 vector has length 5; the vector (−3,4,12) has length 13; the fraction-row length is approximately 2.549510. Apple explicitly illustrates the simpler [SQRT(SUMSQ(3,4))] hypotenuse formula in its SUMSQ help. This table generalizes the idea to three dimensions.

In the same table, plain B2:D2 is sufficient. When referring to another Numbers table, use the formula editor or qualified syntax such as Vector Checks::B2 where needed; different sheets can require Sheet Name::Vector Checks::B2 (Apple cell references).

Create a different table named Moves with one header row and this input:

In F2 enter:

=SQRT(SUMSQ(D2-B2,E2-C2))

Expected result: 5. The displacement is (4−1,6−2)=(3,4); the squared-distance sum is 9+16=25. SUMSQ squares the two differences and SQRT converts squared distance to linear distance. This example is arithmetic; it does not verify geographic/geodesic distance on a curved Earth and should not be used as a substitute for a geographic model.

If the worksheet uses a decimal-comma locale, adapt the separator between the two displacement arguments, not the minus signs: =SQRT(SUMSQ(D2-B2;E2-C2)) (Apple Functions overview).

Root mean square summarizes the size of values even when some are negative. For a nonempty collection of n numbers, RMS = √(SUMSQ(values)/n). The denominator must reflect the intended count of numeric observations.

In a new table named Measurements, put 3 in B2, 4 in C2, and enter in D2:

=SQRT(SUMSQ(B2:C2)/COUNT(B2:C2))

Expected result: approximately 3.535533906 = √((9+16)/2) = √12.5. Here COUNT(B2:C2) is 2 because both cells contain numbers, matching n. If your range might have blanks, text or errors, you must decide whether COUNT’s notion of numeric values matches your statistical purpose; verify Apple Numbers’ actual treatment rather than silently assigning a fixed n. An all-nonnumeric or empty range could make the denominator zero; avoid asserting a particular error label without native testing.

The RMS formula squares each measurement before averaging. =SQRT(AVERAGE(B2:C2)) is not equivalent (it takes the square root of their arithmetic average). The shown formula is appropriate for basic positive/negative real-valued observations, not for replacing a validated process-quality metric without checking data type and completeness.

Mathematically, SUMSQ(a,b) equals a²+b² and is not a built-in variance or standard deviation. If you need spread around a mean, subtract the mean first and choose the correct statistic and denominator. SUMSQ also differs from SUMPRODUCT: the latter generally combines corresponding entries of arrays, whereas SUMSQ uses each selected value’s square.

Numeric text or blank cells: Apple’s SUMSQ entry describes number values and collections containing them, but does not detail every coercion behavior for strings, booleans, blank cells or cells containing formula errors. Do not copy Excel’s detailed array coercion rules into Numbers without testing. For reproducible results above, type genuine numbers in every referenced input. Use Apple’s troubleshooting advice to check imported values, formatting and references.

Unexpected large number: =SUMSQ(B2:D2,100) adds 100² = 10,000, not 100, to the other squared values. Apple’s own help illustrates adding a scalar 100 to a range (SUMSQ reference). If you wanted to add 100 to a sum of squares, instead write =SUMSQ(B2:D2)+100.

Overlapping inputs: =SUMSQ(B2:D2,C2) includes C2 in the range and again as a separate argument; both occurrences contribute. Avoid overlaps unless you intentionally want repeated weighting.

Result cell included in its own range: Put E2 outside B2:D2. Entering =SUMSQ(B2:E2) in E2 creates a self-reference; Apple’s error guidance warns against formulas that include themselves.

Misplaced delimiters: The first numeric value/range is required; later ones optional. In semicolon locales use ; between separately listed argument expressions. Do not write =SUMSQ(3,4) intending the single decimal value three-point-four in an English comma-separator locale; cell values and locale formatting must be unambiguous.

Finite precision and overflow: The Apple help does not specify maximum finite magnitudes or exact error messages for numerical overflow. Large inputs are squared, increasing their magnitude; independently test high-value data and consider appropriate scale/units. Do not assume exact decimal precision beyond what the application provides.

Microsoft documents SUMSQ(number1,[number2],...) for Excel with the same broad meaning—sum of squares—and describes a 255-argument bound and array/coercion rules for Excel (Microsoft SUMSQ). Apple’s guide documents numeric values/collections and repeatable optional arguments without establishing that same bound or the same text-handling rule (Apple SUMSQ). The examples in this guide use explicitly numeric cells and so avoid unsupported cross-program coercion assumptions. This tutorial does not claim Google Sheets or historical Numbers versions are equivalent without separately checking them.

• Apple SUMSQ — official reference: exact syntax, ranges, optional further values, and examples.
• Apple SQRT: convert a squared magnitude into a Euclidean length.
• Apple SUM: ordinary sum rather than sum of squares.
• Apple cell references: range and table-reference syntax.
• Apple functions overview: notation and locale delimiters.

1. Syntax/range semantics: Apple SUMSQ, Help 15.4, verified 2026-10-12. Provides SUMSQ(num-value, num-value…) and describes number values/collections and optional additional arguments.
2. Range/scalar examples: same Apple SUMSQ entry, verified 2026-10-12. Includes SUMSQ(3,4), a range A1:A4, an A1:D4 block, SUMSQ(A1:A4,100), and SQRT(SUMSQ(3,4)).
3. Local separators and argument notation: Apple Functions overview, verified 2026-10-12.
4. Cell and range references: Apple refer to cells, verified 2026-10-12.
5. Troubleshooting: Apple formula errors and best practices, verified 2026-10-12.
6. Excel-only differences: Microsoft SUMSQ function, checked 2026-10-12. Does not establish Apple’s own 255-argument or coercion behavior.

• SQRTPI — continue with a related Apple Numbers calculation.
• SQRT — continue with a related Apple Numbers calculation.
• PI — continue with a related Apple Numbers calculation.
• SUMPRODUCT — continue with a related Apple Numbers calculation.

For a software-specific comparison: LibreOffice Calc SUMSQ, Apache OpenOffice Calc SUMSQ, Gnumeric SUMSQ. A shared name does not establish identical argument, error or version behaviour.

The linked official function documentation was reviewed on October 12, 2026. Apple’s Formulas and Functions Help 15.4 identifies the documentation edition, not a minimum Numbers release or a guarantee of historical platform parity. Selected worked examples were checked using independent mathematical or text-processing models; results are expected values, not observations from the spreadsheet application. Native Apple Numbers execution was not performed. Undocumented coercion, exact error messages and platform-specific behaviour remain unverified.

View reproducible example inputs and independent check results. This record is not a native spreadsheet test log.