Zoho Sheet SUMSQ: Sum of Squares, RMS and Centered Deviations

• Introduced: The original introduction release and date are not established by the checked sources.
• Availability: Currently documented in Zoho Sheet’s rolling web-service help; no numbered release or retirement endpoint is established.
• Scope: English-language web-service documentation. Exact mobile and offline-client parity is not established here.
• Checked: October 14, 2026, against the official SUMSQ reference. Documentation and independent exact-arithmetic models; no native Zoho Sheet test.

=SUMSQ(number1; number2; ...)

Zoho accepts numbers or ranges containing numbers. Although the displayed syntax lists multiple positions, its explicit remark confirms that one number is sufficient: SUMSQ returns that number’s square. Further inputs extend the sum; there is no second mandatory numeric value implied by that example notation.

The documentation uses semicolons between arguments. A colon inside B2:B7 denotes a range, not another argument. The page does not publish a maximum count of inputs or complete rules for all nonnumeric values.

SUMSQ answers a different question from SUM. Squaring a final sum includes cross-products; summing individual squares does not.

Create a blank sheet named MeasurementSquares. Put Observation, Measurement and Square in A1:C1. Enter labels M1–M6 in A2:A7 and the following numbers in B2:B7:

Enter =B2^2 in C2 and fill to C7. Use G for result labels and H for these formulas, keeping them outside A:C:

H6 and H7 partition the same six observations. H8 combines the two ranges without changing their input values. H9 is the root mean square, using six as the count of the complete numeric fixture. Update that denominator if you intentionally change the dataset.

The signed total 2 is small because some values cancel. Its square, 4, is not the sum of squares 34. Both calculations are valid, but they describe different quantities.

Keep A:C and G:H intact. Put Centered measurement and Centered square in D1:E1. Enter =AVERAGE(B2:B7) in H11; the exact mean is 1/3.

Enter =B2-$H$11 in D2 and =D2^2 in E2, then fill D2:E2 through row 7. Expected centered values are −10/3, 11/3, −1/3, −7/3, 2/3, 5/3; their squares are 100/9, 121/9, 1/9, 49/9, 4/9, 25/9.

Put =SUM(E2:E7) in H12 and =SUMSQ(D2:D7) in H13. Both targets are 100/3, approximately 33.3333333333. This is smaller than the raw sum of squares because the observations have first been centered.

For a transparent identity check, put =H12/6+H11^2 in H14; expect 17/3, approximately 5.6666666667, which equals H9 squared mathematically. The mean-square about zero decomposes into the mean centered square plus the squared mean.

This does not make raw SUMSQ an automatic sample-variance function. Choosing a mean, denominator and interpretation remains part of the statistical model. AVERAGE supplies the mean here; full stored precision matters more than the displayed fraction or decimal.

On a blank sheet named PointDistance, put x and y in A1:B1. Enter 10,-5 in A2:B2 and 18,1 in A3:B3. In D2 enter =SUMSQ(A3-A2;B3-B2); expect 100 from 8²+6². In D3 enter =SQRT(D2); expect 10.

In D4 enter =SUMSQ(A3:B3); expect 325. That is the second point’s squared distance from the origin, not its squared distance from the first point. Subtract corresponding coordinates before squaring when measuring separation.

Use compatible coordinate units. The SQRT function converts a positive squared distance into a length, but it does not convert incompatible units or supply a physical calibration.

On a separate sheet named SquareControls, put these formulas in B2:B5:

The first two match Zoho’s explicit numeric examples. Its named-range example depends on a separate dataset; a range called Units_sold does not inherently have a sum of squares of 909091.

The help’s error table lists general naming, type and reference problems rather than a complete SUMSQ coercion specification. It does not establish exact behavior for blank cells, numeric text, booleans, propagated errors or overflow. Keep those cases distinct from the numeric controls here.

SUMX2PY2 combines the squares of two arrays. SUMX2MY2 subtracts their squares, while SUMXMY2 squares their paired differences.