Zoho Sheet SUMX2PY2: Combined Squares and Vector RMS
Add squared components from two arrays in Zoho Sheet, distinguish vector RMS from component RMS and verify unit scaling with complete examples.
Verification status: See the evidence and test scope described in this guide. How formula examples are checked
Quick answer: =SUMX2PY2(A2:A5;B2:B5) returns 72.25 for the four two-component vectors below. It adds each x² and y², with no signed cancellation between those squared terms.
Availability and version history
- 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 SUMX2PY2 reference. Documentation and independent exact-arithmetic models; no native Zoho Sheet test.
Syntax and meaning
=SUMX2PY2(x; y)
Zoho documents two arrays or ranges and also gives the scalar example =SUMX2PY2(9;8), which returns 145. The calculation is 81+64, not (9+8)².
Supply both inputs. Use corresponding numeric cells in equally laid-out ranges for these examples; the brief entry does not establish every shape-mismatch or nonnumeric-input behavior. Zoho’s documented argument separator is the semicolon.
For complete real numbers, each square is nonnegative, and swapping the two arrays preserves the total. Signs still matter to a dot product or a square of a sum, which are different calculations.
Practice worksheet: four vectors
Create a blank sheet named VectorSquares. Put x, y, Squared length and Length in A1:D1. Enter A2:B5:
| Row | A: x | B: y | Expected C | Expected D |
|---|---|---|---|---|
| 2 | 3 | 4 | 25 | 5 |
| 3 | 0 | 5 | 25 | 5 |
| 4 | -4 | 0 | 16 | 4 |
| 5 | 1.5 | -2 | 6.25 | 2.5 |
Enter =A2^2+B2^2 in C2 and =SQRT(C2) in D2. Fill C2:D2 through row 5. Every squared length here is positive, within the documented SQRT domain.
Use G for labels and H for these formulas:
| Cell | Formula | Expected result |
|---|---|---|
| H2 | =SUMX2PY2(A2:A5;B2:B5) |
72.25 |
| H3 | =SUM(C2:C5) |
72.25 |
| H4 | =SUMSQ(A2:A5) |
27.25 |
| H5 | =SUMSQ(B2:B5) |
45 |
| H6 | =SUMX2PY2(B2:B5;A2:A5) |
72.25 |
| H7 | =SQRT(H2) |
8.5 |
| H8 | =SQRT(H2/4) |
4.25 |
| H9 | =SQRT(H2/8) |
3.0052038200 approximately |
| H10 | =AVERAGE(D2:D5) |
4.125 |
H4+H5 equals H2 because the separate SUMSQ totals contain all the same squared components. H6 checks symmetry without altering the original input positions.
Advanced: three different length summaries
H7 is the square root of the total squared magnitude, 8.5. H8 is the root mean square of four vector lengths, 4.25. H9 is the root mean square of eight separate component numbers, approximately 3.0052038200.
The denominator changes the question. H10 is different again: the ordinary mean of lengths 5,5,4,2.5 is 4.125. Taking the square root after averaging squared lengths is not the same operation as averaging the individual lengths.
Use the count matching the defined observations, and keep coordinate units consistent. Do not describe all these outputs merely as an “average distance.” The formula does not choose a geometric reference point, a weighting policy or a physical calibration for you.
Converting metres to centimetres
Keep the main worksheet intact. Put x in cm and y in cm in J1:K1. Enter =A2*100 in J2 and =B2*100 in K2, then fill J2:K2 through row 5.
In N2 enter =SUMX2PY2(J2:J5;K2:K5); expect 722500. In N3 enter =SQRT(N2/4); expect 425. Scaling every component by 100 multiplies the sum of squares by 10000 and the vector RMS by 100.
Thus 4.25 metres and 425 centimetres express the same length, while 72.25 square metres becomes 722500 square centimetres. Comparing the raw squared totals without their units would be misleading.
This example assumes both coordinate components started in metres. If only one component changes units, convert the other before applying a geometric interpretation.
Why squaring x+y gives another answer
Put Squared component sum in L1. Enter =(A2+B2)^2 in L2 and fill to L5. Expected values are 49, 25, 16 and 0.25. In N5 enter =SUM(L2:L5); expect 90.25.
In N6 enter =SUMPRODUCT(A2:A5;B2:B5); expect 9. In N7 enter =N5-H2; expect 18, twice the dot product. The identity (x+y)^2=x²+y²+2xy explains the difference without attributing it to a function error.
The SUMPRODUCT function operates on the same complete numeric pairs here. Its own documented input rules do not establish how SUMX2PY2 treats malformed arrays.
Scalar controls and practical limits
On a separate sheet named VectorControls, put =SUMX2PY2(9;8) in B2, =SUMX2PY2(-9;8) in B3 and =SUMX2PY2(0;0) in B4. Expected results are 145,145,0. Negating a component does not alter its square.
The function returns a combined squared magnitude, not a row-by-row array of vector lengths. Use the C helper column when individual observations need inspection.
Zoho’s general error table is not a complete specification for blank cells, numeric text, boolean values, unequal arrays or overflow. Use complete numeric inputs and preserve full calculation precision rather than reconstructing totals from rounded displayed lengths.
SUMX2MY2 subtracts squares and can be negative. SUMXMY2 squares paired differences. The placement of the square determines the meaning even though the function names look similar.