SUMPRODUCT Calculator — Element-wise Products Summed
SUMPRODUCT multiplies each pair of corresponding elements in two arrays and sums the results. Useful for weighted averages, dot products and Excel-style aggregations.
Σ(aᵢ × bᵢ) — sum of element-wise products
How does this calculator work?
SUMPRODUCT = Σ(aᵢ × bᵢ): multiply each pair of matching elements and sum the results. Mathematically identical to the vector dot product. Enter two lists of numbers (minimum 1 pair) to get the sum of products plus a bar chart showing each individual product. Mismatched-length arrays use the shorter length.
Formula
How this is calculated
SUMPRODUCT performs element-wise multiplication on two equal-length arrays, then sums all the products. For A = [2, 3, 4] and B = [5, 6, 7] the result is 2×5 + 3×6 + 4×7 = 10 + 18 + 28 = 56. Mathematically this is the dot product a · b, which also equals |a||b|cos θ where θ is the angle between the vectors — so SUMPRODUCT = 0 means the arrays are orthogonal.
A key use case is weighted averaging: if A holds values (test scores, prices) and B holds weights (fractions summing to 1, or quantities), SUMPRODUCT gives the total weighted value directly. In spreadsheets, SUMPRODUCT is also used with logical arrays (TRUE = 1, FALSE = 0) to count or sum rows meeting multiple criteria without an array-entry shortcut.
This calculator pairs elements by position. If the arrays have different lengths only the shorter length is used and the extra elements in the longer array are ignored. Negative values contribute negative products, which correctly reduces the sum — this is expected behaviour for dot products of vectors with opposite-direction components.
Frequently asked questions
They are mathematically identical: SUMPRODUCT = a · b = Σ(aᵢbᵢ). The dot product also equals |a||b|cos θ, where θ is the angle between the vectors. If SUMPRODUCT is 0 the two arrays are orthogonal (perpendicular) in vector space.
Enter the values in Array A and the corresponding weights in Array B. The weighted average is SUMPRODUCT ÷ sum(B). For example, scores 80, 90, 70 with weights 0.5, 0.3, 0.2 give weighted average = (80×0.5 + 90×0.3 + 70×0.2) / 1.0 = 82.
This calculator uses the shorter length and silently ignores the extra elements in the longer array. In Excel, mismatched array sizes in SUMPRODUCT produce a #VALUE! error, so align your data ranges carefully.
Also known as
TG we-Calculate Editorial Team. (2026). SUMPRODUCT Calculator — Element-wise Products Summed [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/sum-product-calculator
TG we-Calculate Editorial Team. "SUMPRODUCT Calculator — Element-wise Products Summed." TG we-Calculate. 2026. https://we-calculate.com/calculator/sum-product-calculator.
TG we-Calculate Editorial Team, "SUMPRODUCT Calculator — Element-wise Products Summed," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/sum-product-calculator
@misc{wecalculate_sum_product_calculator, title = {SUMPRODUCT Calculator — Element-wise Products Summed}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/sum-product-calculator}}, year = {2026}, note = {TG we-Calculate} }
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