The Sum of Products Calculator provided by Hesapstan multiplies matching rows across 2 to 5 equal-length lists, shows each row product, and adds all row products into one total.
A sum of products multiplies matching rows and then adds the products
In a sum of products, the lists are treated as aligned. The first values are multiplied together, the second values are multiplied together, and the same pattern continues row by row. The final answer is the sum of all row products. For two lists, the basic form is A₁×B₁ + A₂×B₂ + ... .
Giriş / Input: A: 2; 3 — B: 4; 5 — Sonuç / Output: 2×4 + 3×5 = 8 + 15 = 23 — The calculator shows each row product before showing the total.
All lists must have the same length because each row is a match
This calculator does not guess missing values or pad shorter lists. If list A has four values, every other active list must also have four values. Otherwise, the row-by-row multiplication would not be well defined.
Unequal list lengths produce an error. Add the missing value yourself if a row should really count as 0.
The formula works for 2 to 5 aligned lists
The general formula is Σ(Aᵢ × Bᵢ × ... × Eᵢ). With two lists, each row has two factors. With three, four, or five lists, each row product includes all active lists in that same row.
Giriş / Input: A: 2 — B: 3 — C: 4 — Sonuç / Output: 2×3×4 = 24 — There is one row, so the total is also 24.
With two lists, the result is the same value as a dot product
For two equal-length lists, the sum of products is the same numeric value as the dot product. This calculator can help with that calculation, but it is not a full vector calculator: it does not compute vector norms, angles, cross products, or matrix products.
The tool only multiplies aligned row values and sums the row products. It does not perform matrix multiplication, cross products, or other vector operations.
The numerator of a weighted average is a sum of products
In a weighted average, the numerator is the sum of value×weight products. For example, if the values are 80 and 90 and the weights are 2 and 3, the numerator is 80×2 + 90×3. To get the full weighted average, that total must still be divided by the sum of weights.
The sum of products is only the numerator of a weighted average. Use the weighted average calculator when you need the final average.
Negative values and zeros affect each row product normally
You may enter positive numbers, negative numbers, and zeros. If a row contains 0, that row product is 0. Negative values affect the sign of the row product according to the usual multiplication rules.
Giriş / Input: A: -1; 2 — B: 3; 4 — Sonuç / Output: (-1×3) + (2×4) = -3 + 8 = 5 — Negative values are not special cases; they follow ordinary multiplication rules.
Frequently Asked Questions
What is a sum of products?
A sum of products multiplies matching row values from aligned lists and then adds those row products. The general form is Σ(Aᵢ × Bᵢ × ...).
How many lists can I use?
The runtime supports 2 to 5 lists. The calculator starts with two lists, and you can add or remove lists within that range.
Why must all lists have the same length?
Each row is a matched set of values. If the lists have different lengths, the calculator cannot know which values should be multiplied together.
Is sum of products the same as dot product?
For two equal-length lists, the numeric result is the dot product. This page still does not claim to be a full vector calculator.
Is sum of products the same as weighted average?
No. It is the numerator of a weighted average when one list contains values and another contains weights. The weighted average also divides by the sum of weights.
Can I enter negative numbers?
Yes. Positive values, negative values, and zero are accepted. The sign of each row product follows ordinary multiplication rules.
Are missing rows treated as zero?
No. There is no automatic padding. All active lists must have the same number of values.
Does this calculator do matrix multiplication?
No. It only multiplies aligned list values row by row and sums the row products.