Sum of Products Calculator

The sum of products (often denoted mathematically as the dot product or inner product) involves taking two parallel sequences of numbers—let us call them Series X and Series Y—multiplying each corresponding pair together, and then adding all of those individual products into a single cumulative total. The formula is expressed as: Sum = (X₁ × Y₁) + (X₂ × Y₂) + ... + (X_n × Y_n). In sigma notation, it is written as the summation from i = 1 to n of (X_i × Y_i). Both arrays must contain an equal number of elements for the operation to be valid.

Imagine you are calculating the total revenue from selling three different types of merchandise. Series X represents the quantity sold of each item: [10, 5, 8]. Series Y represents the respective price per unit in dollars: [$12, $25, $15]. To find the grand total revenue, we multiply each corresponding pair and sum the results. First pair: 10 × $12 = $120. Second pair: 5 × $25 = $125. Third pair: 8 × $15 = $120. Finally, add these products together: $120 + $125 + $120 = $365. The total sum of products is $365.

Always ensure that your corresponding data sets are properly aligned before inputting them into the calculator; misaligned indices will yield incorrect analytical results. Verify that both Series X and Series Y contain an identical count of numerical values to prevent data mismatch errors. When working with large datasets, double-check decimal placements to maintain high mathematical precision throughout your workflow.