Sum of Products Calculator
Multiply matching values from two lists, add the products, and review dot-product, weighted-mean, and pair-by-pair checks.
Last Updated: May 2026
Paired products
Multiply matching pairs, then add the products
Enter two lists with the same length. The calculator multiplies each aligned pair, sums the products, and shows dot-product and weighted-mean checks.
Examples
Summary formulas
| Metric | Formula | Result |
|---|---|---|
| Formula | sum x_i y_i | 140 |
| List A sum | sum x_i | 20 |
| List B sum | sum y_i | 24 |
| Sum of A squares | sum x_i^2 | 120 |
| Sum of B squares | sum y_i^2 | 164 |
| Weighted mean | sum x_i y_i / sum y_i | 5.833333 |
Pair-by-pair products
| Pair | A | B | Product setup | Product |
|---|---|---|---|---|
| 1 | 2 | 3 | 2 x 3 | 6 |
| 2 | 4 | 5 | 4 x 5 | 20 |
| 3 | 6 | 7 | 6 x 7 | 42 |
| 4 | 8 | 9 | 8 x 9 | 72 |
Numeric Lists Notice
This calculator evaluates finite numeric lists. It does not simplify Boolean algebra sum-of-products expressions or symbolic polynomial terms.
Checked by Jitendra Kumar
Sum of Products Calculator is checked for formula labels, source links, and result limits.
Jitendra Kumar, Founder & Editorial Standards Lead. Updated May 2026. Scope: math calculators.
How to Use the Sum of Products Calculator
Enter the first list and second list with matching lengths. Values can be separated by commas, spaces, semicolons, or new lines.
Review the main sum of products, each pair product, the product-sign counts, and the weighted mean if the second list represents weights.
Step 1: Enter List A
Add the first set of numeric values, such as scores, quantities, or vector components.
Step 2: Enter List B
Add the matching weights, prices, frequencies, or second vector components.
Step 3: Check pair count
Both lists must contain the same number of values so each product has two factors.
Step 4: Read the product table
The table shows every x_i y_i product before the final sum is calculated.
How This Sum of Products Calculator Works
The calculator parses both lists into numbers, checks that their lengths match, and pairs values by position.
Each pair is multiplied, and those pair products are added to produce sum x_i y_i. The same value is the dot product when the inputs are vectors.
When the second list is used as weights, the weighted mean is calculated as sum x_i y_i divided by sum y_i, provided the weight total is not zero.
Sum of Products Guide
Sum of Products Rules
| Concept | Formula or Example | Meaning |
|---|---|---|
| Pair values | x_i with y_i | Each value in List A is matched with the value in the same position in List B. |
| Multiply pairs | x_i y_i | Create one product for each aligned pair. |
| Sum products | sum x_i y_i | Add all pair products to get the final result. |
| Dot product | [2, 4] dot [3, 5] = 26 | Vector dot product is a sum of products. |
| Weighted mean | sum x_i w_i / sum w_i | When List B contains weights, divide the sum of products by total weight. |
Examples
| Lists | Sum of Products | Note |
|---|---|---|
| 2, 4, 6, 8 and 3, 5, 7, 9 | 140 | 2x3 + 4x5 + 6x7 + 8x9. |
| 88, 92, 79, 95 and 20, 30, 20, 30 | 8,950 | Weighted-score numerator. |
| 12, 8, 15, 6 and 24.99, 49.50, 12.75, 99.00 | 1,481.13 | Quantity times price lines. |
| -3, 4, -2, 5 and 6, -1, 8, 2 | -28 | Signed products can offset each other. |
Common Uses
Sum of products appears in dot products, weighted averages, revenue calculations, frequency tables, spreadsheet formulas, and matrix multiplication. The common pattern is always the same: multiply matching entries, then add the products.
Keep the research moving with Multiplication Calculator, Mean Calculator, Matrix Calculator, and Root Mean Square Calculator.
Frequently Asked Questions
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- 1.Wikipedia - Dot product(Accessed May 2026)
- 2.OpenStax - Vectors in the Plane(Accessed May 2026)
- 3.OpenStax - Weighted Mean(Accessed May 2026)