Math

Sum of Products Calculator

Compute Σ(aᵢ × bᵢ) for paired values.

a₁

b₁

a₂

b₂

a₃

b₃

Calculated Output

Sum of products 26

Formula: Σ aᵢ·bᵢ = a₁b₁ + a₂b₂ + …

Step-by-Step Breakdown

1. Values used:

2. a₁ = 2

3. b₁ = 3

4. a₂ = 4

5. b₂ = 5

6. a₃ = 0

7. b₃ = 0

9. Sum of products = 26

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The math behind it

Multiply each pair aᵢ·bᵢ and add them all together. Leave a pair at 0 to skip it.

(2×3) + (4×5) = 6 + 20 = 26.

How is this used?

In weighted totals, dot products and expected-value calculations.