Last updated October 5, 2026 · Report an error
Sum of products is exactly what it sounds like: multiply each pair of corresponding values together, then add up all those products. This tool calculates Σ(aᵢ × bᵢ) for up to 5 paired entries, without any weighting or averaging framing.
How it works
Each pair (aᵢ, bᵢ) is multiplied together to get a product, and all the products are then summed for the final result.
- Enter a₁.
- Enter b₁.
- Enter a₂.
- Enter b₂.
- Enter a₃ (optional).
- Enter b₃ (optional).
- Enter a₄ (optional).
- Enter b₄ (optional).
- Enter a₅ (optional).
- Enter b₅ (optional).
- Click Calculate to see your results.
Examples
Three pairs of values
(2, 5), (3, 4): (2×5) + (3×4) = 10 + 12 = 22.
Who should use it
- Simple dot-product-style calculations without vector notation.
- Calculating total cost from paired quantity and unit-price lists.
Industry applications
- Finance and accounting (quantity × price totals)
- Statistics and linear algebra basics
- Education
Advantages
- Supports up to 5 paired entries in a single calculation.
- Works with positive and negative values alike.
Limitations
- Does not divide by a total weight — use the Weighted Average Calculator instead if an average (not just a raw sum) is needed.
Common mistakes to avoid
- Adding the a and b values together instead of multiplying each pair first — sum of products always multiplies within pairs before summing across pairs.
Best practices
- Double-check that each a value is correctly paired with its intended b value before entering them, since pairing order changes the result.
Tips
- If you actually need an average rather than a raw total, divide the sum of products by the sum of the "weight" values, or use the dedicated Weighted Average Calculator.
Frequently asked questions
A weighted average divides the sum of products by the sum of the weights to get an average value. This tool simply reports the raw sum of products itself, with no division — useful in its own right for calculations like a simple dot product.
Yes — both the a and b values can be negative, and the sum of products will reflect the correct signed result.