Weighted Sum Calculator
Multiply each value by its matching weight and add the products. The weighted sum is a total; it is not divided by the sum of weights.
How to use Weighted Sum Calculator
1. Enter Values and Weights as matching lists where weights are used; separate numbers with commas, spaces, semicolons or new lines. 2. Keep all observations on one unit or scoring scale. 3. Select Calculate or press Enter, then read weighted sum. 4. Copy result copies the answer; Reset clears the form. Do not use thousands separators inside lists.
Why use this tool?
Calculate a linear combination or total contribution when each item has a stated coefficient.
How the calculation works
Weighted sum = value₁ × weight₁ + value₂ × weight₂ + … . The two lists must have the same length. Signed weights are allowed. The interpretation and output unit depend on your chosen values and coefficients. This page does not normalise weights. Results use up to six decimal places, or six significant digits in scientific notation for nonzero magnitudes below 0.000001. Calculations use browser floating-point arithmetic. Each list supports up to 20,000 numbers. Entry and result magnitudes must not exceed 9,007,199,254,740,991; unrepresentable variance or weighted products are rejected.
Example
Values = 10,20,30 and Weights = 1,2,-1 give 10 + 40 − 30 = 20.
Practical tip
Use Weighted Values Mean Calculator if you need an average normalised by total weight.
Frequently asked questions
Can weights be negative?
Yes. A weighted sum is a signed linear combination. Negative coefficients subtract a contribution; zero coefficients contribute nothing.
Why is this different from a weighted mean?
A weighted mean divides the sum of products by the total weight. This tool stops at the sum and can use coefficients whose total is zero.
How should I separate numbers and interpret rounding?
Use commas, spaces, semicolons or new lines between entries. Enter 1000 rather than 1,000: commas separate observations. Repeated values are retained. Displayed results are rounded as stated; keep original readings for later calculations.