Calculating your weighted sum is straightforward once you know the Weighted Sum formula and what each input means. This guide explains the method in plain language, walks through a manual calculation, and gives worked examples you can follow — then you can do it instantly with the Weighted Sum Calculator.
What is Weighted Sum?
The Weighted Sum calculation tells you your weighted sum from a few simple inputs. The figure you are solving for here is the weighted sum.
The Weighted Sum formula
The core formula is:
Weighted sum = Value 1 × Weight 1 + Value 2 × Weight 2 + Value 3 × Weight 3Here is what each input means:
- Value 1 — a number. Example: 10.
- Weight 1 — a number. Example: 2.
- Value 2 — a number. Example: 20.
- Weight 2 — a number. Example: 3.
- Value 3 — a number. Example: 30.
- Weight 3 — a number. Example: 1.
How to calculate it step by step
- Write down the value 1 (for example, 10).
- Write down the weight 1 (for example, 2).
- Write down the value 2 (for example, 20).
- Write down the weight 2 (for example, 3).
- Write down the value 3 (for example, 30).
- Write down the weight 3 (for example, 1).
- Apply the formula above to get your weighted sum.
- Double-check the result with the Weighted Sum Calculator.
Worked examples
Example 1
| Input / Output | Value |
|---|---|
| Value 1 | 10 |
| Weight 1 | 2 |
| Value 2 | 20 |
| Weight 2 | 3 |
| Value 3 | 30 |
| Weight 3 | 1 |
| Weighted sum | 110.0000 |
With value 1 of 10, weight 1 of 2, value 2 of 20 and weight 2 of 3, the weighted sum works out to 110.0000.
Example 2
With value 1 of 20, weight 1 of 2, value 2 of 20 and weight 2 of 3, the weighted sum works out to 130.0000.
| Result | Value |
|---|---|
| Weighted sum | 130.0000 |
Example 3
With value 1 of 5, weight 1 of 2, value 2 of 20 and weight 2 of 3, the weighted sum works out to 100.0000.
| Result | Value |
|---|---|
| Weighted sum | 100.0000 |
Tips for an accurate result
- Keep your units consistent — mixing, say, months with years or grams with kilograms is the most common source of error.
- Round only at the very end. Rounding inputs early can shift the final answer noticeably.
- Re-run the numbers whenever an input changes, rather than estimating from an old result.
Prefer not to do the maths by hand? — the Weighted Sum Calculator does it instantly, for free, with the formula and a worked example built in.
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