⚖️ Weighted Average Calculator
Calculate a weighted average from any list of values and weights — raw counts or percentages — plus a reverse solver for the value you need to hit a target.
| Value | Weight | |
|---|---|---|
What Weighted Average Calculator Does
A weighted average answers a slightly different question than a plain average: not "what is typical across these numbers" but "what is typical once some of them count for more than others." A 4.0 earned in a 1-credit seminar and a 4.0 earned in a 4-credit core class both raise a GPA, but not by the same amount — the second one is worth four times as much weight in the final number. The same idea covers a course grade built from a 20% midterm and a 30% final, or an average purchase price across stock buys of very different sizes.
The one thing worth being explicit about, because it quietly worries people who learned the formula for one specific use case, is that it makes no difference whether the weights are raw counts (3 credit hours, 4 credit hours) or percentages meant to add up to 100. The formula — sum of (value times weight), divided by the sum of the weights — divides by whatever the weights actually total, so it self-corrects either way. A percentage set that sums to 100 and a raw-count set that sums to some other number produce the identical, correct answer through the same arithmetic; this was verified directly before shipping, comparing a percentage-weighted case against an equivalent raw-weighted case.
The reverse solver exists because the far more common real question is not "what is my average" but "what do I need to get to reach one." Anyone who has worked out by hand what they need on a final exam to land a target course grade has already done this algebra once; this tool generalizes it to any set of prior values and weights, not just a single missing final.
How to Use Weighted Average Calculator
- Choose raw weights (credit hours, quantities) or percentage weights
- Enter each value and its weight, adding or removing rows as needed
- Read the weighted average, or open the reverse solver to find the value needed to hit a target
Formula Used by Weighted Average Calculator
Weighted average
weighted average = Σ(valueᵢ × weightᵢ) ÷ Σ(weightᵢ)
- valueᵢ
- Each individual value (a grade, a price, a score)
- weightᵢ
- How much that value counts — credit hours, purchase quantity, or a percentage
Worked example
Three grades on a raw credit-hour basis: 4.0 (3 credits), 3.0 (4 credits), 3.7 (3 credits).
- Σ(value × weight) = 4.0×3 + 3.0×4 + 3.7×3 = 12 + 12 + 11.1 = 35.1
- Σ(weight) = 3 + 4 + 3 = 10
- Weighted average = 35.1 ÷ 10 = 3.51
Result: 3.51 — confirmed in node -e before publishing.
Percentage weights give the identical formula
Same formula, weights sum to 100 instead of an arbitrary total
Worked example
Course grades weighted 30%, 40%, 30%: scores of 90, 85, and 95.
- Σ(value × weight) = 90×30 + 85×40 + 95×30 = 2700 + 3400 + 2850 = 8950
- Σ(weight) = 30 + 40 + 30 = 100
- Weighted average = 8950 ÷ 100 = 89.5
Result: 89.5 — the same division-by-total-weight formula as the raw-weight example above, confirmed separately in node -e.
Reverse solver: value needed to hit a target average
x = [target × (Σweight_known + w_x) − Σ(value_known × weight_known)] ÷ w_x
- target
- The overall weighted average you want to reach
- w_x
- The weight of the one value you are solving for
Worked example
Two known scores — 85 (weight 30) and 92 (weight 40) — a target overall average of 90, and one more item worth weight 30.
- Known totals: Σ(value×weight) = 85×30 + 92×40 = 2550 + 3680 = 6230. Σ(weight) = 30 + 40 = 70.
- x = [90 × (70 + 30) − 6230] ÷ 30 = [9000 − 6230] ÷ 30 = 2770 ÷ 30 = 92.333…
- Check: (6230 + 92.333×30) ÷ (70 + 30) = 9000 ÷ 100 = 90 — matches the target exactly.
Result: x ≈ 92.33, verified by plugging the solved value back into the original weighted-average formula and confirming it reproduces the target exactly.
How to Read Your Result
Why raw and percentage modes give the same number
The toggle exists for clarity of input, not different math. If you enter weights that are meant to be percentages but they do not sum to 100, the calculator still divides by whatever they actually total and gives a mathematically correct answer — it just flags the mismatch, since that usually means a data-entry mistake rather than an intentional choice.
This is the general engine behind narrower tools
This site's GPA calculator and stock average calculator both compute a weighted average under the hood — credit-hour-weighted grade points in one case, share-count-weighted purchase price in the other. This tool is the same math with an open input list, for anyone whose weighting scheme does not fit either of those specific shapes.
Limitations & Accuracy Notes
- Assumes every weight is a non-negative number known in advance; it does not handle weights that are themselves uncertain or estimated.
- The reverse solver treats every row you entered as fixed and known, solving for exactly one missing value — it will not simultaneously solve for two or more unknowns.
- Reports an error rather than a result when every weight is zero, since a weighted average is undefined with no weight to divide by.