Weighted Average Calculator
Not every number in a list deserves an equal say. Exams carry marks per paper, portfolios carry money per holding, deliveries carry litres per supplier — and the honest average lets the bigger share speak louder. This page blends three values by their weights, shows the plain mean beside it for comparison, and reports what the weights added up to.
Enter values
Results
- Weighted average
- 84.4
- Plain average (equal weights)
- 84.33
- Total weight
- 100
How is the Weighted Average calculated?
Six fields: three values and the weight attached to each. Weights are relative — 30, 40 and 30 behave exactly like 3, 4 and 3 — so they need not total 100, though the total row flags it whenever they do not. Each value is multiplied by its weight, the products are summed, and that sum is divided by the total weight. The plain average sits alongside, and the gap between the two shows what the weighting changed.
Formula
Weighted average = (value 1 × weight 1 + value 2 × weight 2 + value 3 × weight 3) ÷ (weight 1 + weight 2 + weight 3). Plain average = sum of the three values ÷ 3. Weights may be marks, points or shares; a weight of 0 drops its value out entirely, and when every weight is 0 the weighted average is undefined.
Example
A student scores 78, 85 and 90 in papers weighted 30, 40 and 30 marks. The blend is (78×30 + 85×40 + 90×30) ÷ 100 = 8,440 ÷ 100 = 84.4, while the plain average is 253 ÷ 3 = 84.33 — the heavier middle paper lifts the result by 0.07. Reweighting to 50, 25 and 25 pushes the low score of 78 into the driver's seat and the weighted mark falls to 82.75.
Things to remember
The two averages part company exactly when the weights lean away from the middle, so check which figure your syllabus or report actually wants before quoting either. Confirm the total row reads 100 when your weights are meant to be percentages, and keep the values and weights covering the same period.
Frequently Asked Questions
What is a weighted average in maths?
An average where each value counts in proportion to its weight rather than equally. Scoring 78, 85 and 90 in papers worth 30, 40 and 30 marks gives (78×30 + 85×40 + 90×30) ÷ 100 = 84.4 instead of the 84.33 that an unweighted mean reports.
Do weights have to add up to 100?
No. Weights are relative, so 3, 4 and 3 produces the same answer as 30, 40 and 30 — only their ratios matter. The calculator still reports the total and flags anything that is not 100, because people reading your working usually expect percentages.
When should I use a weighted average?
Whenever contributions differ in importance: exam marks per paper, money per holding, or hours at each pay rate. If every item genuinely counts the same, the plain average is simpler and gives an identical answer — weighting only earns its keep when the weights are real.
What happens if one of the weights is zero?
That value drops out completely: a paper worth 0 marks cannot move the final result, and the remaining weights are rescaled among themselves. If every weight is 0 the calculation has nothing to divide by, so the calculator shows a dash instead of a number.
Related Calculators
- Average CalculatorMath & ArithmeticFind the mean of up to five numbers, with the sum and the count of the values that were actually used.
- Percentage CalculatorMath & ArithmeticCalculate percentages, percentage increase and percentage decrease in one step, with a worked example for each case.
- Profit Margin CalculatorBusiness & StartupCalculate profit, profit margin percentage and markup from your revenue and total cost, with a worked example.
- Interest Rate CalculatorFinance & InterestFind the annual interest rate needed to turn an amount today into a target sum over a fixed number of years.