Weighted Average Calculator
Type each value and how much it counts, or paste two columns. Advanced adds weighted grades by category, average buy price, weighted standard deviation and the value you need to hit a target.
Paste a list instead
Paste two columns from a spreadsheet, or type pairs like “85 20” (spaces, tabs or commas). One long line of value, weight, value, weight… works too. Up to 30 rows.
Finds the value this row needs, or the weight it would need instead.
Scores as percentages (85, 90) or points (45/50, 18/20). Leave the scores blank for anything not marked yet, like the final exam.
For shares with fees and sales too, try the stock average calculator.
Row by row working
How your weighted average is worked out
Weighted average = sum of (value × weight) ÷ sum of the weights.
- 1
Value × weight
85×20 + … + 90×50
= 8,360 - 2
Add the weights
20 + 30 + 50
= 100% - 3
Divide
8,360 ÷ 100
= 83.6 - 4
Versus plain mean
plain mean 82.3333
weights add +1.2667
Read more: the formula, a worked example, grades, average price and spread
A weighted average lets some values count more than others. Each value is multiplied by its weight, the results are added up, and the total is divided by the sum of the weights. When every weight is the same, it gives the plain average. For a plain list of numbers, use the average calculator.
The formula
weighted average = sum of (value × weight) ÷ sum of the weights
share of a row = its weight ÷ sum of the weights
value a row needs = (target × all the weights − sum of the other rows' value × weight) ÷ that row's weight
weighted SD = square root of (sum of weight × (value − weighted average)²) ÷ sum of the weights
Worked example
Homework of 85 worth 20%, a midterm of 72 worth 30% and a final of 90 worth 50%: 85 × 20 = 1,700, 72 × 30 = 2,160 and 90 × 50 = 4,500, which add up to 8,360. The weights add up to 20 + 30 + 50 = 100, so the weighted average is 8,360 ÷ 100 = 83.6. The plain average of 85, 72 and 90 is 247 ÷ 3 = 82.33, so the big final pulls the weighted answer up by 1.27. To reach an average of 85 by changing the final, it would need (85 × 100 − 1,700 − 2,160) ÷ 50 = 4,640 ÷ 50 = 92.8.
When the % weights don't add to 100
The calculator always divides by what the weights add up to, so the answer is a true average of what you entered. If only the homework (20%) and midterm (30%) are marked, (1,700 + 2,160) ÷ 50 = 77.2 is your grade so far. Weights of 2, 3 and 5, or 0.2, 0.3 and 0.5, give exactly the same 83.6 as 20, 30 and 50, because only the shares matter.
Weighted grade by category
Each category's score is the average of its marks (or, for points like 18/20 and 14/20, the total got ÷ the total possible: 32 ÷ 40 = 80%). With homework 85 (20%), quizzes 80 (15%) and a midterm of 72 (25%), you have 20 × 85 + 15 × 80 + 25 × 72 = 4,700 weighted points from 60% of the course, so your grade so far is 4,700 ÷ 60 = 78.33. To finish on 80 with the 40% final still to come, you need (80 × 100 − 4,700) ÷ 40 = 82.5 on it. Scoring 0 on the final would leave 47; scoring 100 would give 87. For letter grades and dropping the lowest score, see the grade calculator and the final grade calculator.
Average buy price (cost basis)
For things bought at different prices, the units are the weights. 10 at 100, 30 at 80 and 20 at 91 cost 1,000 + 2,400 + 1,820 = 5,220 for 60 units, so the average price is 5,220 ÷ 60 = 87. At a price of 95 they are worth 5,700, a gain of 480 (9.2%). To bring the average down to 85 by buying at 80, you need (5,220 − 85 × 60) ÷ (85 − 80) = 24 more units, costing 1,920.
Weighted standard deviation
This shows how spread out the values are once the weights are counted. For the example, the gaps from 83.6 are 1.4, −11.6 and 6.4. Squared and weighted: 20 × 1.96 + 30 × 134.56 + 50 × 40.96 = 6,124. Divided by the 100 total weight gives a variance of 61.24, so the SD is 7.83. If the values are a sample, the calculator also gives a sample SD using “reliability” weights (divide by total weight − sum of squared weights ÷ total weight = 100 − 3,800 ÷ 100 = 62), which is 9.94 here. When each weight is a count of identical values, the frequency version divides by total weight − 1. For unweighted spread, see the standard deviation calculator.
Where weighted averages are used
- Grades and GPA: scores weighted by credits or by how much each part counts.
- Prices: average buy price of shares, crypto or stock, weighted by units bought.
- Business: average cost of stock, weighted average interest rate on several loans, average selling price.
- Surveys: average rating where each star level is weighted by how many people chose it.
Common questions
How do I calculate a weighted average?
Multiply each value by its weight, add those up, and divide by the total of the weights. Scores of 85, 72 and 90 worth 20%, 30% and 50% give (1,700 + 2,160 + 4,500) ÷ 100 = 83.6.
What if my percentage weights don’t add up to 100?
Divide by what they do add up to. Weights of 20% and 30% (50% in all) on scores of 85 and 72 give (1,700 + 2,160) ÷ 50 = 77.2. For a course, that is your grade so far on the work marked.
What is the difference between a weighted and a plain average?
A plain average counts every value the same. A weighted average lets some count more. The plain average of 85, 72 and 90 is 82.33; with the 90 worth half the grade, the weighted average is 83.6.
How do I work out my average buy price?
Use the number of units as the weight. 10 shares at 100, 30 at 80 and 20 at 91 cost 5,220 for 60 shares, so the average price is 5,220 ÷ 60 = 87, not the plain 90.33.
What score do I need on the final to get a target grade?
Take the target × the total weight, subtract the points you already have, and divide by the weight still to come. With 4,700 weighted points from 60% of the course, an 80 overall needs (8,000 − 4,700) ÷ 40 = 82.5 on a 40% final.
Can weights be decimals or zero?
Yes. Any weight of 0 or more works, so 0.2, 0.3 and 0.5 give the same answer as 20, 30 and 50. A weight of 0 leaves that value out. Only the total of the weights can’t be 0.
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