Weighted Average Calculator
Average a set of values where some count for more than others, with the working shown.
Details
Weights do not have to add up to 100. Percentages, credits, hours or shares all work, because the result is divided by whatever the weights total.
Weighted average
87
From 3 items, total weight 100
Weighted total
8,700
Total weight
100
This works out a weighted average from any list of values and weights, and shows the whole calculation, so you can see which items pulled the result up or down.
It also answers the reverse question: given what you have already scored, what you need on what is left to reach a target.
What a weighted average is
A weighted average is an average where some values count for more than others. A plain average treats every number as equally important; a weighted average lets you say that one of them matters three times as much.
Almost every average that matters in real life is weighted. A course grade where the final is worth half and homework a fifth. A GPA where a 4-credit class counts more than a 1-credit one. An average price paid across purchases of different sizes.
The calculation is short: multiply each value by its weight, add those up, then divide by the total of the weights. The last step is the one that does the work — dividing by the total weight is what makes any set of weights valid.
The plain average of 95, 80 and 88 is 87.7. The weighted average is 87, because the lowest score carried the most weight.
What to enter
- Value
- The number being averaged: a score, a price, a rate, a grade point. There is no ceiling, so it works for money as well as percentages.
- Weight
- How much that value counts. Use whatever unit you actually have — a percentage, a number of credits, hours worked, units bought.
- Label
- Optional, and only for you. It names each row in the working so the steps read as 'Midterm' rather than 'Item 2'.
- Target average
- Switch the mode to work backwards instead: what the remaining item has to score for the whole thing to average what you want.
Weights you can use, and what they mean
- Percentages
- 20, 30, 50. The most common, and the only case where the weights usually do total 100.
- Credits or units
- 4, 3, 1. How a GPA works. The totals are whatever they are, and the maths handles it.
- Counts or quantities
- How many of each you bought, worked or measured. Gives an average price or rate that reflects volume.
- Decimals
- 0.2, 0.3, 0.5. Identical to percentages in effect, because only the ratio between weights matters.
What this assumes
Weights do not need to total 100, or any other number. The result is divided by whatever they come to.
Only the ratio between weights changes the answer. Doubling every weight changes nothing.
A total weight of zero has no defined average, so the result is left blank rather than shown as zero.
How to calculate a weighted average
Multiply, add, divide. The only part people get wrong is the last step.
- Σ(value × weight)
- Each value times its own weight, all added together
- Σ(weight)
- The weights added together — not necessarily 100
Multiply each value by its weight. Take them one row at a time. A score of 80 with a weight of 30 contributes 2,400.
Add those results together. This is the weighted total. It is a large number and it is not the answer yet.
Add the weights together. If they happen to total 100, the next step is easy. If they do not, nothing is wrong — this is the number you divide by either way.
Divide the weighted total by the total weight. That is the weighted average. Skipping this step is the single most common mistake, and it produces a number many times too big.
See a worked example: why the weighted answer is lower than the plain one
- Homework
- 95, worth 20%
- Midterm
- 80, worth 30%
- Final
- 88, worth 50%
Multiply each: 95 × 20 = 1,900. 80 × 30 = 2,400. 88 × 50 = 4,400.
Add them: 1,900 + 2,400 + 4,400 = 8,700.
Add the weights: 20 + 30 + 50 = 100.
Divide: 8,700 ÷ 100 = 87.
The plain average of 95, 80 and 88 is 87.7. The weighted figure is lower because the 80 carried three times the weight of the 95.
87, against a plain average of 87.7
Frequently asked questions
- Do the weights have to add up to 100?
No, and this is the most common misunderstanding about weighted averages. The calculation divides by the total of the weights, whatever that total is.
So 20/30/50, 0.2/0.3/0.5 and 2/3/5 all give exactly the same answer. Only the ratio between the weights matters, which is why credits, hours and quantities work as weights just as well as percentages.
- What is the difference between an average and a weighted average?
A plain average adds the values and divides by how many there are, treating each as equally important. A weighted average multiplies each value by its weight first, then divides by the total weight.
They only agree when every weight is the same. The further apart the weights are, the further apart the two answers get.
- How do I calculate a weighted average by hand?
Multiply each value by its weight, add all those results together, then divide by the sum of the weights.
For 95 at 20%, 80 at 30% and 88 at 50%: (95×20) + (80×30) + (88×50) = 8,700, and 8,700 ÷ 100 = 87.
- Why is my weighted average so much higher than expected?
Almost always because the final division was skipped. Adding 1,900 + 2,400 + 4,400 gives 8,700, which is the weighted total, not the average.
Divide that by the total weight to get the real figure. If your weights total 100, the answer is the total divided by 100.
- Is a GPA a weighted average?
Yes. Grade points are the values and credits are the weights, so a 4-credit A counts four times as much as a 1-credit A.
The GPA calculator does this with the grade scales already built in, so use that one if you are working with letter grades.
- Can a weight be zero or negative?
A zero weight simply removes that item from the result, which is a useful way to see what one piece of work is actually doing.
Negative weights are allowed because they are occasionally genuine, such as a correction entry. If the weights cancel to zero overall there is no defined average, and the result is left blank rather than shown as zero.
Problems people actually run into
Forgetting to divide at the end
Multiplying and adding gives the weighted total, not the average. On a set of percentage weights that number is roughly 100 times too big.
The giveaway is a result in the thousands when you expected something between 0 and 100.
Averaging the averages
Taking the plain average of two weighted averages does not give the combined weighted average, unless both halves carried the same total weight.
A 3.8 across 6 credits and a 3.0 across 15 credits is not 3.4. Put all the items into one calculation instead.
Mixing units in the weight column
Percentages in some rows and credits in others produces a number that means nothing, because the ratios between them are arbitrary.
Pick one unit for the whole column. Any unit works, as long as it is the same one throughout.
Results are estimates for general information only and are not professional financial, medical, or legal advice. Read our full disclaimer.
