Average Percentage Calculator
Three quizzes at 88, 94 and 79 percent average 87 percent when each test counts the same. If the third test has 100 questions and the first two have 10, the weighted average falls to 81 percent because the big test dominates. Enter a percentage and its size for each row to see both averages.
Enter each percentage, and the size behind it (questions, shoppers, orders) when the rows do not represent the same amount.
| Simple average | |
| Weighted average | |
| Weighted minus simple | |
| Total size counted | |
| Rows used |
All calculations run in your browser, and nothing you type is uploaded or stored.
Enter several percentages to get their plain average, then add the size behind each one to see the weighted average next to it.
Key takeaways
- 88, 94 and 79 percent average 87 when every test counts the same
- 90 percent of 10 questions plus 70 percent of 100 combines to 71.82 percent, not 80
- Weighted average: multiply each percentage by its size, add, then divide by the sizes
- Stores at 85, 78 and 91 percent average 84.67 unweighted and 81.27 weighted
- 88 to 92 percent is a gain of 4 points, which is a 4.55 percent rise
On this page
What an average percentage says
What an average percentage says
An average percentage answers one question: what is the typical result when several results already sit on the same 0 to 100 scale? Three quizzes at 88, 94 and 79 percent have a typical score of 87 percent. The reading is only as honest as the thing each percentage divides by, and that is where almost every mistake comes from.
A percentage always hides a fraction. 88 percent means 88 correct out of some number of questions, 85 percent means 85 yes out of some number of shoppers. When those hidden counts differ in size, the plain average treats an 88 on a 10 question quiz the same as an 88 on a 1,000 question exam. The weighted average fixes that by counting each percentage once for every unit behind it.
Both averages have a job. The plain average describes the typical item in your list, like a typical quiz. The weighted average describes the typical unit behind the list, like a typical question. Which one you want depends on whether the quiz or the question is the thing you care about. For percent of, change and reverse percent work on single numbers, the percentage calculator covers the ground this page does not.
The simple average, step by step
The simple average, step by step
The simple average of percentages works like the average of any numbers. Add the percentages, divide by how many there are, and keep the percent label. For 88, 94 and 79: the sum is 88 + 94 + 79 = 261, and 261 / 3 = 87, so the average is 87 percent.
Two percentages follow the same shape. The average of 92 and 78 is (92 + 78) / 2 = 85. Nothing about the percent sign changes the arithmetic, because every value shares the same scale.
This shortcut is legitimate whenever each percentage represents the same amount: quizzes worth the same points, weeks with similar volume, groups of the same size. It is also the right answer to a different question than the weighted average asks. If the school reports one grade per subject and each subject counts equally, the plain average of the subjects is exactly what the transcript shows.
Why group size changes the answer
Why group size changes the answer
Take two quizzes. The first: 90 percent on 10 questions, which is 9 correct. The second: 70 percent on 100 questions, which is 70 correct. Your overall record is (9 + 70) correct out of (10 + 100) questions, and 79 / 110 = 71.82 percent. The simple average of the two scores is 80 percent. The real number is more than 8 points lower, because the 100 question quiz carries ten times the weight of the small one.
| Quiz | Questions | Score | Correct answers |
|---|---|---|---|
| First | 10 | 90% | 9 |
| Second | 100 | 70% | 70 |
| Both together | 110 | 71.82% | 79 |
The weighted average formula says the same thing in general terms: multiply each percentage by its group size, add those products, then divide by the sum of the sizes. Written out: (90 x 10 + 70 x 100) / 110 = (900 + 7,000) / 110 = 71.82 percent. The sizes in the denominator are what pull the result toward the big group.
The gap between the two readings is not an error on either side. It is the difference between "my typical quiz score" and "my typical question answered correctly". Reports that sound contradictory usually just picked different denominators.
When the simple average is the right one
When the simple average is the right one
Use the plain average when the pieces behind the percentages are the same size or close to it. Three tests each worth 100 points. Four weeks of sales with similar volume each week. Five calls rated on the same scale. When the sizes differ by a few percent, the weighted answer barely moves, and the simple average is easier to explain.
A useful threshold: if the largest group is less than about one and a half times the smallest, the two averages usually land within a point or two of each other. In the quiz example the largest group is 10 times the smallest, and the gap is 6 points. In the store example below it is nearly 5 times, and the gap is more than 3 points. The bigger the spread in group sizes, the more the choice of average matters.
There is also a reporting convention angle. Some published figures, like the averages the Bureau of Labor Statistics publishes for employment and prices, are weighted by design, because a worker or a purchase in a big group counts the same as any other. When you rebuild such a number from percentages you found separately, weight it the way the source did or the comparison breaks.
School statistics follow the same rule. The National Center for Education Statistics weights its enrollment and achievement figures by student counts, because a percentage from a district of 40,000 students says more about the national picture than one from a district of 400. Any average you rebuild from published percentages inherits whatever weighting the source chose.
Worked example: three stores, three sample sizes
Worked example: three stores, three sample sizes
Suppose you survey shoppers at three stores about whether they would return. Store A: 85 percent of 40 shoppers. Store B: 78 percent of 120 shoppers. Store C: 91 percent of 25 shoppers. Which number describes the whole chain?
| Store | Shoppers surveyed | Would return | Shoppers behind it |
|---|---|---|---|
| Store A | 40 | 85% | 34.00 |
| Store B | 1,20 | 78% | 93.60 |
| Store C | 25 | 91% | 22.75 |
The simple average is (85 + 78 + 91) / 3 = 84.67 percent. The weighted average is 150.35 / 185 = 81.27 percent, because Store B alone contributes more than half the sample and drags the reading toward its 78 percent. The gap is 3.40 points, and either number can be the headline: 84.67 describes the typical store, 81.27 describes the typical shopper. Marketing wants the first number, operations wants the second.
Percentage points are not percent change
Percentage points are not percent change
Moving from 88 percent to 92 percent is a gain of 4 percentage points. As a percent change it is 4 / 88 = 4.55 percent, because the change is measured against where you started. Both statements are correct; they answer different questions and mixing them up inflates or shrinks stories by an order of magnitude.
| Move | Percentage points | Percent change |
|---|---|---|
| 88 to 92 percent | +4 | +4.55% |
| 90 to 85 percent | -5 | -5.56% |
| 50 to 75 percent | +25 | +50.00% |
| 20 to 60 percent | +40 | +200.00% |
The same pair of readings shows the pattern at its most dramatic from 50 to 75 percent: 25 points, but a 50 percent rise, because 25 / 50 = 0.5. News headlines say "up 50 percent" when the underlying rate went from half to three quarters. When you average percentages over time and then describe the movement, decide first whether your audience expects points or percent.
A practical guardrail: points describe the distance between two percentages on the same base. Percent change describes the relative size of the move. If the base is small, the two numbers diverge fast, and the percent change is the one that misleads.
How much precision to keep
How much precision to keep
Two decimal places are the working standard: 84.67 percent carries the story, and 84.6667 percent adds noise without information. Compute with full precision and round once, at the end. Rounding each percentage to a whole number before averaging shifts the answer by up to half a point, and the shifts can pile in one direction.
Weights deserve more care than the percentages do. A group size of 1,847 should stay 1,847, not become 1,800, because it multiplies every product in the numerator. The percentage itself is usually the coarser measurement; the count behind it is exact. When a published table gives you percentages but not sizes, treat any weighted average you build as an estimate and say so.
Finally, match the rounding to the decision. A teacher rounding 87.4 to 87 changes nothing. A warehouse cutting 99.2 percent accuracy to 99 in a dashboard hides roughly one missed order in every 125, and that is a real package.
Mistakes that skew an average of percentages
Mistakes that skew an average of percentages
- Averaging across different bases. The 90 percent on 10 questions and 70 percent on 100 example again: 80 percent is wrong for "how did I do overall". Weight whenever the sizes differ meaningfully.
- Averaging a rate with its complement. 60 percent correct and 40 percent wrong average to 50 percent, a number that describes nothing. List each measurement once, in one direction.
- Mixing percent of and percent change. A list holding "12 percent of revenue" and "8 percent growth" has no meaningful average. The two figures divide by different things.
- Assuming weighted is always more correct. If the question is about typical stores, not typical shoppers, the unweighted 84.67 is the honest answer. The average follows the question.
- Dropping weights when rows are filtered. Removing Store C from the set changes the weighted answer more than the simple one, because its 25 shoppers leave the denominator too.
When grades are the subject and points differ per assignment, the marks percentage calculator handles the weighted schoolwork case directly, and the weighted average calculator generalizes to any values and weights, not only percentages.
Frequently asked questions
What is the average of 85, 90 and 95 percent?
(85 + 90 + 95) / 3 = 90 percent. With three equal values it is also the middle one, so the mean and the median agree.
How do I average two percentages?
Add them and divide by 2. The average of 92 and 78 is 85 percent. If the two represent different sized groups, weight them instead: multiply each by its size first.
Why is the weighted average lower than the simple one?
It leans toward the largest group. 90 percent of 10 questions and 70 percent of 100 questions combine to 79 / 110 = 71.82 percent, not 80, because the big quiz dominates the denominator.
When can I just add percentages and divide?
When each percentage stands for the same amount of work: equal point quizzes, weeks of similar volume, groups of the same size. Then the weighted and simple averages come out the same.
What is a weighted average with weights 2, 3 and 5?
Multiply each value by its weight, add, and divide by the sum of the weights. For 80, 90 and 70 that is (160 + 270 + 350) / 10 = 78.
What is a percentage point?
The gap between two percentages measured directly. Going from 88 to 92 percent is 4 points. Points compare levels; percent change compares the size of the move.
Is 4 points from 88 to 92 a 4 percent increase?
No. It is a 4.55 percent increase, because 4 / 88 = 0.0455. The smaller the starting percentage, the bigger the gap between points and percent change.
Can I average percentages above 100 percent?
Yes. Sales teams hit 105 percent of quota and battery readings can exceed a nominal 100. The math works, though check that each figure shares the same base before averaging.
How many decimals should I keep?
Two for reporting: 84.67 percent. Carry full precision through the calculation and round once at the end, so rounding errors do not pile up row by row.
Why does my grade average differ from the school's?
Schools weight by points or credit hours, not by a plain mean of subject percentages. Weight each percentage by its size and the numbers line up with the transcript.
What if one group is much larger than the rest?
The weighted average lands near that group's percentage. 99 percent of 9,000 orders and 50 percent of 100 combine to 8,960 / 9,100 = 98.46 percent, which the simple average of 74.5 would badly misstate.
What is the average of 0 percent and 100 percent?
50 percent by either method, because the weights are equal. Whether that number means anything depends on whether the two items are comparable measurements at all.
Can I average negative percentages, like declines?
Yes, the signs carry through. A minus 20 percent month and a plus 10 percent month average minus 5 percent, but only when the two months had similar volume; otherwise weight them.
Does the order of the rows change the answer?
No. Addition treats rows the same in both averages. What matters is that each size travels with its own percentage when you weight, since pairing them wrong changes the result.
Spotted a wrong number or a broken result?
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