What this calculator does
How to work out average percentage sounds like it should just mean adding the percentages and dividing by how many there are, and often that simple average is exactly right. But when each percentage comes from a different sample size, for example 80% of 10 people and 50% of 200 people, a plain average treats both groups as equally important, even though one represents twenty times as many people as the other.
This calculator works out both figures side by side: the simple average, treating every percentage equally, and the weighted average, which accounts for how large each underlying group actually was. The weighted average is the mathematically correct overall percentage when the groups differ in size; the simple average is only correct when every group is the same size.
The formula
The simple average adds up all the percentages and divides by how many there are. The weighted average instead multiplies each percentage by its sample size first, sums those, and divides by the total sample size across every group, so larger groups pull the overall figure more strongly toward their own result.
| Term | Meaning |
|---|---|
| Simple average | Every percentage counted equally: sum of percentages ÷ count. |
| Weighted average | Each percentage counted in proportion to its sample size: Σ(percentage × sample size) ÷ Σ sample size. |
| Sample size | How many people, items or trials each percentage is based on. |
The inputs explained
| Field | What to enter |
|---|---|
| Percentages (comma separated) | Each percentage figure, in the same order as its sample size below. |
| Sample size for each, same order (comma separated) | The sample size behind each percentage, in the same order as the percentages above. |
When to use it
Combining survey results from different-sized groups
If 80% of 10 respondents in one region approve of something, and 50% of 200 respondents in another region do, the overall approval rate across both regions is much closer to 50% than to the midpoint of 80% and 50%, because the larger group dominates the total.
Averaging pass rates across classes of different sizes
A small class with a high pass rate and a large class with a lower pass rate combine into an overall pass rate weighted toward the larger class, not a simple midpoint of the two rates.
Spotting when the two answers are the same
When every group being combined is exactly the same size, the weighted and simple averages come out identical, since the weighting has nothing to differentiate between groups.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How the percentage average calculator result changes with the percentages, at fixed sample sizes
A small group of 10 and a large group of 200, run across a range of percentage pairs.
| Percentages entered | Weighted average | Simple average |
|---|---|---|
| 80,50 | 51.4% | 65.0% |
| 90,40 | 42.4% | 65.0% |
| 70,70 | 70.0% | 70.0% |
| 95,20 | 23.6% | 57.5% |
| 60,90 | 88.6% | 75.0% |
| 100,10 | 14.3% | 55.0% |
How to calculate average percentage as the group sizes themselves change
The same two percentages, 80% and 50%, run against a range of different sample-size pairs.
| Sample sizes used | Weighted average | Simple average |
|---|---|---|
| 10,200 | 51.4% | 65.0% |
| 50,50 | 65.0% | 65.0% |
| 100,100 | 65.0% | 65.0% |
| 500,10 | 79.4% | 65.0% |
| 10,10 | 65.0% | 65.0% |
| 1,1000 | 50.0% | 65.0% |
Questions
How do I calculate average percentage when the groups are different sizes?
Use the weighted average: multiply each percentage by its sample size, add those products together, then divide by the total sample size across all groups. Simply averaging the percentages themselves ignores how many people or items each one represents.
How to work out average percentage from just two figures with no sample size given?
Without sample sizes, a simple average, adding the percentages and dividing by two, is the only option available, and it implicitly assumes the two figures carry equal weight.
Why do the simple and weighted averages sometimes match?
They match exactly whenever every group being combined has the same sample size, because in that case there is nothing for the weighting to differentiate between the groups on.
Is the weighted average always more correct than the simple average?
For combining percentages that each represent a different underlying group size, yes, the weighted average correctly reflects the true overall proportion. The simple average is appropriate only when the groups are equally sized, or when there genuinely is no size information to weight by.
For a straightforward average of a list of plain numbers, see the average calculator. For overall course grades built from weighted assignment scores, see the grade calculator.