Average Percentage Calculator
Averaging percentages by adding them up only works when every group is the same size. Give each one a weight and this does it properly.
Each percentage and what it covers
Simple average (usually wrong)
70%
Total weight
100
The simple average is out by 16 points, because the groups are not the same size.
Weighted average
54%
Total ÷ 100
Why you cannot just average percentages
A percentage is a ratio, and a ratio carries a hidden denominator. Adding percentages up and dividing by the count throws that denominator away, which silently treats every group as the same size.
Where it goes wrong — two classes
Class A: 90% passed, 10 students → 9 passes
Class B: 50% passed, 90 students → 45 passes
Total: 54 passes out of 100 students = 54%
Simple average of 90 and 50 = 70%. Out by 16 points.
The simple average gave class A's ten students the same influence as class B's ninety. Weighting fixes exactly that.
The weighted average formula
Weighted average = Σ(Percent × Weight) ÷ Σ(Weight)
Multiply each percentage by its weight, add those up, then divide by the total weight.
Choosing the weight
The weight is whatever the percentage was taken out of:
- Test scores — the points available on each test.
- Survey results — the number of people who answered.
- A course grade — the share of the final mark each assessment carries.
- Sales figures — the revenue or unit count behind each rate.
When every weight is the same, the weighted average and the simple average agree. That is the only case where the shortcut is safe.
Percentages of different things never average
Weighting fixes different group sizes. It cannot rescue percentages measuring different quantities. A 20% interest rate and a 20% fat content have no meaningful average at any weight, because they are not the same kind of number.
Common questions
- Can I average percentages by adding them and dividing?
- Only when every percentage covers a group of the same size. If the groups differ, you must weight each percentage by its group size, or the answer will be wrong.
- What is the weighted average percentage formula?
- Multiply each percentage by its weight, add the results, then divide by the total weight. Weight means group size, or the share of the final mark.
- What should I use as the weight?
- Whatever the percentage was taken out of. For test scores it is the points available. For survey results it is the number of respondents. For a course grade it is the share each assessment carries.
- How wrong can a simple average be?
- Very. 90% of 10 students and 50% of 90 students is 54% overall, but a simple average reports 70% — a 16-point error.