Math
Average Percentage Calculator
Type one percentage per line, optionally followed by the sample size it came from.
With sample sizes, the calculator finds the true overall rate by weighting each percentage by its group; without them, it gives the simple mean. Both results, the total counts, and the gap between them are shown so you can pick the right one.
One per line: percentage, then a space or comma, then the sample size (optional). For example '80 30' means 80% of 30 items.
Try an example
Result
Average percentage
—
- Simple average
- —
- Weighted by sample size
- —
- Total sample size
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- Lowest to highest
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Study path
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When a simple average of percentages is wrong
Percentages from groups of different sizes cannot simply be averaged. If 80% of 30 students passed and 90% of 10 students passed, the simple average is 85%, but the true pass rate is (24 + 9) / 40 = 82.5%. The larger group should count more. Weighting each percentage by its A smaller group taken from a population, used to estimate facts about the whole group. size fixes this.
| Group | Percentage | Sample size | Count |
|---|---|---|---|
| A | 80% | 30 | 24 |
| B | 90% | 10 | 9 |
| C | 70% | 60 | 42 |
| Total | weighted 75% | 100 | 75 |
The simple average of 80%, 90%, and 70% is 80%, but the weighted average is 75% because the 70% group is the largest. The check line in the work converts each percentage back to a count, adds the counts, and divides by the total, which is the definition of the overall rate.
How to use it
- Type each percentage on its own line. Percent signs are optional.
- If the percentages come from groups of different sizes, add the sample size after each one, separated by a space or comma.
- Read the average. With sample sizes it is the weighted average; without them it is the simple mean.
- Compare the simple and weighted values; a large gap means the group sizes vary a lot.
How to read the answer
The weighted average is the overall percentage you would get by pooling all the groups together. The simple average treats every group as equal. When they differ, the weighted one is usually the number to report, unless you intentionally want to average the groups themselves.
Common mistakes and edge cases
- Averaging percentages from different-sized groups without weights overstates small groups and understates large ones.
- Either give a sample size for every line or for none; mixing the two makes the weights meaningless.
- Weights of 0 add nothing; if all weights are 0 the weighted average is undefined.
- Percentages over 100% or negative percentages are accepted, but check that they make sense for your data.
- The average of percent changes over time is not the total percent change; that needs compounding, not averaging.
Worked examples
Weighted by sample size
80% of 30, 90% of 10, 70% of 60
Average percentage
75%
Simple average
No sample sizes
Average percentage
80%
Two groups
80% of 30 and 90% of 10
Average percentage
82.5%
Equal sizes match simple mean
Each of 50
Average percentage
70%
Decimals and percent signs
12.5% and 37.5%
Average percentage
25%
One value
Single percentage
Average percentage
42%
Mixed weights
Sample size on only one line
Average percentage
Error
Zero weights
All sample sizes 0
Average percentage
Error
Frequently asked questions
Can you just average percentages?+
Only when each percentage represents the same number of items. Otherwise weight each one by its sample size, or the small groups will count too much.
How do you find the weighted average of percentages?+
Multiply each percentage by its sample size, add the products, and divide by the total sample size. 80% of 30 and 90% of 10 gives (2400 + 900) / 40 = 82.5%.
Why is the weighted average different from the simple average?+
Because the groups are different sizes. The weighted average leans toward the percentages from the larger groups.
Which average should I report?+
The weighted average when you want the overall rate across everyone. The simple average when you want the typical group's rate.
Can I average percentage changes over several years?+
Not with this calculator. Percent changes compound, so use the geometric mean or the total change instead of an arithmetic average.
What if some groups have a sample size of 0?+
They contribute nothing to the weighted average. If every group has size 0, there is no weighted average.
About this calculator
- Written by
- mathcheck editorial team
- Last reviewed
- September 4, 2026
Method
- Uses the values entered by the user and stable formulas documented on the page.
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Last updated: September 4, 2026