Average Calculator · Practical guide
How to Average Percentages Correctly
Sometimes a plain average of percentages is right — and sometimes it badly misleads. Here is how to tell.
At a glance
When a Plain Average Works
If every percentage is measured against the same base, average them like any numbers: 10%, 20%, and 30% average to (10 + 20 + 30) ÷ 3 = 20%. Enter them in the calculator above as 10, 20, 30 and the arithmetic mean confirms it. This is correct for things like three quizzes each worth 100 points, or monthly error rates on equal production volumes.
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Result
When It Goes Wrong: Different Bases
Store A sells 20 of 200 items (10%). Store B sells 15 of 50 items (30%). The plain average of 10% and 30% is 20% — but the true combined rate is (20 + 15) ÷ (200 + 50) = 35 ÷ 250 = 14%. The big store dominates, so the real figure sits much closer to its 10%.
The Fix: Weight by the Base
Convert each percentage back to counts, add the numerators and denominators separately, and divide. Equivalently, weight each percentage by its base: (10% × 200 + 30% × 50) ÷ 250 = 14%. The plain mean treats every percentage as equally important; the weighted mean treats every underlying item as equally important — which is usually what you want.
A Special Case: Growth Percentages
Percentages that compound, like annual returns, need the geometric mean rather than the arithmetic one. Gains of 10% and 30% in consecutive years multiply to 1.10 × 1.30 = 1.43, and the true yearly average is 1.43^(1/2) − 1 ≈ 19.6%, not the arithmetic 20%. Select Geometric Mean in the tool above and enter 1.10, 1.30 to see it.
Frequently Asked Questions
Can you ever just average two percentages?
Yes, when both are shares of the same total or equal-sized groups — for example, two exams both out of 100 points. Equal bases make the plain average exact.
Why does averaging percentages of different totals give the wrong answer?
Because a percentage compresses away the size of its group. A 10% rate on 1,000 cases carries far more real weight than a 30% rate on 20 cases, and a plain average ignores that.
How do I average survey percentages with different sample sizes?
Weight each percentage by its sample size: sum (percentage × n) over all groups, then divide by the total n. That reproduces the result you would get by pooling all responses.
What about average percentage change over time?
Use the geometric mean of the growth factors. Convert each change to a multiplier (a 25% increase is 1.25), average those geometrically, and convert back.