Average Percentage Calculator: Weighted by Sample Size or Simple Mean
Average percentages correctly: weight each percentage by its sample size (or enter count/total), compare with the simple mean, and see each group’s share, with steps.
How it works
Weighted average % = (p₁ × n₁ + p₂ × n₂ + … + pₖ × nₖ) ÷ (n₁ + n₂ + … + nₖ) · simple average % = (p₁ + p₂ + … + pₖ) ÷ k · from counts: overall % = (c₁ + c₂ + …) ÷ (t₁ + t₂ + …) × 100
A percentage is a share of some base, so two percentages can only be averaged directly when their bases are the same size. If 90% of 300 customers at one store are satisfied and 67% of 45 at another, the overall figure is not halfway between: the larger store counts for more. Weighting each percentage by its sample size gives the true overall share, which is the same as adding up the underlying counts (90% × 300 = 270 people, 67% × 45 = 30.15) and dividing by everyone surveyed. Enter each group as "percentage, sample size" or as "count/total" (for example 45/60 for 45 passes out of 60). The calculator shows the weighted average, the plain mean of the percentages and the gap between them in percentage points, plus each group’s weight. Use the simple average only when every group is the same size or you deliberately want each group to count equally, such as averaging a teacher’s class pass rates as classes. Percentage changes over consecutive periods (growth rates, returns) should be compounded, not averaged with either formula. The weighted mean calculator handles any values and weights; this page is set up for percentages, accepts count/total pairs and compares the weighted result with the naive mean. The percentage calculator solves single X% of Y problems.
Worked example
Three stores report satisfaction of 82% (120 replies), 67% (45 replies) and 90% (300 replies). The weighted average is (82 × 120 + 67 × 45 + 90 × 300) ÷ (120 + 45 + 300) = 39,855 ÷ 465 = 85.71%. The simple average (82 + 67 + 90) ÷ 3 = 79.67% is 6.04 percentage points too low because it gives the small 45-reply store as much say as the 300-reply one. In total 398.55 of 465 customers (85.71%) were satisfied.
Sources: Omni Calculator: Average percentage (simple and sample-size weighted, pancake survey example)
Frequently asked questions
Can you average percentages?
Only directly when they come from groups of the same size. Otherwise multiply each percentage by its group size, add the results and divide by the total size. That weighted average equals the percentage you would get by pooling all the raw counts.
How do I calculate the average of percentages with different sample sizes?
Use the weighted formula: Σ(percentage × sample size) ÷ Σ sample size. For 64% of 300, 42% of 450 and 36% of 250: (19,200 + 18,900 + 9,000) ÷ 1,000 = 47.1%.
Why is the simple average of percentages wrong?
It treats a group of 10 the same as a group of 1,000. If four students score 80% and one scores 40%, averaging the two distinct values gives 60%, but the class average is (4 × 80 + 40) ÷ 5 = 72%.
How do I average percentages in Excel?
Put the percentages in one column and the sample sizes in the next, then use =SUMPRODUCT(A2:A10,B2:B10)/SUM(B2:B10). A plain =AVERAGE(A2:A10) gives the unweighted mean.
Should I average percentage growth rates?
No. Growth or return percentages over successive periods compound, so use the geometric mean, e.g. ((1 + r₁)(1 + r₂)…)^(1/n) − 1, which is what an annualized-return or CAGR calculator does.
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This calculator is for educational purposes. Double-check important results before acting on them.