Math & Percentage

Average Percentage Calculator

Calculate the simple or weighted average of multiple percentages with sample sizes.

Math

Average Percentage Calculator

Compute the exact average of percentages with equal or varying sample sizes.

#1
#2
#3
Average Result
%37.50
Weighted by sample size
Weighted Average %37.50
Simple Average %36.67
Total Sample Size 400
Weighted Value Sum 15.000
Number of Values 3

Average Percentage Calculation Guide

Calculating the average of multiple percentages requires care. While percentages can simply be averaged arithmetically when sample sizes are identical, datasets with varying sample sizes require weighted averaging.

Mathematical Formulas

1. Simple Average (Arithmetic Mean)

When all percentages represent equal sample sizes or weights:

Simple Average (%) = (P₁ + P₂ + ... + Pₙ) / n

2. Weighted Average

When each percentage (Pᵢ) is based on a distinct sample size or weight (Wᵢ):

Weighted Average (%) = Σ (Pᵢ × Wᵢ) / Σ Wᵢ = [(P₁ × W₁) + (P₂ × W₂) + ...] / (W₁ + W₂ + ...)

Practical Example

Suppose a school gives exams to two classes:

  • Class A: 20 students with an average score of 80%
  • Class B: 80 students with an average score of 90%

The simple average would be (80 + 90) / 2 = 85%. However, the weighted average correctly accounts for the larger class size:

Weighted Average = [(80 × 20) + (90 × 80)] / (20 + 80) = (1,600 + 7,200) / 100 = 88%