Percentage of a Percentage Calculator
Calculate compound percentages, commission splits, and chained discounts with exact decimal steps.
Percentage of a percentage
Percentage of a percentage formula
When solving compound percentages or stacked rates, multiply both percentages and divide by 100:
In decimal notation: (P₁ ÷ 100) × (P₂ ÷ 100) × 100 = (P₁ × P₂) ÷ 100.
Worked examples with real numbers
Step-by-step arithmetic for common percentage of a percentage calculations:
20% of 50%
Multiply: 20 × 50 = 1,000
Divide by 100: 1,000 ÷ 100 = 10
15% of 30%
Multiply: 15 × 30 = 450
Divide by 100: 450 ÷ 100 = 4.5
25% of 6% commission
Multiply: 25 × 6 = 150
Divide by 100: 150 ÷ 100 = 1.5
Frequently asked questions
How do you calculate a percentage of a percentage?
Multiply both percentage values together and divide by 100. Formula: Result (%) = (P1 × P2) ÷ 100. For example, 20% of 50% is (20 × 50) ÷ 100 = 1000 ÷ 100 = 10%.
Why isn't 20% of 50% equal to 30%?
Taking a percentage of a percentage is multiplication, not addition or subtraction. You are taking a fraction (20/100) of another fraction (50/100): 0.20 × 0.50 = 0.10, which equals 10%.
Where is percentage of a percentage used in real life?
It is frequently used in tiered royalties, probability trees, stacked retail promotions, commission splits, and equity dilution.
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