What is Percentage of a Percentage?
Calculating a percentage of a percentage means applying one proportional rate to another. The result is a smaller (or larger) percentage that represents the compound effect of both rates. This arises frequently in commission structures, tax-on-tax scenarios, compound discounts, and statistical analysis.
For example: A product has a 30% profit margin. The salesperson earns 15% commission on profits. Their commission as a percentage of the sale price is 15% of 30% = 4.5%. These nested calculations can become confusing, but the math is simple once you understand the principle.
The Formula
📐 Result = (First % ÷ 100) × Second %
Convert the first percentage to a decimal by dividing by 100, then multiply by the second percentage. The result is a new percentage value.
Real-World Examples
Commission on Margin: If profit margin is 40% and commission is 20% of margin: 20% of 40% = (20/100) × 40 = 8%. The salesperson earns 8% of the sale price.
Tax on Tax: Some jurisdictions apply multiple tax layers. A 10% state tax and a 5% city tax levied on the state tax means the city adds 5% of 10% = 0.5% to the total, for a combined rate of 10.5%.
Compound Discount: A product has a 20% wholesale discount, plus retailers get an additional 15% off the discounted price. The total effective discount is NOT 35% — it's: 20% off (you pay 80%), then 15% off that 80%. The second discount is 15% of 80% = 12%, so total discount = 20% + 12% = 32%.
Important Distinction: % of % vs. Adding Percentages
A 20% discount followed by a 10% discount is NOT a 30% discount. It's 20% + 10% of the remaining 80% = 20% + 8% = 28% total discount. This calculator helps you find the second step — what the percentage of the remaining/other percentage is — before combining them.
| First % | Second % | Result (% of %) |
|---|---|---|
| 50% | 50% | 25% |
| 20% | 30% | 6% |
| 15% | 40% | 6% |
| 10% | 10% | 1% |