Percentage of Percentage Calculator
Calculate compound percentages, nested discounts, and complex percentage operations with step-by-step solutions
Calculate Percentage of Percentage
The base percentage value
Percentage to take from the first percentage
Calculation Results
Formula: (0% × 0%) ÷ 100 = 0%
In decimal form: (0 × 0) = 0.0000
Real-World Examples
Double Discount
20% off, then another 15% off
First discount reduces price by 20%, then second discount of 15% applies to already reduced price
Tax on Tax
10% state tax, then 5% federal tax
Federal tax of 5% applies to the amount that already includes 10% state tax
Investment Returns
8% annual return, 25% of which is taxed
25% of the 8% return (which is 2%) is subject to taxation
Quick Reference
Basic Formula
(A% × B%) ÷ 100 = Result%
Where A is first %, B is second %
Decimal Method
Convert to decimals, multiply, then convert back
More accurate for calculations
Common Uses
Discounts, taxes, commissions, interest
Any nested percentage calculation
Common Calculations
Understanding Percentage of Percentage
What is Percentage of Percentage?
A percentage of a percentage is a compound calculation where you take a certain percentage of another percentage value. This is commonly encountered in real-world scenarios involving multiple discounts, taxes, or nested calculations.
Mathematical Foundation
When calculating A% of B%, you're essentially multiplying two fractions:
A% × B% = (A/100) × (B/100) × 100%
Key Properties
- •The result is always smaller than both original percentages
- •Order matters: A% of B% ≠ B% of A% (unless A = B)
- •The operation is equivalent to division by 100
Common Applications
Double Discounts
When a store offers 20% off, then an additional 15% off the already discounted price, you're calculating 15% of the remaining 80%, not 35% total.
Tax Calculations
When federal tax applies to income that already includes state tax, or when calculating tax on items that have already been marked up by a percentage.
Investment Returns
Calculating what portion of investment returns are subject to taxes, or determining management fees as a percentage of gross returns.
Commission Structure
When calculating bonuses that are a percentage of commission, or determining split percentages in multi-level commission structures.
Advanced Concepts
Compound Percentages
Multiple percentage calculations applied sequentially, where each builds on the previous result.
Percentage Points vs Percentages
Understanding the difference between relative percentage changes and absolute percentage point changes.
Reverse Calculations
Working backwards from a final percentage to determine the original percentages that produced it.