Percentage of Percentage Calculator
A percentage of a percentage is a compound calculation where you find what one percentage is of another percentage. It's essentially multiplying two percentages together and converting the result back to a percentage.
This concept is particularly useful in situations where you need to calculate nested or compound percentages, such as tax calculations, multi-level discounts, or compound growth rates.
To calculate a percentage of another percentage, follow these steps:
- Convert both percentages to decimals (divide by 100)
- Multiply the two decimal numbers together
- Convert the result back to a percentage (multiply by 100)
For example, to calculate 50% of 30%:
- Convert to decimals: 50% = 0.5, 30% = 0.3
- Multiply: 0.5 × 0.3 = 0.15
- Convert to percentage: 0.15 × 100 = 15%
Tax on Discounted Items
If an item is discounted by 20% and has a sales tax of 10%, you're calculating 10% of 80% (the remaining amount after discount). This would be 8% of the original price.
Compound Interest
When calculating partial year interest, you might need to find 75% of a 5% annual rate to determine the interest for 9 months (75% of a year).
Market Share Changes
If a company has 40% market share and loses 25% of that share, you're calculating 25% of 40% to find the percentage points lost.
Adding Instead of Multiplying
A common mistake is adding percentages instead of multiplying them. Remember that 50% of 30% is not 80%, but rather 15%.
Forgetting to Convert Back
After multiplying the decimal values, don't forget to multiply by 100 to convert back to a percentage.
Order of Operations
While the order doesn't matter when simply multiplying two percentages, it can matter in more complex calculations involving additions or subtractions.