Percentage of Percentage Calculator
Calculate sales tax, compound interest, markups and markdowns, commissions, tips, and more.
Use this free percentage to a percentage calculator to solve all your percentage problems.
% to % Formula:
Percentage to Percentage (Percentage 1 ➗ 100) ✖️ (Percentage 2 ➗ 100) ✖️ 100
What is Percentage of a Percentage, Anyway?
The concept of finding a percentage of a percentage essentially involves applying two successive percentage calculations. When you calculate a percentage of a percentage, you’re applying one percentage calculation to another percentage, rather than to a base number.
Here’s a step-by-step breakdown using an example:
Suppose you want to find 25% of 30%.
- Convert Percentages to Decimals:
- Convert the first percentage to a decimal by dividing by 100: 25/100=0.25.
- Convert the second percentage to a decimal by dividing by 100: 30/100=0.30.
- Multiply the Decimals:
- Multiply the decimal values together: 0.25×0.30=0.075.
- Convert Decimal to Percentage:
- Convert the decimal result back to a percentage by multiplying by 100: 0.075×100=7.5%.
So, 25% of 30% is 7.5%.
You first apply a percentage reduction based on the first percentage to the second percentage. It’s a two-step reduction, first applying one percentage and then the other.
Percentage of a Percentage Calculator: Use Cases
- Calculating sales tax on a discounted item. For example, if a shirt is originally priced at $100 and is on sale for 20% off, and you live in a state with a 6% sales tax, you can use a percentage of a percentage calculator to find the total amount of sales tax you will pay.
- Calculating compound interest. Compound interest is interest that is earned on both the principal amount and the accumulated interest. For example, if you invest $100 at a 5% annual interest rate, you will earn $5 in interest the first year. In the second year, you will earn interest on both the original $100 and the $5 in interest you earned the first year. A percentage of a percentage calculator can be used to calculate the total amount of interest you will earn over a period of time.
- Calculating markups and markdowns. Retailers use markups and markdowns to determine the selling price of their products. A markup is a percentage of the wholesale price that a retailer adds to get the selling price. A markdown is a percentage of the selling price that a retailer subtracts to get the sale price. A percentage of a percentage calculator can be used to calculate markups and markdowns.
- Calculating commissions. Commissions are payments that are made to salespeople based on the value of the sales they make. For example, a salesperson may earn a 10% commission on all of the sales they make. A percentage of a percentage calculator can be used to calculate commissions on sales that are discounted.
- Calculating tips. Tips are customary payments that are made to service workers for their services. For example, it is customary to tip a waiter or waitress 15% to 20% of the bill amount. A percentage of a percentage calculator can be used to calculate tips on bills that include discounts.
TL;DR: Calculating a percentage of a percentage involves converting the percentages to decimals, multiplying the decimals together, and then converting the result back to a percentage.