Quick answer
X% of Y% is X × Y ÷ 100 (as a percent). 50% of 20% is 10%.
Enter X and Y, and optionally a base amount. The calculator returns the combined percentage.
Related tools: Percentage Calculator: Calculate a percentage of a number, what percent one number is of another, or the whole from a part. Percentage Change Calculator: Find the percentage increase or decrease from an old value to a new value. Ratio Percentage Calculator: Percentage share of each part of a ratio.
How to use the Percentage of a Percentage Calculator
- Enter x (%).
- Enter y (%).
- Optionally, enter base amount.
- Press Calculate to see the result, and use Reset to start again.
| Input | What to enter | Allowed values |
|---|---|---|
| X | A number, in % | — |
| Y | A number, in % | — |
| Base amount (optional) | A number | — |
Formula and method
Formula
X% of Y% = X × Y ÷ 100 (%)
IEEE-754 double precision; shown to at most 6 decimal places.
Multiply the percentages; apply to a base amount when given.
Worked examples
This example is verified: each one is an automated test case that the live calculator must reproduce exactly.
Example 1
Inputs: X = 50; Y = 20.
| Result | Value |
|---|---|
| Result | 10 % |
The first line is the headline result (result). IEEE-754 double precision; shown to at most 6 decimal places.
Multiplying fractions
50% × 20% = 0.5 × 0.2 = 0.1 = 10%. Applied to a base of 200: 20% of 200 is 40 and 50% of that is 20, which is 10% of 200.
Common uses
Layered discounts, tax on a portion, or the share of a subgroup. Note that two discounts of 20% and 10% give 28% off, not 30%.
How the result changes with x
Holding every other input at the first worked example, this table changes only x. It shows how sensitive the answer is to that one value; each row was produced by running this calculator.
| X | Result |
|---|---|
| 25 | 5 % |
| 50 | 10 % |
| 100 | 20 % |
| 200 | 40 % |
What happens with invalid input
These messages are produced by the calculator itself, so you know what to fix.
- X: left empty shows "Enter x." beside that field and no result.
Choosing between the Percentage of a Percentage Calculator and similar calculators
Each row shows what a related calculator on this site asks for and what it returns, so you can pick the one that matches your question.
| Calculator | You enter | It returns |
|---|---|---|
| [Percentage Calculator](/math/percentage-calculator/) | what do you want to find?, a and b | 15% of 200 |
| [Percentage Change Calculator](/math/percentage-change-calculator/) | old value and new value | Percentage change |
| [Ratio Percentage Calculator](/math/ratio-percentage-calculator/) | part A and part B | Part A |
| [Reverse Percentage Calculator](/math/reverse-percentage-calculator/) | final amount, percentage applied and it was | Original amount |
| [Fraction Calculator](/math/fraction-calculator/) | numerator 1, denominator 1 and operation | Result |
Background: rounding and basic arithmetic
Rounding to a place looks at the digit just to its right: 0 to 4 rounds down and 5 to 9 rounds up (the half-up convention, so 2.5 becomes 3). Rounding 838.274 gives 800 to the nearest hundred, 840 to the nearest ten and 838 to the nearest one.
Some systems use banker's rounding (half to even), which sends 2.5 to 2 and 3.5 to 4; check which convention your task requires, and round only at the end of a multi-step calculation.
Assumptions and limitations
- Base optional
If a required value is empty, not a number, or outside its allowed range, the form marks that field with a message and shows no result instead of a misleading number. The automated checks deliberately try invalid entries for x to confirm this.
Frequently asked questions
What is 10% of 10%?
10% of 10% = 0.1 × 0.1 = 0.01, or 1%.
What is 25% of 40%?
25% of 40% = 0.25 × 0.40 = 0.10, or 10%.
Is it the same as adding?
No. Percentages of percentages multiply: 50% of 20% is 10%, not 70%.
What does the Percentage of a Percentage Calculator calculate?
Find X% of Y%, optionally applied to a base amount. It returns Result.
What formula does the Percentage of a Percentage Calculator use?
X% of Y% = X × Y ÷ 100 (%). Multiply the percentages; apply to a base amount when given.
What do I need to enter in the percentage of a Percentage Calculator?
You enter X (%) and Y (%). Optional: Base amount.
How is the result rounded or limited?
IEEE-754 double precision; shown to at most 6 decimal places. Base optional.
What is an example of a percentage of a Percentage result?
With x 50 and y 20, the result is 10 %.
Related calculators
- Percentage Calculator — Calculate a percentage of a number, what percent one number is of another, or the whole from a part.
- Percentage Change Calculator — Find the percentage increase or decrease from an old value to a new value.
- Ratio Percentage Calculator — Percentage share of each part of a ratio.
- Reverse Percentage Calculator — Work backwards from a final amount to the original value before a percentage increase or decrease.
- Fraction Calculator — Add, subtract, multiply and divide fractions with simplified and mixed-number results.
- Ratio Calculator — Simplify a ratio of two whole numbers.
Sources
- OpenStax, Prealgebra 2e (Rice University): fractions, decimals, percents, ratios and rounding
Content last reviewed 2026-11-04. Formulas and worked examples are checked by automated tests against independently computed values.