# Percentage of Percentage Calculator

(Base Percentage)

%

(Percentage on Base Percentage)

%

## How to use this Percentage of Percentage Calculator 🤔

- Enter ✎ value for Base Percentage (X).
- Enter ✎ value for Percentage on Base Percentage (Y).
- As soon as you enter the required input value(s), the Percentage of Percentage is calculated immediately, and displaed in the output section (present under input section).

## Calculating Percentage of a Percentage

Calculating the percentage of a percentage is a common operation, particularly in situations where one percentage is applied to another. This is often seen in scenarios such as compounded discounts, multi-level commissions, or layered interest rates.

The formula to calculate the percentage of a percentage is expressed as:

\( \text{Result} = \dfrac{ X \times Y }{ 100 } \)

where:

**X**represents the base percentage.**Y**represents the percentage applied to the base percentage.

By multiplying the two percentages and then dividing by 100, you obtain the percentage of the percentage.

## Examples

The following examples demonstrate how to calculate the percentage of a percentage using the given formula.

### 1. A real estate agent earns 5% commission on the sale price of a house. The agent’s broker takes 20% of the agent’s commission as a fee. What percentage of the house’s sale price does the broker take?

#### Answer

Given:

**X**= 5% (Agent’s commission percentage on the sale price)**Y**= 20% (Broker’s percentage of the agent’s commission)

The formula to calculate the percentage of a percentage is:

\( \text{Result} = \dfrac{ X \times Y }{ 100 } \)

Substituting the given values into the formula:

\( \text{Result} = \dfrac{ 5 \times 20 }{ 100 } \)

Simplifying further:

\( \text{Result} = 1\% \)

Therefore, the broker takes 1% of the house’s sale price.

### 2. A company offers a 30% bonus to its employees based on their annual performance. Out of this bonus, 15% is allocated to the employee’s retirement fund. What percentage of the employee’s annual salary is added to the retirement fund?

#### Answer

Given:

**X**= 30% (Bonus percentage)**Y**= 15% (Percentage of the bonus allocated to the retirement fund)

The formula to calculate the percentage of a percentage is:

\( \text{Result} = \dfrac{ X \times Y }{ 100 } \)

Substituting the given values into the formula:

\( \text{Result} = \dfrac{ 30 \times 15 }{ 100 } \)

Simplifying further:

\( \text{Result} = 4.5\% \)

Therefore, 4.5% of the employee’s annual salary is added to the retirement fund.

## Formula

To calculate the percentage of percentage, you can use the following formula.

where

## Calculation

Once you enter the input values in the calculator, the output parameters are calculated.