Percentage of a percentage calculator

What is a Percentage

A percentage is a ratio expressed as a fraction of 100. The percentage is commonly represented by the percent sign, %, or the abbreviation “pct.” The term “per cent” is derived from the Latin word “per centum,” which means “per hundred.” The percentage is sometimes written as two words in British English: “percentage” (although percentage and percentile are reported as one word).

How to Find Percentage of a Percentage

Sometimes you have to find the percentage of a percentage, which can be difficult. For example, converting both to decimal form and multiplying them together yields the percent of a percent.

To convert each percentage to decimal form, divide it by 100. The result is obtained by multiplying the decimals together. To convert a decimal to a percentage, multiply the result by 100.

The formula for the Percentage of a Percentage

Use the following formula to calculate the percentage of a percentage:

Percentage of a percentage = \( (\dfrac{percent 1}{100} × \dfrac{percent 2}{100}) × 100 \)

Examples

Example 1: Find 25% of 60%.

We will start with the formula to calculate a percentage of a percentage which is:

\( P = (\dfrac{percent 1}{100} × \dfrac{percent 2}{100}) × 100 \)

Now, substitute the given values in the equation.

\( P = (\dfrac{25}{100} × \dfrac{60}{100}) × 100 \)

By simplifying them, we will get the following:

\( P = (0.25 × 0.6) × 100 = 0.15 × 100 = 15 \)

\( P = 15\% \)

Example 2: Find 50% of 40%

\( P = (\dfrac{50}{100} × \dfrac{40}{100}) × 100 \)

Simplifying,

\( P = (0.50 × 0.40 ) × 100 = 0.20 × 100 = 20 \)

\( P = 20\% \)

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