Percentage of a Percentage Calculator

Calculate Percentage of a Percentage

Enter two percentages below to find the compound percentage. This calculator will show you the result and provide step-by-step explanations.

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Please enter a valid number for the first percentage.
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Please enter a valid number for the second percentage.

How to Calculate Percentage of a Percentage

Calculating the percentage of a percentage is a common task in various fields, including finance, statistics, and everyday calculations. This process involves finding a fraction of a fraction, expressed as percentages.

Percentage of a Percentage Formula

The formula to calculate the percentage of a percentage is:

\[ Result = \frac{Percentage1}{100} \times \frac{Percentage2}{100} \times 100\% \]

Where:

  • Percentage1 is the first percentage you want to take of the second percentage
  • Percentage2 is the second percentage
  • The result is expressed as a percentage of the original whole

Calculation Steps

  1. Convert both percentages to decimals by dividing by 100
  2. Multiply these two decimal values
  3. Multiply the result by 100 to convert back to a percentage

Example Calculation

Let's calculate 30% of 50%.

Step 1: Convert percentages to decimals

30% = 30 ÷ 100 = 0.30

50% = 50 ÷ 100 = 0.50

Step 2: Multiply the decimals

0.30 × 0.50 = 0.15

Step 3: Convert back to a percentage

0.15 × 100 = 15%

Step 4: Interpret the result

30% of 50% is equal to 15% of the original whole.

Visual Representation

Calculating 30% of 50% Original 100% Original Amount (100%) 50% of original 50% of Original 15% (30% of 50%) 15% Step 1: 50% = 0.50 Step 2: 30% = 0.30 Step 3: 0.50 × 0.30 = 0.15 Final Result: 15% 0% 25% 50% 75% 100%

This diagram illustrates how 30% of 50% results in 15% of the original whole. The entire rectangle represents 100%, the gray area represents 50%, and the blue area represents 15%, which is 30% of the 50%.

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