Percentage of a Percentage Calculator

Calculate what one percentage of another percentage equals, with step-by-step explanation.

Enter Percentages

Result

Percentage of a Percentage
10%
First Percentage 20%
Second Percentage 50%
Combined Percentage 10%
As a Decimal 0.1
Applied to Base Value 10

Step-by-Step Solution

Result = (20/100) x (50/100) x 100 = 10%

Understanding Percentage of a Percentage

A percentage of a percentage is a common concept that arises when you need to find a fraction of a fraction. For example, "What is 20% of 50%?" means you are taking 20% of the value that represents 50% of something. This type of calculation appears frequently in business discounts, tax calculations, and probability.

The Formula

To find a percentage of a percentage, convert both percentages to decimals and multiply them together, then convert back to a percentage:

Basic Formula

Multiply the two percentages as decimals, then express as a percentage.

Result = (P1/100) x (P2/100) x 100

Simplified Formula

Equivalently, multiply the two percentages and divide by 100.

Result = (P1 x P2) / 100

With a Base Value

Apply the combined percentage to a base value.

Value = Base x (P1/100) x (P2/100)

Real-World Examples

Stacked Discounts

A store offers 30% off, and you have an additional 20% coupon applied after the first discount. The total discount is not 50%, but rather: 30% of the original is removed first, then 20% of the remaining 70% is removed. The extra discount is 20% of 70% = 14%. So the total discount is 30% + 14% = 44%, not 50%.

Commission Splits

An agent earns 15% commission, and shares 40% of that with their team. The team gets 40% of 15% = 6% of the total sale. The agent keeps 15% - 6% = 9%.

Key Points

  • Percentage of a percentage always yields a smaller percentage than either input.
  • The order does not matter: 20% of 50% equals 50% of 20%.
  • This operation is multiplication, not addition.
  • It is commonly confused with adding percentages, which gives incorrect results.