Percentage Of Percentage Calculator

Mathematical Formula For Calculating Percentage Of Percentage

$$\text{Result} = \frac{\text{First Percentage}}{100} \times \text{Second Percentage}$$

Example Broken Down With Steps

$$
\text{Given: First Percentage = 50, Second Percentage = 80}
$$
$$
\text{Step 1: Divide 50 by 100: } \frac{50}{100} = 0.5
$$
$$
\text{Step 2: Multiply 0.5 by 80: } 0.5 \times 80 = 40
$$
$$
\text{Result: 50% of 80% is 40%.}
$$

Further Explained

Example: Find 50% of 80%.

Steps:

1. Convert the first percentage to a decimal: Divide 50 by 100:
   $$ \frac{50}{100} = 0.5 $$
2. Multiply the decimal by the second percentage: Multiply ( 0.5 ) by ( 80 ):
   $$ 0.5 \times 80 = 40 $$
3. Conclusion: 50% of 80% is 40%.

Applying Percentages Sequentially

When one percentage is applied to the result of another percentage, the combined result is found by multiplying — not adding — the two percentages.
x% of y% = (x / 100) × (y / 100) × 100%
Example Broken Down With Steps
What is 80% of 50%?
Step 1: Convert both to decimals: 0.80 and 0.50
Step 2: Multiply: 0.80 × 0.50 = 0.40
Step 3: Convert back: 0.40 × 100 = 40%
Result: 80% of 50% is 40%.
Real-World Application: Stacked Discounts
This is why stacked discounts do not add up. A “20% off plus 10% off” sale means you pay 80% of the price, and then 90% of that reduced price:
0.80 × 0.90 = 0.72 = 72%
You pay 72% of the original price, which is a 28% total discount — not 30%.
For more on how discounts work with percentages, see our Discount Calculator.