Calculation
Mathematical Formula For Calculating Percentage Decrease
$$\text{Percentage Decrease} = \frac{\text{Initial Value} – \text{New Value}}{\text{Initial Value}} \times 100$$
Example Broken Down With Steps
$$
\text{Given: Initial Value = 500, New Value = 400}
$$
$$
\text{Step 1: Subtract 400 from 500: } 500 – 400 = 100
$$
$$
\text{Step 2: Divide 100 by 500: } \frac{100}{500} = 0.2
$$
$$
\text{Step 3: Multiply 0.2 by 100: } 0.2 \times 100 = 20
$$
$$
\text{Result: The price dropped by 20%.}
$$
Further Explained
Example: A book’s price dropped from 500 to 400.
Steps:
- Find the decrease in value: Subtract the new price from the original price:
$$ 500 – 400 = 100 $$ - Divide the decrease by the original price:
$$ \frac{100}{500} = 0.2 $$ - Convert to a percentage: Multiply the result by 100:
$$ 0.2 \times 100 = 20\% $$ - Conclusion: The price decreased by 20%.
Recovery After a Decrease: Why You Need a Bigger Increase
After any percentage decrease, getting back to the original value requires a larger percentage increase — not an equal one. This is because the increase is calculated on the reduced (smaller) base.
Quick Reference
DecreaseIncrease needed to recover10% loss11.1% gain20% loss25% gain25% loss33.3% gain50% loss100% gain (must double)75% loss300% gain (must quadruple)
Example Broken Down With Steps
A product’s price drops by 20%, from $100 to $80. What increase is needed to return to $100?
Step 1:
$$\text{New price after 20% decrease: } 100 \times 0.80 = 80$$
Step 2: Difference to recover: 100 − 80 = 20
Step 3: Required increase: 20 / 80 × 100 = 25%
Result: A 25% increase is needed to recover from a 20% decrease.
The key insight is that the 20% decrease removed $20 from a base of $100, but the recovery must add that same $20 to a smaller base of $80 — which is why it takes 25%, not 20%.
For a detailed breakdown of how percentage increases work, see our Percentage Increase Calculator.