Calculation
Mathematical Formula For Calculating Percentage Increase
$$\text{Percentage Increase} = \frac{\text{New Value} – \text{Initial Value}}{\text{Initial Value}} \times 100$$
Example Broken Down With Steps
$$
\text{Given: Initial Value = 150, New Value = 200}
$$
$$
\text{Step 1: Subtract 150 from 200: } 200 – 150 = 50
$$
$$
\text{Step 2: Divide 50 by 150: } \frac{50}{150} = 0.3333
$$
$$
\text{Step 3: Multiply 0.3333 by 100: } 0.3333 \times 100 = 33.33
$$
$$
\text{Result: Percentage increased by 33.33%.}
$$
Further Explained
Example: A plant grew from 150 cm to 200 cm.
Steps:
- Find the increase in value: Subtract the original height from the new height:
$$ 200 – 150 = 50 $$ - Divide the increase by the original height:
$$ \frac{50}{150} = 0.3333 $$ - Convert to a percentage: Multiply the result by 100:
$$ 0.3333 \times 100 = 33.33\% $$ - Conclusion: The plant grew by 33.33%.
After a Loss, Recovery Requires a Bigger Percentage Gain
An important property of percentage increase is that recovering from a percentage loss always requires a larger percentage gain. The bigger the loss, the more dramatic this difference becomes.
Why This Happens
After a loss, your base value is smaller. A percentage gain is calculated on that reduced base, so you need a proportionally larger percentage to get back to the original amount.
The Formula
Required gain to recover = Loss% / (100 − Loss%) × 100
Recovery Table
LossGain needed to recover10%11.1%20%25%25%33.3%30%42.9%40%66.7%50%100%75%300%90%900%
Example Broken Down With Steps
An investment drops by 50%. What percentage increase is needed to recover?
Step 1: After a 50% loss, $1,000 becomes $500
Step 2: To get from $500 back to $1,000 requires gaining $500
Step 3: 500 / 500 × 100 = 100%
$$\text{Result: You need a 100% gain to recover from a 50% loss.}$$
Using the formula:
$$ \frac{50}{100 – 50} \times 100 = \frac{50}{50} \times 100 = 100% $$
This is why protecting against large losses matters so much in investing. A 50% loss does not need a 50% gain to recover — it requires a full 100% gain, which means the value must double.
Use our Percentage Decrease Calculator to calculate the loss, then use the calculator above to find the gain needed for recovery.