To calculate percentage increase or decrease, compare the change between two values with the original value. The basic formula is:
\text{Percentage change} = \frac{\text{New value} - \text{Original value}}{\text{Original value}} \times 100A positive result is a percentage increase. A negative result is a percentage decrease.
Percentage Increase Formula
Use this formula when the new value is higher than the original value:
\text{Percentage increase} = \frac{\text{New value} - \text{Original value}}{\text{Original value}} \times 100Example: Price increase
A product’s price rises from $40 to $50.
\frac{50 - 40}{40} \times 100 = \frac{10}{40} \times 100 = 25\%The price increased by 25%.
Example: Salary increase
A monthly salary rises from $2,500 to $2,750.
\frac{2,750 - 2,500}{2,500} \times 100 = \frac{250}{2,500} \times 100 = 10\%The salary increased by 10%.
Percentage Decrease Formula
Use this formula when the new value is lower than the original value:
\text{Percentage decrease} = \frac{\text{Original value} - \text{New value}}{\text{Original value}} \times 100Example: Price reduction
A jacket’s price falls from $80 to $60.
\frac{80 - 60}{80} \times 100 = \frac{20}{80} \times 100 = 25\%The price decreased by 25%.
Example: Website traffic drop
Monthly visits fall from 8,000 to 6,000.
\frac{8,000 - 6,000}{8,000} \times 100 = \frac{2,000}{8,000} \times 100 = 25\%Traffic decreased by 25%.
Calculate Percentage Change in Excel or Google Sheets
Use a simple formula to calculate percentage change automatically.
If the original value is in cell A2 and the new value is in cell B2, enter:
=(B2-A2)/A2Then format the result as a percentage.
| Original value | New value | Formula result | Percentage change |
|---|---|---|---|
| 40 | 50 | 0.25 | 25% increase |
| 80 | 60 | -0.25 | 25% decrease |
| 2,500 | 2,750 | 0.10 | 10% increase |
| 8,000 | 6,000 | -0.25 | 25% decrease |
The formula produces a negative number for a decrease. Format the cell as a percentage, or multiply the result by 100 if you want to display it as a plain number.
Find the New Value After a Percentage Change
Sometimes you know the original value and the percentage change, but need the new value.
Increase formula
\text{New value} = \text{Original value} \times \left(1 + \frac{\text{Percentage increase}}{100}\right)Example: A $200 item increases by 15%.
200 \times 1.15 = 230The new price is $230.
Decrease formula
\text{New value} = \text{Original value} \times \left(1 - \frac{\text{Percentage decrease}}{100}\right)Example: A $200 item is discounted by 15%.
200 \times 0.85 = 170The discounted price is $170.
Find the Original Value After a Percentage Change
If you know the new value and the percentage change, work backward.
After an increase
\text{Original value} = \frac{\text{New value}}{1 + \frac{\text{Percentage increase}}{100}}Example: A price after a 20% increase is $240.
\frac{240}{1.20} = 200The original price was $200.
After a decrease
\text{Original value} = \frac{\text{New value}}{1 - \frac{\text{Percentage decrease}}{100}}Example: A price after a 20% discount is $160.
\frac{160}{0.80} = 200The original price was $200.
Common Mistakes to Avoid
Using the new value as the base
Always divide by the original value, not the new value.
If a price rises from $50 to $75:
\frac{75 - 50}{50} \times 100 = 50\%Using $75 as the base would give the wrong result:
\frac{75 - 50}{75} \times 100 = 33.3\%The correct percentage increase is 50%.
Treating an increase and decrease as reversible
A 25% increase followed by a 25% decrease does not return to the starting value.
Starting with $100:
- A 25% increase:
100 \times 1.25 = 125 - A 25% decrease:
125 \times 0.75 = 93.75
The final value is $93.75, not $100.
Confusing percentage points with percentages
If an interest rate rises from 4% to 6%, it increased by 2 percentage points. In relative terms, it increased by:
\frac{6 - 4}{4} \times 100 = 50\%Both statements can be correct, but they describe different things.
Comparing values with different time periods
A 10% monthly increase and a 10% yearly increase are not directly comparable. Always check whether the values cover the same period before drawing conclusions.
Real-World Examples
Sales performance
A store sells 320 units in January and 400 units in February.
\frac{400 - 320}{320} \times 100 = 25\%Sales increased by 25%.
Weight change
A person’s weight changes from 90 kg to 81 kg.
\frac{90 - 81}{90} \times 100 = 10\%The weight decreased by 10%.
Investment value
An investment grows from $1,200 to $1,500.
\frac{1,500 - 1,200}{1,200} \times 100 = 25\%The investment increased by 25%.
Quick Reference
| Task | Formula |
|---|---|
| Percentage increase | \frac{\text{New} - \text{Original}}{\text{Original}} \times 100 |
| Percentage decrease | \frac{\text{Original} - \text{New}}{\text{Original}} \times 100 |
| New value after increase | \text{Original} \times (1 + \text{rate}) |
| New value after decrease | \text{Original} \times (1 - \text{rate}) |
| Original value after increase | \frac{\text{New}}{1 + \text{rate}} |
| Original value after decrease | \frac{\text{New}}{1 - \text{rate}} |
Always identify the original value first, calculate the difference, divide by the original value, and multiply by 100. A positive result means an increase; a negative result means a decrease.