How to Calculate Percentage Increase & Decrease
Percentage increase and percentage decrease measure how much a value changes compared with its original value. Use the original value as the base, then compare it with the new value.
Percentage increase formula: ((New value - Original value) / Original value) x 100
Percentage decrease formula: ((Original value - New value) / Original value) x 100
If the original value is zero, the standard percentage-change formula is undefined because it would require division by zero.
What percentage increase and decrease mean
Percentage increase shows how much a number has grown compared with where it started. Percentage decrease shows how much a number has reduced compared with where it started. In both cases, the original value is the comparison base.
- Original value: the starting number or old value.
- New value: the changed number or latest value.
- Absolute change: the difference between the original value and the new value.
- Percentage change: the absolute change expressed as a percentage of the original value.
Percentage increase formula
Use this formula when the new value is higher than the original value:
Percentage increase = ((New value - Original value) / Original value) x 100
First subtract the original value from the new value. Then divide that difference by the original value. Finally, multiply by 100 to convert the decimal result into a percentage.
Percentage increase example
Suppose a price increases from 80 to 100.
- Find the increase:
100 - 80 = 20 - Divide by the original value:
20 / 80 = 0.25 - Convert to a percentage:
0.25 x 100 = 25%
The value increased by 25%.
Percentage decrease formula
Use this formula when the new value is lower than the original value:
Percentage decrease = ((Original value - New value) / Original value) x 100
The original value still stays in the denominator. This is why an increase and a decrease with the same number difference can produce different percentage results.
Percentage decrease example
Suppose a price decreases from 100 to 80.
- Find the decrease:
100 - 80 = 20 - Divide by the original value:
20 / 100 = 0.20 - Convert to a percentage:
0.20 x 100 = 20%
The value decreased by 20%.
Why the original value matters
The same absolute change can create different percentage changes because the base value is different. Going from 80 to 100 is a 25% increase, but going from 100 back to 80 is a 20% decrease.
This also explains why a 25% increase is not reversed by a 25% decrease. The denominator changes after the first movement.
When to use the calculator
Manual formulas are useful when you want to understand the method. For quick checks, use the Percentage Increase Calculator and enter the original value and new value. It is especially helpful for price changes, salary changes, sales growth, discounts, and comparison checks.
If your task is different, use a more specific calculator: the Fraction to Percentage Calculator for fraction conversions, the Average Percentage Calculator for average percentage problems, or the Simple Calculator for basic arithmetic.
Common mistakes to avoid
- Using the new value as the base: percentage change normally uses the original value as the denominator.
- Forgetting the direction: increase and decrease use the same idea, but the interpretation is different.
- Dividing by zero: if the original value is zero, the standard percentage-change formula does not work.
- Confusing percent change with percentage points: a move from 20% to 25% is 5 percentage points, but the relative increase is 25%.
- Assuming reverse changes cancel out: a 25% rise and a 25% fall do not return to the same number.
How to interpret the result
A positive percentage change means the new value is higher than the original value. A negative percentage change means the new value is lower. If you calculate increase and decrease separately, write the result with the direction so the meaning is clear.
For example, 25% increase and 20% decrease are not the same result. They describe different movements from different starting values.
Quick percentage change questions
Which value goes in the denominator?
Use the original value in the denominator. It is the base you are comparing against.
Can I calculate percentage change from zero?
Not with the standard formula. When the original value is zero, division by zero is undefined. In that case, describe the absolute change instead.
Is percentage decrease the same as a negative percentage increase?
You can express a decrease as a negative percentage change, but many everyday explanations use the percentage decrease formula so the result is easier to read.
Conclusion
Percentage increase and decrease are simple once you keep the original value as the base. Use the formula for manual work, check the direction of change, and use the calculator when you want a faster result.