UtilityBase2 min read
How to Calculate Percentage Increase and Decrease
The one formula behind every percentage change, how to tell an increase from a decrease, and the difference between a percent and a percentage point that trips up even careful readers.
One formula for both directions
Percentage change measures how much a value grew or shrank relative to where it started. The formula is: percentage change = (new value - old value) / old value x 100.
If the result is positive, it's an increase; if it's negative, it's a decrease. There's no separate formula for each — the sign of the answer tells you the direction. A price that goes from $80 to $100 changed by (100 - 80) / 80 = 25%; from $100 to $80 it changed by (80 - 100) / 100 = -20%.
Why the base matters
Notice that a $20 move was 25% in one direction and 20% in the other. That's because percentage change always divides by the starting value, and the starting value was different each way. This is why a 50% drop needs a 100% gain to recover: after falling from 100 to 50, getting back to 100 is a 50-point rise on a base of 50.
Always be clear about which number is the 'old' value — it's the denominator, and choosing the wrong one flips the whole calculation.
Calculating it step by step
The process is the same whether values are going up or down.
- 1Identify the old (starting) value and the new (ending) value.
- 2Subtract the old value from the new value to get the change.
- 3Divide that change by the old value.
- 4Multiply by 100 to express it as a percentage.
- 5A positive result is an increase; a negative result is a decrease.
Frequently asked questions
What's the difference between a percent and a percentage point?
If an interest rate rises from 4% to 5%, that's a 1 percentage-point increase but a 25% increase (1 divided by 4). Percentage points describe the gap between two percentages; percent describes the relative change. News stories often blur the two, which can make a change sound far bigger or smaller than it is.
Can a percentage increase be more than 100%?
Yes. Anything that more than doubles has increased by over 100% — going from 10 to 30 is a 200% increase. A decrease, though, can't go below -100%, because a value can't drop by more than its entire self.
How do I reverse a percentage change?
To undo a known increase, divide rather than subtract: if a price rose 25% to $100, the original was 100 / 1.25 = $80. Subtracting 25% of $100 would wrongly give $75, because the 25% was based on the smaller original number.
Tools mentioned in this guide
Keep reading