How to use Percentage Change Between Two Values
Enter the starting value and the new value. The result is positive for an increase and negative for a decrease.
Worked example
A price that goes from $80 to $100 has risen by (100 − 80) ÷ 80 × 100 = 25%. If it falls back from $100 to $80, that is a 20% drop, because the change is measured against a bigger starting value. Ups and downs of the same size in percent do not cancel out.
Percent versus percentage points
When a rate itself changes, be careful with the words. An interest rate going from 4% to 5% has risen by 1 percentage point, but by 25% in relative terms. News reports often mix the two, so check which one is meant before comparing numbers.
Percent increase and percent decrease
The percent change formula is the new value minus the old value, divided by the absolute value of the original, multiplied by 100. A positive number is a percent increase and a negative number is a percent decrease. Going from 40 to 50 is +25%, and going from 50 to 40 is −20%.
When the starting value is negative
Dividing by the absolute value keeps the sign meaningful when the original is below zero, such as a company moving from a loss of 200 to a loss of 100. That is a change of +100, or +50%, which correctly shows an improvement. If the starting value is zero, a percent change cannot be calculated at all, because you cannot divide by zero.
The formula
Change % = (final − initial) ÷ |initial| × 100.
Examples
- From 1,000 to 1,500
Change: 500 Percentage change: 50%
- From 1,500 to 1,000
Change: -500 Percentage change: -33.33333333%
- From 48 to 60
Change: 12 Percentage change: 25%
Limitations and assumptions
The starting value cannot be zero, because a change from nothing has no percentage.
Frequently asked questions
What is the formula?
(Final − initial) ÷ |initial| × 100.
Why are up 50% and down 50% not the same distance?
The base changes, so 1,000 up 50% is 1,500, but 1,500 down 33.3% returns to 1,000.
What about percentage points?
Use the percentage point difference calculator for changes between two percentages.
What if the starting value is zero?
The percentage change is undefined.