Percentage Change Calculator
Percent change from an initial value to a final value. A positive result is an increase; a negative result is a decrease.
From old value to new value
Percentage increase
+25%
- Absolute change+25
- Ratio (new / orig)1.25
- Percentage difference (symmetric)22.2222%
Reverse: find the new value
100 with +25% change
125
Percentage change is the directed change from an initial value to a final value, as a percent of the initial value. A positive result is an increase; a negative result is a decrease. This is not “x% of y” (percentage calculator) and it is not percentage difference, which uses the average of the two numbers as the base and has no sign.
Formula
% change = 100 × (final − initial) / |initial|
How to calculate
- Subtract the initial value from the final value.
- Divide by the absolute value of the initial value — drop the minus sign on the starting number, not on the difference.
- Multiply by 100. If the result is negative, the quantity decreased.
Example
From 60 to 72: (72 − 60) / |60| × 100 = 12 / 60 × 100 = 20%, a 20% increase. From 20 to 10: (10 − 20) / |20| × 100 = −50%, a 50% decrease. From 5 to 20: (20 − 5) / 5 × 100 = 300%.
Common mistake
On a negative start, the denominator is still |initial|. From −10 to −25: (−25 − (−10)) / |−10| × 100 = −15 / 10 × 100 = −150%. If you divide by −10 instead, the sign flips and you get a fake 150% increase.
FAQ
What is the percentage change from 5 to 20?
20 is a 300% increase of 5. (20 − 5) / 5 = 3, and 3 × 100% = 300%.
What is the percentage change from 20 to 10?
10 is a 50% decrease of 20. (10 − 20) / 20 = −0.5, and −0.5 × 100% = −50%.
Is percentage difference equal to percentage change?
No. Percentage change uses one of the two numbers (the initial) as the reference and can be negative. Percentage difference uses the average of the two numbers and is always positive. This page’s main result is percentage change; the symmetric figure is labeled separately.
What is the percentage change from 2 to 3?
3 is a 50% increase of 2. (3 − 2) / 2 = 0.5, and 0.5 × 100% = 50%.
How do I calculate percent change with negative numbers?
Same formula: divide by |initial|. From −10 to −25 the change is −150% (a decrease). Forgetting the absolute value in the denominator reverses the sign.