How to Calculate Percentage Change: Increase and Decrease

Formula

percentage change = (new − old) / |old| × 100

• old: the starting value; it cannot be zero
• new: the final value
• |old|: the absolute value of the old value; it keeps an increase positive when the old value is negative
• difference = new − old: the change itself, in the unit of the values
• ratio = new / old: above 1 the value went up, below 1 it went down

Step-by-step example

The price of a product went from 1,200 to 1,500.

1. Find the difference: 1,500 − 1,200 = 300.
2. Divide the difference by the old value and multiply by 100: 300 / 1,200 × 100 = 25. The price rose by 25%.
3. Check the ratio: 1,500 / 1,200 = 1.25. The new price is 1.25 times the old one.
4. Check it backwards: 25% of 1,200 is 300, and the percentage calculator gives 1,500 as the value after the increase.

An increase and a decrease are not symmetric

You always divide by the old value, so the same two numbers give different results going up and going down.

The last three rows show a trap: a 20% increase followed by a 20% decrease takes 100 down to 96. The total change is not zero but −4%.

Percentage change and percentage points

When the values are themselves percentages, the two measures differ. If an interest rate goes from 10% to 12%, the difference is 2 percentage points, but the percentage change is 2 / 10 × 100 = 20, or 20%. Check which measure a news report on inflation or rent increases uses.

When the old value is negative or zero

When the old value is negative, its absolute value is the divisor. Going from −50 to −20 is a difference of 30, and the percentage change is 30 / 50 × 100 = 60, a 60% increase. When the old value is zero, division by zero is undefined, so there is no percentage change; compare the difference instead.