Percentage Change
Calculate the percent increase or decrease from an old value to a new value, with the formula, a worked example and the 25% versus 20% asymmetry.
Results
Percentage change
- Change
- 20
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Formula / how it works
Percentage change = (new − old) ÷ |old| × 100. A positive result is an increase and a negative result is a decrease. The old value must not be zero.
Read the guide: Percentage Change vs Percentage Points
Detailed guide
What it is, how to use it, how to read the numbers, common mistakes, a worked example, formulas, and FAQs.
What this calculator is
Percentage change measures how much a value has grown or shrunk relative to where it started. Going from 80 to 100 is an increase of 20, which is 25% of the original 80. Going back from 100 to 80 is a decrease of 20, but only 20% of 100. The base changes, so the percentages differ. This calculator takes a starting value and an ending value and returns the absolute change and the percentage change. It is used for prices, wages, population, website traffic, investment returns and test scores. It cannot compute change from zero, since the base would be zero.
When to use / who it helps
- You want the percent rise in a price, salary or population.
- You want the percent drop in sales, traffic or temperature.
- You are comparing results across different scales.
- You are checking a headline that quotes a percent change.
- You need the return on an investment between two values.
How to use
Steps
- Enter the starting (old) value in the From field.
- Enter the ending (new) value in the To field.
- Read the absolute change.
- Read the percentage change and its sign.
- To reverse, swap the values and see that the percentage differs.
- Use the percentage points tool if you are comparing two percentages.
How to interpret results
- A positive percentage means the value rose; a negative one means it fell.
- The base is always the starting value.
- A 100% increase means doubling; a 50% decrease means halving.
- An increase followed by the same percentage decrease does not return to the start.
- Large percentage changes from small bases can be misleading.
Common mistakes & gotchas
- Using the new value as the base.
- Confusing percentage change with percentage points.
- Adding successive percentage changes instead of compounding them.
- Trying to compute change from zero.
- Reporting a percent change without the absolute numbers.
Worked example
Worked example — from 80 to 100 and back
- Change: 100 − 80 = 20.
- Percentage change: 20 ÷ 80 × 100 = 25%.
- Reverse: from 100 to 80 the change is −20, so −20 ÷ 100 × 100 = −20%.
- Doubling from 50 to 100 is a 100% increase, but dropping from 100 to 50 is only a 50% decrease.
Result: 80 to 100 is a 25% increase; 100 back to 80 is a 20% decrease.
To load the form's own demo values, tap Try example above the Calculate button.
How to calculate / formula
Percentage change = (new − old) ÷ |old| × 100. A positive result is an increase and a negative result is a decrease. The old value must not be zero.
Frequently asked questions
How do I calculate percentage change?
Subtract the old value from the new, divide by the old, and multiply by 100.
Why is the increase different from the decrease?
The base differs: the increase is measured against 80 and the decrease against 100.
What is the difference between percent and percentage points?
Percent compares relative size; percentage points are the arithmetic difference between two percentages.
Can the change be more than 100%?
Yes, when the new value is more than double the old.
What if the old value is zero?
The percentage change is undefined.
How do I combine two percentage changes?
Multiply the growth factors, for example 1.10 × 0.90 = 0.99, a 1% net decrease.