How to calculate percentage change
Percentage change = ((New − Original) ÷ |Original|) × 100 Subtract the original value from the new value to get the change. Divide that change by the absolute value of the original value and multiply by 100. A positive result is an increase and a negative result is a decrease.
For an original value of 150 and a new value of 180:
- Absolute change: 180 − 150 = +30
- Divide by the original: 30 ÷ 150 = 0.2
- Multiply by 100: 0.2 × 100 = 20% increase
If you only need to calculate an increase, use the Percentage Increase Calculator. For a decrease, use the Percentage Decrease Calculator.
Absolute change and percentage change
The two answer different questions. The absolute change is the raw difference in the value's own units: a price went up by 30, a population fell by 1,200. The percentage change scales that difference against where you started, which is what lets you compare changes of very different sizes.
A rise of 30 means something very different starting from 150 (a 20% increase) than starting from 3,000 (a 1% increase). The absolute change is identical; only the percentage shows how significant it is.
Why the original value is divided by its absolute value
The vertical bars in |Original| mean "the size of the original value, ignoring its sign". For positive starting values it makes no difference at all. It matters when the original value is negative, because it keeps the result's sign tied to the direction the value actually moved.
Take a business that went from a −50 loss to a −25 loss. The value went up — the loss halved. Dividing by the plain original value gives (−25 − −50) ÷ −50 = −50%, which reads as a decrease and is backwards. Dividing by |−50| gives +50%, a 50% increase, which is what happened.
- −50 to −25: 50% increase (the value rose)
- −50 to −75: 50% decrease (the value fell)
- −50 to 50: 200% increase (crossing zero)
Percentage changes involving negative numbers are unusual, and some fields avoid quoting them at all because they read oddly. If you do need one, this is the convention that keeps the direction honest.
When the original value is 0
Percentage change is undefined when the original value is 0, because the calculation divides by it. Going from 0 to 50 is a real change of +50 — the calculator still shows that — but there is no percentage that describes it. The starting value provides no nonzero reference for the calculation.
This is why reports sometimes say a figure "rose from zero" or give the absolute number alone instead of a percentage. If you see a percentage quoted for a change that started at zero, it has been calculated against something else.
Percentage change is not symmetric
A 20% increase followed by a 20% decrease does not bring you back to where you started. From 150, a 20% increase gives 180. From 180, a 20% decrease gives 144, not 150 — because the second 20% is taken of a larger number.
The same asymmetry works the other way: getting from 180 back to 150 is only a 16.67% decrease. Whenever you compare a rise and a fall, check which value each percentage is measured from.
Percentage change vs percentage points
When the values are themselves percentages, the two are easy to confuse. If an interest rate rises from 4% to 5%, that is a change of 1 percentage point but a 25% increase, since 1 is 25% of 4. Both are correct; they describe different things. News reports that say a rate "rose 1%" usually mean one percentage point. If you want to calculate a percentage of a number rather than compare two values, use the Percentage Calculator.
Percentage change vs percentage difference
Percentage change has a direction: there is an original value and a new one, and the result is measured against the original. Percentage difference compares two values with no before and after, so it divides by their average instead and never has a sign. Use percentage change when something moved from one value to another over time; use percentage difference when comparing two things side by side.
If you are comparing two values without treating either one as the starting value, use the Percentage Difference Calculator.Frequently asked questions
How do I calculate percentage change?
Subtract the original value from the new value, divide by the original value, and multiply by 100. From 150 to 180: (180 − 150) ÷ 150 × 100 = 20%, a 20% increase.
Can percentage change be more than 100%?
An increase can be any size — going from 100 to 1,000 is a 900% increase. A decrease is capped at 100% while the value stays positive, since 100% means falling all the way to zero. A decrease beyond 100% is only possible if the value crosses into negative numbers.
Why can't I calculate a percentage change from 0?
Because the calculation divides by the original value, and dividing by zero is undefined. The change itself is real and the calculator still shows it — going from 0 to 50 is a change of +50 — but it can't be expressed as a percentage.
Does the order of the two values matter?
Yes. The percentage is always measured from the original value, so swapping the two gives a different answer: 150 to 180 is a 20% increase, while 180 to 150 is a 16.67% decrease.
What is the difference between percentage change and percentage points?
Percentage points are the plain difference between two percentages; percentage change measures that difference relative to the starting percentage. A rate moving from 4% to 5% has risen by 1 percentage point, which is a 25% increase.