How to Calculate Percentage Increase and Decrease
Percentage change tells you how much something rose or fell, measured against where it started. The formula is (new − old) ÷ old × 100 — and the key word is old, because the starting value is always the base you divide by. Get a positive number and it went up; negative, it went down. The percent change calculator handles the sign for you, but here's how to do it by hand.
The formula, step by step
- Subtract the old value from the new value to get the amount of change.
- Divide that change by the old value.
- Multiply by 100 to turn it into a percentage.
An increase. Your rent went from $1,200 to $1,320:
- 1,320 − 1,200 = 120
- 120 ÷ 1,200 = 0.1
- 0.1 × 100 = a 10% increase
A decrease. A $80 jacket is marked down to $60:
- 60 − 80 = −20
- −20 ÷ 80 = −0.25
- −0.25 × 100 = a 25% decrease
Why you always divide by the old value
The starting number is the reference point — it's what "100%" represents. Divide by the new value instead and you'll get a different, wrong answer. Going from 80 to 60 is a 25% drop (20 ÷ 80), not a 33% drop (20 ÷ 60). If you ever mix them up, that's the tell.
The reversal trap
Here's the one that surprises people: a percentage increase and the equal-looking decrease don't cancel out. Take $100, add 50% to reach $150, then take 50% off — you land at $75, not back at $100. The second percentage is calculated on a bigger number, so it removes more. Percentage changes never simply reverse, because the base shifts each time.
Increase vs. difference
Percentage change has a direction — a before and an after. If you're instead comparing two independent values where neither is the "starting" one, you want percentage difference, which uses their average as the base. Our note on the percentage calculator covers the plain "percent of a number" case, and the percent difference calculator handles the no-direction comparison. This post is part of our percentage and everyday math calculators.
Frequently asked questions
What is the formula for percentage increase?
(new − old) ÷ old × 100. Subtract the original value from the new one, divide by the original, and multiply by 100. A positive result is an increase.
How do I calculate a percentage decrease?
Use the same formula — the result just comes out negative. From 80 to 60: (60 − 80) ÷ 80 × 100 = −25%, a 25% decrease.
Do I divide by the old or the new value?
Always the old value. It's the starting point that represents 100%. Dividing by the new value gives a different, incorrect percentage.
Why doesn't a 50% increase then a 50% decrease return to the start?
Because the second percentage is taken from a larger number. $100 up 50% is $150; 50% of $150 is $75 removed, leaving $75. The base changes between the two steps, so they don't cancel.
What's the difference between percentage change and percentage difference?
Percentage change has a direction — it measures a new value against an old one. Percentage difference compares two values with no starting point, dividing by their average instead.
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