Percentage increase tells you how much a value has grown relative to where it started, expressed as a percentage. It is one of the most useful everyday calculations - you reach for it to work out a pay rise, a price hike, investment growth, or how much traffic a website gained month over month. This guide gives you the formula, several worked examples, and the one distinction that trips most people up: percentage change versus percentage points.
The percentage increase formula
To find the percentage increase between an old (starting) value and a new value:
Percentage increase = ((New value - Old value) / Old value) x 100
The steps are: subtract the old value from the new value to get the change, divide that change by the old value, then multiply by 100 to turn the decimal into a percentage. The key is that you always divide by the original value, not the new one - the starting point is your basis for comparison.
A worked example
Say a product's price rose from 80 to 100.
- Change = 100 - 80 = 20
- Divide by the old value = 20 / 80 = 0.25
- Multiply by 100 = 25%
So the price increased by 25%. Notice that the same absolute change measured against a different starting value gives a different percentage: a rise from 80 to 100 is a 25% increase, but a rise from 100 to 120 - also a change of 20 - is only a 20% increase, because the basis is larger.
How to calculate percentage decrease
Percentage decrease uses the same formula; the result simply comes out negative when the new value is smaller. To express it as a positive 'decrease', take the absolute value of the change:
Percentage decrease = ((Old value - New value) / Old value) x 100
For example, if a stock falls from 250 to 200: (250 - 200) / 250 x 100 = 50 / 250 x 100 = 20%. The stock dropped 20%.
A common trap: increase then decrease
Percentages do not cancel out the way you might expect. If a 100 item goes up 20% to 120, then drops 20%, you do not return to 100 - you land at 96. That is because the second 20% is calculated on the larger 120, not the original 100. This is exactly why a stock that falls 50% then rises 50% is still down 25% overall, and it is worth keeping in mind whenever you chain percentage changes together.
Percentage change vs percentage points
This is the distinction that causes the most confusion, especially in news headlines. Suppose an interest rate rises from 4% to 6%.
- The change is 2 percentage points (6 minus 4).
- But the percentage increase is (6 - 4) / 4 x 100 = 50%.
Both statements are correct, but they mean very different things. Saying the rate 'rose 2 points' and saying it 'rose 50%' describe the same event. When you read that something changed by a percentage, always check whether the source means a relative change or an absolute change in percentage points - the difference can be enormous.
Three ways people use percentages
Beyond increase and decrease, two related calculations come up constantly, and the Percentage Calculator handles all three:
- What is X% of Y? Multiply: 15% of 200 is 0.15 x 200 = 30.
- X is what percent of Y? Divide: 30 is what percent of 200? 30 / 200 x 100 = 15%.
- Percentage increase or decrease, as covered above.
How to reverse a percentage change
A frequent real-world need is working backwards from a final figure. If a price already includes a 20% increase and you want the original, do not subtract 20% - that gives the wrong answer. Instead divide by 1.20. A price of 120 that already includes a 20% markup came from 120 / 1.20 = 100. The same logic applies to discounts: a sale price of 80 after a 20% discount started at 80 / 0.80 = 100. Reversing a percentage means dividing by the growth factor, not subtracting the percentage.
Everyday places this shows up
Percentage increase and decrease quietly run through daily life. A salary that rises from 50,000 to 55,000 is a 10% raise. A 25% off coupon turns a 60 item into 45. An investment that grows from 1,000 to 1,150 has returned 15%. Tracking website visits, exam marks, body weight or electricity bills month to month all use the same single formula. Once you can run it confidently, you can sanity-check the percentage claims you meet in adverts, news and spreadsheets rather than taking them at face value.
Once the formula clicks, the arithmetic is quick - but for pay rises, discounts and investment returns where the numbers are awkward, the fastest route is to drop them straight into the Percentage Calculator and read the answer.
Frequently asked questions
- What is the formula for percentage increase?
- Percentage increase = ((new value - old value) / old value) x 100. Always divide the change by the original starting value, then multiply by 100.
- What is the difference between percentage change and percentage points?
- Percentage points measure the absolute gap between two percentages (4% to 6% is 2 points), while percentage change measures the relative growth (4% to 6% is a 50% increase). They describe the same event in different ways.
- Why doesn't a 20% increase then a 20% decrease return to the original value?
- Because the decrease is calculated on the new, larger value rather than the original. A 100 item up 20% is 120, and 20% off 120 is 96 - not 100.