The short answer
Percentage change = (new value − old value) ÷ old value × 100.
From 80 to 100: (100 − 80) ÷ 80 × 100 = +25%. From 100 to 80: (80 − 100) ÷ 100 × 100 = −20%. A positive result is an increase, a negative one a decrease. The percentage calculator does this for you and shows the working.
The formula fits on one line, yet percentage changes are misreported constantly — in sales reports, news articles and “50% off” signs. The math is rarely the problem. The mistakes come from dividing by the wrong number, mixing up percent and percentage points, and assuming percentages add up. Here's the method, then the traps.
On this page
How to calculate it, step by step
- 1Subtract the old value from the new value. This is the change.
- 2Divide the change by the old value — the one you started from.
- 3Multiply by 100 to turn it into a percentage.
Example: a website had 950 visitors last month and 1,200 this month. The change is 1,200 − 950 = 250. Divided by 950 that's 0.263, so traffic grew by about 26.3%.
Why going up and coming back down aren't the same percentage
Going from 80 to 100 is +25%, but going from 100 back to 80 is −20%. Same two numbers, different percentages — because each calculation divides by a different starting value.
This trips people up most with successive changes:
| Start | Change | Then | Result | Overall |
|---|---|---|---|---|
| 100 | +10% | −10% | 99 | −1% |
| 100 | −50% | +50% | 75 | −25% |
| 80 | +25% | −20% | 80 | 0% |
A stock that falls 50% has to rise 100% — not 50% — to get back to where it was. To combine changes, multiply the factors instead of adding the percentages: +10% then −10% is 1.10 × 0.90 = 0.99, a 1% drop.
Percent vs percentage points
When the values are already percentages, there are two different ways to describe a change, and they give very different numbers. If an interest rate goes from 10% to 15%:
- It rose by 5 percentage points (15 − 10).
- It rose by 50 percent (5 ÷ 10 × 100).
Both are correct; they answer different questions. Saying the rate “rose 5%” is the mistake — it's neither. Use “points” for the plain difference between two percentages and “percent” for the relative change.
Working backwards: finding the original price
A jacket costs 80 after a 20% discount. What was the original price? The tempting answer — add 20% back, 80 × 1.2 = 96 — is wrong, because the 20% was taken from the original price, not from 80.
Original = final price ÷ (1 − discount). So 80 ÷ 0.8 = 100. Check: 20% of 100 is 20, and 100 − 20 = 80. ✓
The same works for increases: if a price after a 25% rise is 150, the original was 150 ÷ 1.25 = 120. And for taxes: a total of 115 including 15% tax means a pre-tax price of 115 ÷ 1.15 = 100.
When the old value is zero or negative
- Old value of zero: percentage change is undefined — you can't divide by zero. Going from 0 to 40 sales is “up by 40”, not “up by infinity percent”. Report the actual numbers.
- Negative old value: a company going from a loss of −50 to a profit of +25 has clearly improved, but the plain formula gives (25 − (−50)) ÷ (−50) = −150%, which reads like a decline. The usual fix is to divide by the absolute old value: 75 ÷ 50 = +150%. Our calculator does this; spreadsheets don't unless you use
ABS().
Percentage change vs percentage difference
Percentage change has a direction: there's a before and an after. When you're comparing two things side by side — two prices, two products, two measurements — with neither being “the original”, use percentage difference, which divides by the average:
Percentage difference = |a − b| ÷ ((a + b) ÷ 2) × 100
For 80 and 100: 20 ÷ 90 × 100 = 22.2% — the same whichever order you put them in.
Change over several years
Revenue grew from 100 to 150 over three years. The total change is +50%, but the yearly growth is not 50 ÷ 3 = 16.7%, because each year compounds on the last. The average yearly rate is the compound annual growth rate:
CAGR = (end ÷ start)^(1 ÷ years) − 1 → (150 ÷ 100)^(1/3) − 1 = 14.5% a year.
The compound interest calculator shows the same effect going forward: how a yearly rate builds up over time.
In Excel or Google Sheets
With the old value in A2 and the new value in B2, enter =(B2-A2)/A2 and format the cell as a percentage. Leave out the “× 100” — the percentage format does that for you, and multiplying as well is a classic way to end up with 2,500%.
To handle negative starting values, use =(B2-A2)/ABS(A2), and wrap it as =IF(A2=0, "", (B2-A2)/ABS(A2)) to avoid divide-by-zero errors.
Frequently asked questions
What is the formula for percentage change?
(New value − old value) ÷ old value × 100. A positive answer is an increase; a negative answer is a decrease.
How do I calculate a percentage decrease?
Use the same formula; the result will be negative. From 250 to 200: (200 − 250) ÷ 250 × 100 = −20%, a 20% decrease.
Is a 100% decrease possible?
Yes — it means the value fell to zero. A decrease can't be more than 100%, but an increase can be any size: doubling is +100%, tripling is +200%.
What's the difference between percent and percentage points?
Percentage points are the plain difference between two percentages (10% to 15% is +5 points). Percent is the relative change (10% to 15% is a 50% increase).
Why does a 50% loss need a 100% gain to recover?
Because the gain is calculated on the smaller, reduced amount. 100 falls 50% to 50; getting back to 100 means adding 50, which is 100% of 50.
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