Percentage change is everywhere. Your salary went up. A stock dropped. Revenue grew by some amount. Enrollment fell. In every case, the question is the same: how much did it change, expressed as a percentage of where it started? This guide explains the formula clearly, walks through real examples, and covers the traps that trip people up.
The Formula
Percentage Change = ((New Value - Old Value) / Old Value) x 100
A positive result means an increase. A negative result means a decrease. The old value (starting point) is always the denominator -- this is the most important thing to get right.
Worked Examples
| Scenario | Old Value | New Value | Calculation | Result |
|---|---|---|---|---|
| Salary increase | $55,000 | $58,300 | (3,300 / 55,000) x 100 | +6% |
| Stock drop | $240 | $192 | (-48 / 240) x 100 | -20% |
| Monthly users | 4,200 | 5,460 | (1,260 / 4,200) x 100 | +30% |
| Rent increase | $1,600 | $1,720 | (120 / 1,600) x 100 | +7.5% |
| Weight loss | 195 lbs | 175.5 lbs | (-19.5 / 195) x 100 | -10% |
The Most Common Mistake: Using the Wrong Base
The old value goes in the denominator -- always. This is where people slip up most often. If you accidentally use the new value as the base, you get a different (and wrong) answer.
Example: a price rises from $80 to $100. Correct: (100 - 80) / 80 x 100 = 25% increase. Wrong: (100 - 80) / 100 x 100 = 20%. These are different questions. The first asks "what percent did the price increase from its original level?" The second would be asking something else entirely.
Percentage Change Is Not Symmetric
A 50% decrease followed by a 50% increase does not return you to the starting value. This surprises many people.
- Start: $100. Down 50%: $50. Up 50% from $50: $75. You are still down 25%.
This is because the gain percentage is applied to a smaller base than the loss was. The larger the initial loss, the bigger the recovery gain needed to break even. To recover from a 50% loss, you need a 100% gain. To recover from a 25% loss, you need a 33.3% gain.
Multi-Period Changes: Don't Just Add the Percentages
If something grows 10% in year one and 8% in year two, the total growth is not 18%. You need to multiply the growth factors.
- Year 1: $1,000 x 1.10 = $1,100
- Year 2: $1,100 x 1.08 = $1,188
- Total change: ($1,188 - $1,000) / $1,000 x 100 = 18.8%, not 18%
For rough estimates over a few periods, adding is close enough. For anything precise -- like compound returns, compound growth rates, or multi-year business performance -- always multiply the factors.
When Percentage Change Is Misleading
Percentage change can exaggerate or minimize the story depending on the base. A new product going from 2 sales to 4 sales is a 100% increase -- which sounds dramatic but means almost nothing in absolute terms. Conversely, a large company's revenue dropping from $10B to $9.5B is "only" a 5% change -- but represents $500 million in lost revenue.
Always pair a percentage change with the absolute numbers. One without the other can be misleading.
Calculating Percentage Change in Your Head
For quick mental estimates: find the difference, express it as a fraction of the original, then convert to a percentage. If a price went from $200 to $240, the difference is $40. $40 out of $200 is 1/5 = 20%. For small changes on round numbers, this fraction method is faster than the full formula. For everything else, our Percentage Change Calculator gives you the answer instantly.