How to calculate percentage increase and decrease
Percentage change compares a new value with an old one: change = (new − old) ÷ old × 100. A positive result is an increase, a negative one a decrease. Always divide by the old (starting) value.
Increase example
Your rent goes from 1,200 to 1,290. The change is 90, and 90 ÷ 1,200 × 100 = 7.5%. Rent went up 7.5%.
Decrease example
A laptop drops from 899 to 749. The change is −150, and −150 ÷ 899 × 100 ≈ −16.7%. The price fell by about 16.7%.
Applying a percentage change
To raise a number by a percentage, multiply by (1 + rate). A 4% raise on a 52,000 salary is 52,000 × 1.04 = 54,080. To lower it, multiply by (1 − rate): 52,000 cut by 4% is 52,000 × 0.96 = 49,920.
Undoing a change: finding the original value
If a price after a 25% increase is 150, the original is not 150 minus 25% (that gives 112.50). Divide instead: 150 ÷ 1.25 = 120. The same goes for decreases: an item that costs 68 after 15% off originally cost 68 ÷ 0.85 = 80. This is how you back out sales tax or VAT from a total: a 120 total with 20% VAT is 120 ÷ 1.2 = 100 before tax.
Why +50% then −50% does not get you back
Start at 100. Up 50% is 150. Down 50% from 150 is 75, not 100. Each percentage is taken from a different base. The same thing happens with investments: a 20% loss needs a 25% gain to break even, because the gain is measured from the smaller number.
Percent change vs percentage points
When the values are themselves percentages, say which you mean. An interest rate moving from 3% to 4% has risen by 1 percentage point, but by 33.3% relative to where it started. News reports and loan offers often mix the two up.
Percent change vs percent difference
Percent change has a direction: there is a before and an after. When you just want to compare two values with no "before" (two shop prices, two test results), people often use percent difference, which divides by the average of the two: |a − b| ÷ ((a + b) ÷ 2) × 100. For 40 and 50, that is 10 ÷ 45 × 100 ≈ 22.2%, while the change from 40 to 50 is 25%.
Common mistakes
- Dividing by the new value instead of the old one. From 40 to 50 is +25%; from 50 to 40 is −20%.
- Subtracting a percentage to reverse an increase, instead of dividing.
- Adding several yearly changes together. Growth of 10% two years running is 1.1 × 1.1 = 1.21, a 21% total rise, not 20%.
- Starting from zero. A change from 0 has no defined percentage, because you cannot divide by zero. The calculator will tell you rather than show a misleading number.
The "% change" mode in PercentSnap takes an old and a new value and tells you the size and direction of the change.