The idea in one sentence
Percentage change compares the size of a change with the starting value. First find the numerical difference, then divide by the old value, and finally convert the result to a percent.
The absolute-value bars around the old value keep the denominator positive. For ordinary prices, populations, scores and other positive quantities, they do not change the number.
Percentage increase, step by step
Use percentage increase when the new value is larger than the old value.
- Find the increase.
Subtract the old value from the new value. - Compare with the starting point.
Divide the increase by the old value, not the new value. - Convert to percent.
Multiply the decimal result by 100 and add the percent sign.
Worked example: a price rises from $80 to $92
The increase is $92 − $80 = $12. Compare that $12 increase with the original $80 price.
Answer: the price increased by 15%.
Worked example: attendance grows from 240 to 300
The head count rose by 60. The original attendance of 240 is the reference.
Answer: attendance increased by 25%.
Percentage decrease, step by step
For a decrease, you can use the same percentage-change formula and read a negative answer as a decline. If you want the size of the decrease as a positive number, subtract the new value from the old value instead.
Worked example: a balance falls from $250 to $210
The decrease is $250 − $210 = $40. Divide by the original $250 balance.
Answer: the balance decreased by 16%.
Worked example: travel time drops from 50 minutes to 42 minutes
The trip is 8 minutes shorter. The comparison begins with the old 50-minute trip.
Answer: travel time decreased by 16%.
Why the starting value matters
The denominator answers “compared with what?” A move from 40 to 50 adds 10, and 10 is one quarter of 40, so the increase is 25%. Reversing the direction gives a drop from 50 to 40. The same difference of 10 is only one fifth of 50, so the decrease is 20%.
This is why a 25% increase followed by a 25% decrease does not return a number to its starting point. Starting at 100, a 25% increase creates 125. A 25% decrease from 125 removes 31.25, leaving 93.75.
Finding the original or final value
Find a final value after an increase
Turn the rate into a decimal, add 1, and multiply. After a 12% increase, $500 becomes $500 × 1.12 = $560.
Find a final value after a decrease
Turn the rate into a decimal, subtract it from 1, and multiply. After a 30% decrease, 90 becomes 90 × 0.70 = 63.
Work backward to the original
Do not simply subtract the stated percentage from the final number. Divide by the change factor. If $138 is the price after a 15% increase, the original is $138 ÷ 1.15 = $120.
Common mistakes to avoid
Dividing by the new value: this changes the reference and produces a different percentage. Using the raw difference: a change of 20 means little until it is compared with a baseline. Adding repeated rates: consecutive changes compound because each new rate applies to a new base. Confusing change with percentage points: a rate moving from 30% to 36% rises 6 percentage points, but it increases by 20% relative to 30%.
Try it: use the free percentage change calculator for instant results.