Percentages & Everyday Math
Percentage Increase/Decrease
Calculate percentage increase, decrease, absolute change, and compound growth between two values.
Result
Example with the values filled in above
Percent change
25%
Value change: 25
Average per period: 25%
Change any value and press Calculate for your own result.
Calculating…
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A fall versus the rise needed to recover it
- Fall
- Rise needed to recover
Show the numbers
| Starting point | Fall | Rise needed to recover |
|---|---|---|
| 10% fall | 10% | 11.1% |
| 20% fall | 20% | 25% |
| 25% fall | 25% | 33.3% |
| 33.3% fall | 33.3% | 50% |
| 50% fall | 50% | 100% |
| 75% fall | 75% | 300% |
How percentage increase and decrease work
Percent change measures how much a value grew or shrank relative to where it started. It is the standard way to compare a price rise, a salary bump, or a drop in traffic regardless of the absolute numbers involved.
Percent change = ((new − old) ÷ old) × 100
A positive result is an increase, a negative one a decrease, and the calculator keeps the sign so the two are never confused. Always divide by the original value: a price falling from $80 to $60 is a 25% decrease (20 ÷ 80), not 33% (20 ÷ 60).
Worked examples
- Increase: a price rising from $240 to $270 changes by $30, and 30 ÷ 240 × 100 = +12.5%.
- Decrease: inventory falling from 800 units to 620 changes by −180, and −180 ÷ 800 × 100 = −22.5%.
- Over several periods: 100 → 121 over 2 periods averages ((121 ÷ 100)^(1/2) − 1) × 100 = 10% per period, because 100 × 1.10 × 1.10 = 121.
Year-over-year growth and CAGR
Year-over-year growth compares one period with the equivalent previous one. Enter a number of periods and the calculator also gives the compound average change per period — CAGR when the periods are years:
Average per period = ((end ÷ start)^(1 ÷ periods) − 1) × 100
Revenue moving from $100,000 to $150,000 over four years is a 50% total increase but a CAGR of about 10.67% a year. CAGR is the single steady rate connecting the first and last values; it says nothing about how bumpy the years in between were.
Why gains and losses are not symmetric
| Decrease | Value left from 100 | Increase needed to recover |
|---|---|---|
| 10% | 90 | 11.11% |
| 20% | 80 | 25% |
| 25% | 75 | 33.33% |
| 50% | 50 | 100% |
The recovery is measured from the reduced value, so it always needs a bigger percentage than the fall. The same logic means a 20% rise followed by a 20% fall does not return you to the start: $100 becomes $120, then $96. It matters for investment losses, a sale followed by a price rise, and traffic that drops and comes back.
Percentage points, percent change, and percentage difference
| Measure | Formula | 4% → 5%, or 40 → 50 | Use it for |
|---|---|---|---|
| Percentage points | new % − old % | +1 point | The gap between two rates |
| Percent change | (new − old) ÷ old | +25% (and 50 → 40 is −20%) | Before and after |
| Percentage difference | |a − b| ÷ average(a, b) | 22.2% either way | Two independent measurements |
A conversion rate moving from 4% to 5% rose by one percentage point and by 25% — both true, answering different questions. Percent change has a direction, so swapping the values changes the answer; percentage difference divides by the average and gives the same result in either order.
When the start value is zero or negative
Percent change divides by the starting value, so a zero start makes it undefined — going from 0 to anything is an infinite percentage, which is why "up from zero" is reported as a count. With a negative start, moving from −100 to −50 is an improvement of 50, but the signed percentage reads as a fall. The "use absolute denominator" option divides by the magnitude of the start, which describes changes around negative values more naturally. For accounting losses or lab measurements, report the absolute change alongside whichever method you used.
Where else the formula shows up
- Percentage change in mass — standard in chemistry for reactions and hydration experiments: (final mass − initial mass) ÷ initial mass × 100. A negative result means mass was lost.
- Percentage change in quantity demanded — the numerator of price elasticity of demand. Divide it by the percentage change in price; a result beyond −1 means demand is elastic, so revenue falls when the price rises.
- Pay and inflation — a 4% raise in a year with 3% inflation is roughly a 1% real increase.
Percentage change in Excel and Google Sheets
Neither program has a percent-change function. With the old value in A2 and the new value in B2:
| What you want | Formula |
|---|---|
| Percentage change | =(B2-A2)/A2 |
| Guarded against a zero old value | =IF(A2=0,"",(B2-A2)/A2) |
| Percentage difference | =ABS(B2-A2)/AVERAGE(A2,B2) |
| CAGR over n years (n in C2) | =(B2/A2)^(1/C2)-1 |
Format the cell as Percentage rather than multiplying by 100 — doing both gives 2,500% where you wanted 25%.
Common mistakes
- Dividing by the new value instead of the original one.
- Calling a move from 5% to 10% "a 5% increase" — it is 5 points, or 100%.
- Adding sequential changes instead of compounding them: +10% then +10% is +21%, not +20%.
- Comparing figures measured with different units, definitions, or time periods.
For "what is X% of Y" questions, use the percentage calculator.
Percentage Increase/Decrease — frequently asked questions
How do I calculate percentage change in Excel?
With the old value in A2 and the new in B2, use =(B2-A2)/A2 and format the cell as Percentage. Do not also multiply by 100 — Excel stores 25% as 0.25, so the formatting already does it.
What is the difference between percentage change and percentage difference?
Percentage change has a direction and divides by the starting value, so 40 to 50 is +25% while 50 to 40 is -20%. Percentage difference is symmetric and divides by the average of the two, giving 22.2% either way.
How do I calculate a percentage decrease between two numbers?
Subtract the new value from the old, divide by the old value, then multiply by 100. A drop from 80 to 60 is (80-60)/80 = 25%.
How do I calculate percentage increase?
Subtract the starting value from the final value, divide by the starting value, and multiply by 100: ((end − start) ÷ start) × 100. Going from 80 to 100 is a (20 ÷ 80) × 100 = 25% increase.
Why is my percent change negative?
A negative result means the value decreased. For example, going from 100 to 75 gives ((75 − 100) ÷ 100) × 100 = −25%, a 25% decrease.
What does "average per period" mean?
It is the compound average growth rate (CAGR): the constant percentage change per period that would take the start value to the end value over the number of periods you entered. It uses the formula ((end ÷ start)^(1 ÷ periods) − 1) × 100.
Can a percentage increase be more than 100%?
Yes. An increase of more than 100% means the value more than doubled. Going from 50 to 150 is a 200% increase, because the change (100) is twice the starting value (50).