Percentages & Everyday Math
Percentage Increase/Decrease
Calculate percentage increase, decrease, absolute change, and compound growth between two values.
Result
Enter your numbers and press Calculate to see the result.
Calculating…
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.
Formula
Percent change = ((end − start) ÷ start) × 100
A positive result is an increase, a negative result a decrease. When you enter a number of periods, the calculator also shows the compound average change per period (CAGR):
Average per period = ((end ÷ start)^(1 ÷ periods) − 1) × 100
Worked examples
- 80 → 100 — change is 20, so (20 ÷ 80) × 100 = +25%.
- 100 → 75 — change is −25, so −25% (a 25% decrease).
- 100 → 121 over 2 periods — the average is ((121 ÷ 100)^(1/2) − 1) × 100 = 10% per period, because 100 × 1.10 × 1.10 = 121.
Where percent change is used
- Prices and inflation — how much a bill, rent, or grocery basket has risen year over year.
- Pay — the size of a raise, or the real value of a bonus against last year's figure.
- Performance — growth or decline in sales, traffic, followers, or test scores.
- Investments — the return on a holding, and its compound average when spread over several years.
A caveat when the start value is zero or negative
Percent change divides by the starting value, so it breaks down when that start is zero — going from 0 to any number is an infinite percentage, which is why "up from zero" is reported as a plain count, not a percentage. When the start is negative (a loss turning into a profit, say), the sign of the result can be misleading, and the absolute figures usually tell the story more clearly than a percentage.
Note that increases and decreases are not symmetric: a 25% drop from 100 leaves 75, but recovering from 75 to 100 requires a 33.3% rise. For simple "X% of Y" questions, use the percentage calculator.
Percentage increase calculator
To find a percentage increase from an old value to a new value, subtract old from new and divide by the old value. A price rising from $240 to $270 changes by $30; $30 ÷ $240 × 100 = 12.5%. The same formula works for a salary increase, revenue growth, population change, website traffic, test scores, or any pair of comparable values with a non-zero starting point.
Percentage decrease calculator
When the ending value is lower, the difference is negative. Inventory falling from 800 units to 620 changes by −180; −180 ÷ 800 × 100 = −22.5%, usually described as a 22.5% decrease. The calculator keeps the signed result so an increase and decrease are immediately distinguishable.
Percent change versus percentage-point change
Percentage points compare two percentages directly. If a conversion rate moves from 4% to 5%, it increased by one percentage point. Relative percent change is (5 − 4) ÷ 4 × 100 = 25%. Both statements are correct, but they answer different questions. Use percentage points for the absolute gap between rates and percent change for growth relative to the original rate.
Year-over-year growth and CAGR
Year-over-year growth compares one period directly with the equivalent previous period. CAGR, or compound annual growth rate, smooths a multi-period change into one constant rate. If revenue moves from $100,000 to $150,000 over four years, the total increase is 50%, but CAGR is about 10.67% per year. CAGR does not show volatility or the actual change in each year; it describes the single compounded rate connecting the first and last values.
Why percentage gains and losses are asymmetric
| Decrease | Value left from 100 | Increase needed to recover |
|---|---|---|
| 10% | 90 | 11.11% |
| 25% | 75 | 33.33% |
| 50% | 50 | 100% |
The recovery percentage uses the reduced value as its denominator. This is important when interpreting investment losses, discounts followed by price rises, traffic declines, and performance changes.
How to interpret negative and zero starting values
Percentage change in Excel and Google Sheets
Neither program has a percent-change function, so you write the arithmetic yourself. 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 between two numbers | =ABS(B2-A2)/AVERAGE(A2,B2) |
Format the cell as Percentage rather than multiplying by 100 — if you do both, you get 2,500% where you wanted 25%. Excel stores 25% as the number 0.25, so the formatting is the multiplication.
Percentage change and percentage difference are not the same
Percentage change has a direction: it measures from a starting value to an ending one, and swapping them gives a different answer. Going from 40 to 50 is a 25% increase; going from 50 to 40 is a 20% decrease. The gap is 10 both times.
Percentage difference is symmetric — it compares two values where neither is "first", dividing by their average instead. Between 40 and 50 that is 10 ÷ 45 = 22.2%, whichever order you write them in. Use change for before-and-after; use difference for comparing two independent measurements.
Percentage decrease between two numbers
decrease % = (old − new) ÷ old × 100
Always divide by the original value. A price falling from $80 to $60 is a 25% decrease (20 ÷ 80), not 33% (20 ÷ 60) — dividing by the new value answers a different question, namely how much the old price exceeded the new one.
Where this shows up: price, mass, and quantity demanded
- Price changes — the same formula, and the base matters: a 20% rise followed by a 20% fall does not return you to the start. $100 becomes $120, then $96.
- Percentage change in mass — standard in chemistry for reactions and hydration experiments, measured as (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 the percentage change in quantity by the percentage change in price; a result beyond −1 means demand is elastic, so revenue falls when you raise the price.
A zero start makes ordinary percent change undefined because the formula divides by zero. Negative starting values also require context: moving from −100 to −50 is an improvement of 50 in absolute terms, but a signed percentage can be counterintuitive. The “use absolute denominator” option uses the magnitude of the start, which often makes increases and decreases around negative values easier to describe. For accounting losses or scientific measurements, report both the absolute change and the percentage method used.
Common mistakes in percent-change calculations
- Dividing by the ending value instead of the starting value.
- Confusing a 5% relative increase with five percentage points.
- Adding sequential changes instead of compounding them.
- Ignoring that the formula is undefined when the original value is zero.
- Comparing values measured with different units, definitions, or time periods.
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).