To calculate a percentage increase, subtract the old value from the new value, divide by the old value and multiply by 100. A price that rises from $40 to $50 has gone up ($50 − $40) ÷ $40 × 100 = 25%. A negative result is a decrease.
Percentage change is one of those calculations everyone learned once and half-remembers. A price went from $40 to $50: is that a 20% or a 25% increase? Your rent went up 5% and then 5% again: is that 10%? A stock fell 50% and then rose 50%: are you back where you started? The answers are 25%, a little over 10%, and no. This guide explains why, with the one formula that covers all of it.
If you only need the number, the percentage calculator handles increases, decreases and “what percent of” questions. Read on if you want to understand the result and avoid the common mistakes.
What is the percentage increase formula?
Percentage change compares the difference between two values with the value you started from:
Percentage change = (new value − old value) ÷ old value × 100
If the result is positive it is an increase. If it is negative it is a decrease. The U.S. Bureau of Labor Statistics uses exactly this method to report changes in the Consumer Price Index: subtract the earlier index value from the later one, divide by the earlier value, and multiply by 100.
How do you calculate a percentage increase?
A product’s price rises from $40 to $50.
- Difference: $50 − $40 = $10
- Divide by the old value: $10 ÷ $40 = 0.25
- Multiply by 100: 25%
The price rose 25%. The most common mistake is dividing by the new value ($10 ÷ $50 = 20%). Always divide by the value you are changing from.
How do you calculate a percentage decrease?
A jacket drops from $80 to $60.
- Difference: $60 − $80 = −$20
- Divide by the old value: −$20 ÷ $80 = −0.25
- Multiply by 100: −25%, a 25% decrease
Shops usually describe this the other way round, as “25% off.” The discount calculator works from the original price and the discount rate to give you the sale price.
Going the other way: applying a percentage
Often you know the percentage and need the new value. Multiply the old value by (1 + rate) for an increase, or by (1 − rate) for a decrease.
- A $3,000 monthly salary with a 4% raise: $3,000 × 1.04 = $3,120.
- A $250 bill with a 15% reduction: $250 × 0.85 = $212.50.
To find the original value before a change, divide instead. If a price after a 20% increase is $96, the original was $96 ÷ 1.20 = $80. Subtracting 20% of $96 would give $76.80, which is wrong, because the 20% was calculated on $80, not $96.
Why don’t increases and decreases cancel out?
Because each percentage is calculated from a different starting point, an equal rise and fall do not bring you back to the start.
- $100 falls 50% to $50.
- $50 rises 50% to $75.
You are still down 25%. To recover from a 50% fall you need a 100% gain. The same thing happens on a smaller scale with every pair of equal ups and downs: a 10% drop followed by a 10% rise leaves you 1% below where you began.
Successive changes multiply
When changes stack, multiply the factors instead of adding the percentages. Two 5% rent increases:
1.05 × 1.05 = 1.1025, which is a 10.25% total increase, not 10%.
The gap grows over longer periods. Three years of 8% growth is 1.08 × 1.08 × 1.08 = 1.2597, about 26%, not 24%. This is the same effect that makes compound interest powerful, covered in our guide on how compound interest works.
What is the difference between percentage points and percent?
When the values you are comparing are already percentages, such as interest rates or tax rates, there are two ways to describe the change, and they mean different things.
- A mortgage rate moving from 6% to 7% has risen by 1 percentage point.
- The same move is a 16.7% increase in the rate itself, because 1 ÷ 6 = 0.1667.
Both statements are correct, but they are easy to mix up. News reports on rates and polls normally use percentage points; using “percent” instead can make a small change sound large.
Picking the right comparison period
For anything seasonal, compare like with like. The BLS points out that a 12-month change in the CPI compares the same month a year apart, for example December to December. January to December is only an 11-month change. The same idea applies to sales figures, energy bills or website traffic: comparing December with July tells you more about the season than about the trend.
When the starting value is zero, percentage change cannot be calculated, because you cannot divide by zero. Report the absolute change instead. When the starting value is very small, percentages can look dramatic: going from 2 to 6 customers is a 200% increase but only four people.
Worked example: a pay rise against inflation
Suppose your salary rose from $52,000 to $54,600 and prices rose 3.2% over the same year.
- Pay increase: (54,600 − 52,000) ÷ 52,000 × 100 = 5%.
- Real increase: 1.05 ÷ 1.032 − 1 = about 1.7%.
Subtracting 3.2 from 5 gives 1.8%, which is close but not exact. For small rates the shortcut is fine; for larger ones, divide the factors. The inflation calculator does this adjustment across years of price data.
Percentage difference and percentage error
Two related measures are often confused with percentage change.
- Percentage difference compares two values when neither is the “original,” such as prices at two stores. It divides the difference by the average of the two values.
- Percentage error compares a measured or estimated value with a known true value, dividing by the true value. It is common in science classes and quality checks. The percent error calculator handles it.
Quick checklist
- Subtract old from new, divide by old, multiply by 100.
- Divide by the starting value, not the ending one.
- Multiply factors for successive changes; do not add percentages.
- Say “percentage points” when the values are already rates.
- Compare the same period a year apart for seasonal data.
Sources
- U.S. Bureau of Labor Statistics: Calculating percent changes
- U.S. Bureau of Labor Statistics: How to use the Consumer Price Index for escalation
FAQ
What does “How to Calculate a Percentage Increase or Decrease” explain?
To calculate a percentage increase, subtract the old value from the new value, divide by the old value and multiply by 100. A price that rises from $40 to $50 has gone up ($50 − $40) ÷ $40 × 100 = 25%. A negative result…
How should I use this guide with a calculator?
Read the definitions and assumptions first, then open the linked calculator with the same inputs. Treat results as estimates, not professional advice.
Is this financial or medical advice?
No. Calcenzo content is educational. Confirm important decisions with a qualified professional and official sources for your situation.