To calculate a percentage change, subtract the original number from the new number, divide the difference by the original number, then multiply by 100. A positive result is an increase and a negative result is a decrease, assuming the original value is positive.
The formula is simple. Most mistakes happen because people divide by the wrong number, confuse percentage change with percentage points, or try to use the formula when the starting value is zero.
What is the formula for percentage change?
Use:
((new value - original value) / original value) × 100
Suppose a monthly bill increases from 800 to 1,000.
First calculate the difference:
1000 - 800 = 200
Then divide that difference by the original value:
200 / 800 = 0.25
Convert the decimal to a percentage:
0.25 × 100 = 25%
The bill increased by 25%.
The denominator is the part people most often get wrong. You divide by the original value because the question is asking how large the change was relative to where you started.
How do I calculate a percentage increase?
For an increase, subtract the old value from the new one and compare the difference with the old value.
Suppose a product originally costs 2,400 and later costs 3,000.
The increase is:
3000 - 2400 = 600
Now calculate:
600 / 2400 = 0.25
Then:
0.25 × 100 = 25%
The price increased by 25%.
You can write the complete calculation as:
((3000 - 2400) / 2400) × 100 = 25%
This same calculation works for increases in revenue, users, expenses, weight, distance, page views, production, or other quantities.
How do I calculate a percentage decrease?
The logic is the same, but the new value is smaller.
Suppose a subscription drops from 1,500 to 1,200.
Calculate the difference:
1200 - 1500 = -300
Then divide by the original value:
-300 / 1500 = -0.2
Multiply by 100:
-0.2 × 100 = -20%
The negative sign tells you the direction of the change. In normal writing, you would usually say the price decreased by 20% rather than saying it changed by -20%.
You can also calculate the magnitude of the decrease directly:
((1500 - 1200) / 1500) × 100 = 20%
Both approaches describe the same change.
Which number should I divide by?
Divide by the original value, not the new value.
Suppose traffic rises from 400 visits to 500 visits.
The difference is:
500 - 400 = 100
The correct calculation is:
100 / 400 × 100 = 25%
If you divide by 500 instead:
100 / 500 × 100 = 20%
you get a different answer.
That 20% number answers a different question: the difference of 100 is 20% of the new value. It does not tell you the percentage increase from the original 400.
Whenever you get confused, ask: What value did I start with?
That is normally your denominator.
Can I calculate the change without doing the formula manually?
Yes. For quick calculations, Toolorah's Percentage Calculator can calculate percentage relationships without requiring you to rearrange the formula yourself.
For important financial or business calculations, still understand what the inputs mean. A calculator can execute the arithmetic perfectly while giving you a misleading result if you enter the wrong starting value.
The calculation is only as meaningful as the comparison you chose.
Why is a 50% increase followed by a 50% decrease not zero?
Because the second percentage is calculated from a different starting value.
Start with 100.
Increase it by 50%:
100 + 50 = 150
Now decrease 150 by 50%:
150 - 75 = 75
You end with 75, not 100.
The first 50% was calculated from 100. The second 50% was calculated from 150.
The same effect appears with smaller percentages.
Start at 100 and increase by 20%:
100 × 1.20 = 120
Now decrease the result by 20%:
120 × 0.80 = 96
You finish at 96.
Equal percentage increases and decreases do not cancel because their bases are different.
What percentage decrease reverses a 25% increase?
This is a useful extension of the same idea.
Start with 100 and increase it by 25%:
100 × 1.25 = 125
To return from 125 to 100, you need to remove 25.
But 25 is only 20% of 125:
25 / 125 × 100 = 20%
So a 25% increase requires a 20% decrease to return to the original value.
The reverse also behaves differently. If something falls by 25%, it goes from 100 to 75. Returning from 75 to 100 requires an increase of:
25 / 75 × 100 = 33.333...%
A 25% decrease therefore requires about a 33.33% increase to recover.
This matters in investing, revenue analysis, discounts, performance measurements, and anywhere percentage losses and gains are compared.
How do I calculate what a number becomes after a percentage increase?
Sometimes you already know the percentage and want the final number.
For an increase, convert the percentage into a decimal and add 1.
A 15% increase means:
1 + 0.15 = 1.15
If the original amount is 2,000:
2000 × 1.15 = 2300
So increasing 2,000 by 15% gives 2,300.
The general formula is:
new value = original value × (1 + percentage / 100)
For example, increasing 750 by 8%:
750 × (1 + 8 / 100)
750 × 1.08
810
The result is 810.
How do I reduce a number by a percentage?
For a decrease, subtract the percentage expressed as a decimal from 1.
A 15% reduction gives:
1 - 0.15 = 0.85
If an item costs 2,000:
2000 × 0.85 = 1700
The discounted amount is 1,700.
The general formula is:
new value = original value × (1 - percentage / 100)
For a 30% reduction from 800:
800 × 0.70 = 560
This method is useful when calculating discounts because it gives the final amount directly.
Is percentage change the same as percentage points?
No. Confusing the two can make a change sound much larger or smaller than it actually is.
Suppose a conversion rate moves from 10% to 15%.
The difference is:
15% - 10% = 5 percentage points
But the relative percentage increase is:
((15 - 10) / 10) × 100 = 50%
Both statements are mathematically valid:
- The conversion rate increased by 5 percentage points.
- The conversion rate increased by 50% relative to its previous rate.
They describe the same movement from different perspectives.
This distinction matters especially with conversion rates, interest rates, survey results, probabilities, margins, and other quantities that are already expressed as percentages.
What happens if the original value is zero?
The standard percentage-change formula does not produce a finite percentage change when the original value is zero because it requires division by zero.
Consider a new project that goes from zero paying customers to 10.
Trying:
((10 - 0) / 0) × 100
does not give you a valid percentage increase.
You can accurately say that the number increased from 0 to 10, or that 10 customers were added. You should not invent a conventional percentage increase for the change.
This is a common problem in dashboards. A metric may show an enormous, infinite, or missing growth value simply because the previous period was zero.
Displaying the absolute change is often more useful in that situation.
How do percentage changes work with negative numbers?
This is where the standard formula becomes harder to interpret.
Suppose a business result moves from a loss of -100 to a profit of 50.
Blindly applying:
((50 - (-100)) / -100) × 100
gives:
150 / -100 × 100 = -150%
Calling that a "150% decrease" would be deeply misleading because the business actually improved from a loss to a profit.
Percentage change is easiest to interpret when the original value is positive and the values represent a quantity where ratios make sense.
When a metric crosses zero or both values are negative, report the original value, new value, and absolute difference alongside any percentage calculation. Sometimes the percentage should be omitted entirely.
How do I calculate percentage change in Excel or Google Sheets?
Suppose the original value is in cell A2 and the new value is in B2.
Use:
=(B2-A2)/A2
Then format the result cell as a percentage.
If A2 contains 800 and B2 contains 1000, the result is 25%.
You do not need to multiply the spreadsheet formula by 100 if the cell is formatted as a percentage. Spreadsheet percentage formatting already displays a decimal such as 0.25 as 25%.
If the original value can be zero, handle that case explicitly instead of allowing a division-by-zero error.
For example:
=IF(A2=0,"N/A",(B2-A2)/A2)
This displays N/A when the percentage change cannot be calculated using the standard formula.
For other everyday calculations, Toolorah's Calculator Tools provides related browser-based calculators.
How do I calculate percentage change in Python?
For positive starting values, the calculation is straightforward:
def percentage_change(original, new):
if original == 0:
return None
return ((new - original) / original) * 100
result = percentage_change(800, 1000)
print(result)
This prints:
25.0
The zero check matters. Without it, passing an original value of zero raises a ZeroDivisionError.
Returning None is one reasonable way to represent a percentage change that cannot be calculated using this formula. In a real application, you could instead display N/A, return a structured result, or handle the case according to your application's requirements.
How can I check whether my percentage calculation makes sense?
Before trusting the result, estimate the answer mentally.
If something moves from 100 to 200, you know it doubled, so the increase must be 100%.
If it moves from 100 to 110, the increase is clearly 10%.
If your calculator tells you either change is 50%, something is wrong with your inputs or formula.
For less obvious numbers, check four things:
- Identify the original value.
- Calculate the absolute difference.
- Divide that difference by the original value.
- Check whether the direction of the result matches what actually happened.
For percentage-based comparisons involving several calculations, a general Percentage Calculator is useful, but the sanity check still matters.
A mathematically correct percentage can also be a poor way to describe a change. If the starting value is zero, the values cross zero, or the underlying metric is already a percentage, report enough context for the reader to understand what actually changed.
