Percentage Increase, Decrease & Reverse Percentages Explained
Percentages appear everywhere — discounts, pay rises, price changes, interest rates, margins and exam questions.
The basic calculations are simple once you know which formula to use.
This guide explains the most common percentage calculations with worked examples and links to calculators you can use with your own numbers.
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What is a percentage?
A percentage describes an amount out of 100.
For example:
50% means 50 out of 100
25% means 25 out of 100
10% means 10 out of 100
To convert a percentage into a decimal, divide it by 100.
For example:
20% = 0.20
7.5% = 0.075
How do you find a percentage of a number?
Use:
Percentage amount = number × percentage ÷ 100
What is 15% of £80?
£80 × 15 ÷ 100 = £12
So 15% of £80 is:
£12
How do you find what percentage one number is of another?
Use:
Percentage = part ÷ whole × 100
What percentage is 30 of 120?
30 ÷ 120 × 100 = 25%
So 30 is 25% of 120.
How do you increase a number by a percentage?
There are two common methods.
Method 1:
Find the percentage amount and add it to the original.
Method 2:
Multiply by:
1 + percentage ÷ 100
Increase £80 by 15%.
£80 × 1.15 = £92
So after a 15% increase:
£80 becomes £92.
How do you decrease a number by a percentage?
Multiply the original amount by:
1 − percentage ÷ 100
Reduce £120 by 20%.
£120 × 0.80 = £96
So after a 20% decrease:
£120 becomes £96.
How do you calculate percentage change?
Use:
Percentage change = (new value − original value) ÷ original value × 100
A price rises from £120 to £150.
Change:
£150 − £120 = £30
Percentage change:
£30 ÷ £120 × 100 = 25%
The price increased by:
25%
What is a reverse percentage?
A reverse percentage is used when you know the final amount after a percentage change but want to find the original amount.
This often appears with discounts, VAT, pay rises and price increases.
An item costs £80 after a 20% discount.
After a 20% discount, 80% of the original price remains.
So:
Original price = £80 ÷ 0.80
Original price = £100
This is different from simply adding 20% back onto £80.
Why can’t you just add the percentage back?
Percentage increases and decreases are calculated from different starting values.
For example:
Start with £100.
Increase it by 20%:
£100 → £120
Now decrease £120 by 20%:
£120 → £96
You do not return to £100.
That is because the first 20% was calculated from £100, while the second 20% was calculated from £120.
+20% followed by −20% produces an overall change of −4%.
Percentage points vs percentage change
These are not the same thing.
Suppose a rate increases from:
40% to 50%
The increase is:
10 percentage points
But relative to the original 40%, the percentage increase is:
(50 − 40) ÷ 40 × 100 = 25%
So:
40% → 50%
is a 10 percentage-point increase
and a 25% relative increase.
How do percentage discounts work?
A 25% discount means you pay 75% of the original price.
For example:
Original price:
£200
25% discount:
£50
Sale price:
£150
Percentage markup and profit margin are not the same
Markup measures profit relative to cost.
Margin measures profit relative to selling price.
For example:
Cost:
£80
Selling price:
£100
Profit:
£20
Markup:
£20 ÷ £80 × 100 = 25%
Profit margin:
£20 ÷ £100 × 100 = 20%
The same transaction therefore has:
25% markup
but:
20% margin
Common percentage mistakes
Common mistakes include:
• using the new value instead of the original value when calculating percentage change
• adding a discount percentage back to find the original price
• assuming a percentage increase and equal percentage decrease cancel each other out
• confusing percentage points with percentage change
• confusing markup with profit margin
• entering 20 instead of 0.20 when a formula expects a decimal
Percentage formula cheat sheet
Percentage of a number:
Number × Percentage ÷ 100
What percentage is A of B?
A ÷ B × 100
Percentage increase:
(New − Original) ÷ Original × 100
Percentage decrease:
(Original − New) ÷ Original × 100
Increase by X%:
Original × (1 + X ÷ 100)
Decrease by X%:
Original × (1 − X ÷ 100)
Original value after an X% decrease:
Final ÷ (1 − X ÷ 100)
Original value after an X% increase:
Final ÷ (1 + X ÷ 100)
Percentage FAQs
What is 20% of 100?
20. Multiply 100 by 0.20.
How do I add 20% to a number?
Multiply the original number by 1.20.
How do I subtract 20%?
Multiply the original amount by 0.80.
How do I find the original price before a discount?
Divide the final price by the percentage that remains. For a 20% discount, divide the sale price by 0.80.
Does increasing something by 10% and then reducing it by 10% return to the original?
No. The two percentages are calculated from different starting values.
What is the difference between percentage and percentage points?
Percentage points describe the absolute difference between two percentages. Percentage change measures the difference relative to the original percentage.