Percentages are everywhere. You see them in discounts, salary increases, exam scores, profit margins, and website growth reports. But while percentages are common, many people still find them confusing when they need to calculate one quickly.
The good news is that most percentage problems follow a few simple formulas.
In this guide, we explain the main types of percentage calculations, including how to find a percentage of a number, how to calculate percentage increase and decrease, how percentage difference works, and when to use margin or markup. If you want a faster way to check the maths, you can also use our calculators for percentage change, difference, and more.
What is a percentage?
A percentage is a way of expressing a value out of 100.
So:
- 50% means 50 out of 100
- 25% means 25 out of 100
- 1% means 1 out of 100
This makes percentages useful for comparing values in a standard format. Whether you are looking at a price discount or a growth rate, percentages help make numbers easier to understand.
How to find a percentage of a number
This is one of the most common percentage calculations.
Formula:
(Percentage ÷ 100) × Total
Example:
What is 20% of 150?
(20 ÷ 100) × 150 = 30
So, 20% of 150 is 30.
This is useful for working out:
- discounts
- commission
- VAT
- interest
- tips
Try our What Is X% of Y Calculator if you want to calculate this instantly.
How to find what percentage one number is of another
This is the reverse of finding a percentage of a number.
Formula:
(Part ÷ Whole) × 100
Example:
You scored 18 out of 24 on a test:
(18 ÷ 24) × 100 = 75%
So, 18 is 75% of 24.
This is useful for:
- exam scores
- completion rates
- budget tracking
- conversion rates
- progress toward goals
Percentage increase explained
The percentage increase tells you how much a number has increased from its starting value.
Formula:
((New Value – Original Value) ÷ Original Value) × 100
Example:
A price rises from £80 to £100.
- Increase = 100 – 80 = 20
- Divide by the original value = 20 ÷ 80 = 0.25
- Multiply by 100 = 25%
So, the price increased by 25%.
This formula is commonly used for:
- wage increases
- rent increases
- revenue growth
- traffic growth
- price changes
Use our Percentage Increase/Decrease Calculator to work this out in seconds.
Percentage decrease explained
Percentage decrease works the same way, except the value falls instead of rises.
Formula:
((Original Value – New Value) ÷ Original Value) × 100
Example:
A jacket drops in price from £120 to £90.
- Decrease = 120 – 90 = 30
- Divide by original = 30 ÷ 120 = 0.25
- Multiply by 100 = 25%
So, the price decreased by 25%.
This is useful for:
- sale prices
- falling costs
- reduced expenses
- budget cuts
- lower usage figures
Percentage change explained
Percentage change is a general term that can mean either an increase or a decrease.
Formula:
((New Value – Original Value) ÷ Original Value) × 100
If the result is positive, it is an increase. If the result is negative, it is a decrease.
Example:
A value changes from 40 to 30:
((30 – 40) ÷ 40) × 100 = -25%
That means a 25% decrease.
Percentage difference explained
Percentage difference is not the same as percentage change.
Use percentage change when one number is the starting point, and the other is the new value.
Use the percentage difference when comparing two values neutrally, and want to measure how far apart they are relative to their average.
Formula:
(Difference ÷ Average) × 100
Example:
Compare 40 and 50:
- Difference = 50 – 40 = 10
- Average = (40 + 50) ÷ 2 = 45
- Percentage difference = (10 ÷ 45) × 100 = 22.22%
So, the percentage difference is 22.22%.
This is useful for comparing:
- prices
- measurements
- survey results
- performance data
- test outcomes
You can use our Percentage Difference Calculator for quick results.
Percentage points vs percent
This is a common area of confusion.
If a rate moves from 10% to 15%:
- the increase is 5 percentage points
- the percentage increase is 50%
Both are correct, but they do not mean the same thing.
This matters in reporting on:
- conversion rates
- interest rates
- polling
- marketing performance
- financial data
Margin vs markup
Margin and markup are often confused, especially in retail and e-commerce.
Markup
Markup is based on cost.
Formula:
((Selling Price – Cost) ÷ Cost) × 100
Margin
Margin is based on selling price.
Formula:
((Selling Price – Cost) ÷ Selling Price) × 100
Example:
A product costs £40 and sells for £50.
Profit = £10
- Markup = 10 ÷ 40 × 100 = 25%
- Margin = 10 ÷ 50 × 100 = 20%
Same numbers, different formulas.
Use our Margin Markup Calculator if you need to check this quickly.
How to add a percentage to a number
This is useful for adding growth, tax, or an increase.
Formula:
Original × (1 + Percentage ÷ 100)
Example:
Increase £200 by 15%:
200 × 1.15 = 230
So, the new total is £230.
How to subtract a percentage from a number
This is useful for discounts and reductions.
Formula:
Original × (1 – Percentage ÷ 100)
Example:
Reduce £80 by 25%:
80 × 0.75 = 60
So, the new total is £60.
Quick percentage formulas cheat sheet
Here are the main formulas in one place:
Find X% of Y
(X ÷ 100) × Y
What percentage is A of B?
(A ÷ B) × 100
Percentage increase
((New – Original) ÷ Original) × 100
Percentage decrease
((Original – New) ÷ Original) × 100
Percentage change
((New – Original) ÷ Original) × 100
Percentage difference
(Difference ÷ Average) × 100
Markup
((Selling Price – Cost) ÷ Cost) × 100
Margin
((Selling Price – Cost) ÷ Selling Price) × 100
Understanding Percentages
Percentage calculations become much easier once you know which type of problem you are solving.
In most cases, you are either:
- finding a percentage of a number
- finding what percentage one number is of another
- measuring an increase or decrease
- comparing two values
- calculating margin or markup
Once you know the right formula, the maths is straightforward. And if you want to speed things up, you can use our percentage calculators to check your numbers in seconds.