Percentages KS3
This guide covers the percentage topics taught in Key Stage 3 maths (Years 7 to 9, ages 11 to 14). You will learn how to calculate any percentage of an amount, how to apply percentage increases and decreases, how to express one quantity as a percentage of another, and how to use reverse percentages to find an original value.
Calculating any percentage of an amount
The most reliable method is the multiplier method. Convert your percentage to a decimal by dividing by 100, then multiply by the amount.
Percentage of an amount = (Percentage ÷ 100) × Amount
For example, to find 35% of 120:
35 ÷ 100 = 0.35
0.35 × 120 = 42
You can use the Percentage of a Number Calculator to check your working or to handle more difficult values quickly.
Percentage increase
To increase an amount by a percentage, use a multiplier greater than 1. Add 1 to the decimal form of the percentage.
New amount = Original × (1 + Percentage ÷ 100)
To increase £150 by 20%:
Multiplier = 1 + (20 ÷ 100) = 1.20
£150 × 1.20 = £180
The multiplier method is preferred over finding the percentage first and then adding, because it is a single step and less likely to cause errors. The Percentage Increase Calculator shows this working automatically.
Percentage decrease
To decrease an amount by a percentage, use a multiplier less than 1. Subtract the percentage from 100, then divide by 100.
New amount = Original × (1 - Percentage ÷ 100)
To decrease £80 by 15%:
Multiplier = 1 - (15 ÷ 100) = 0.85
£80 × 0.85 = £68
Try the Percentage Decrease Calculator for instant results with full workings.
Expressing one quantity as a percentage of another
To express one value as a percentage of another, divide the first number by the second, then multiply by 100. This is useful for working out test scores, pass rates, and any other proportion.
Percentage = (Part ÷ Whole) × 100
In a class of 30 students, 18 are girls. What percentage are girls?
18 ÷ 30 = 0.6
0.6 × 100 = 60%
Percentage change
Percentage change tells you how much something has increased or decreased relative to its original value. A positive result is an increase; a negative result is a decrease.
Percentage change = (New - Old) ÷ Old × 100
A phone was £200 and now costs £170. What is the percentage change?
(170 - 200) ÷ 200 × 100
-30 ÷ 200 × 100 = -15%
The price decreased by 15%.
The Percentage Change Calculator handles both increases and decreases automatically.
Reverse percentages
Sometimes you know the result of a percentage change but need to find the original value. This is called a reverse percentage. The key is to identify what multiplier was applied, then divide by it.
Original = Result ÷ Multiplier
After a 25% increase, a number is 75. What was the original?
The multiplier for a 25% increase is 1.25
Original = 75 ÷ 1.25 = 60
A common mistake is to find 25% of 75 and subtract it. That gives the wrong answer. Always divide by the multiplier.
Use the Reverse Percentage Calculator to check your answers.
Worked examples
Example 1: Percentage of an amount
Calculate 35% of 240.
Multiplier = 35 ÷ 100 = 0.35
0.35 × 240 = 84
Example 2: Percentage increase
A jacket costs £80. The price increases by 15%. What is the new price?
Multiplier = 1.15
£80 × 1.15 = £92
Example 3: Percentage decrease
A television costs £450. In a sale, the price drops by 20%. What is the sale price?
Multiplier = 1 - 0.20 = 0.80
£450 × 0.80 = £360
Example 4: Expressing as a percentage
In a school of 600 pupils, 252 travel by bus. What percentage travel by bus?
252 ÷ 600 = 0.42
0.42 × 100 = 42%
Example 5: Reverse percentage
After a 15% discount, a price is £340. What was the original price?
A 15% discount means the multiplier was 0.85
£340 ÷ 0.85 = £400
Example 6: Percentage change
A town's population was 12,000. It grew to 13,800. Calculate the percentage increase.
(13,800 - 12,000) ÷ 12,000 × 100
1,800 ÷ 12,000 × 100 = 15%
Try the calculators
Percentage of a Number
Calculate any percentage of any amount instantly.
Percentage Increase Calculator
Work out new values after a percentage increase.
Percentage Decrease Calculator
Find sale prices and discounted values.
Percentage Change Calculator
Calculate the % change between two values.
Reverse Percentage Calculator
Find the original value before a percentage change.
Ready to practise?
Test yourself with KS3 practice questions, each with a worked answer.
KS3 Practice Questions