How to calculate percentages — the complete guide
How do you calculate percentages?
A percentage is a way of describing "part of a hundred" — 25% is exactly 25 out of 100, or 0.25. Almost every percentage question is one of only three types: finding a percentage of an amount, finding what percentage one amount is of another, or finding the whole when you know the part and the percentage. Once you spot which of the three you are looking at, the answer is a matter of substituting into the formula.
Worked examples, step by step
What is 20% of 150?
- The formula: percentage of an amount = (amount × percentage) ÷ 100
- Substitute: (150 × 20) ÷ 100
- 150 × 20 = 3000
- 3000 ÷ 100 = 30
- Answer: 20% of 150 is 30
30 pupils out of a class of 40 passed the test. What percentage is that?
- The formula: percentage = (part ÷ whole) × 100
- Substitute: (30 ÷ 40) × 100
- 30 ÷ 40 = 0.75
- 0.75 × 100 = 75
- Answer: 75% of the pupils passed the test
60 is 40% of which number?
- The formula: whole = (part × 100) ÷ percentage
- Substitute: (60 × 100) ÷ 40
- 60 × 100 = 6000
- 6000 ÷ 40 = 150
- Answer: 60 is 40% of 150
A class has 25 pupils, and 5 of them got full marks. What percentage got full marks?
- We have a part (5) and a whole (25) and need a percentage — that is type 2
- The formula: percentage = (part ÷ whole) × 100
- Substitute: (5 ÷ 25) × 100
- 5 ÷ 25 = 0.2
- 0.2 × 100 = 20
- Answer: 20% of the pupils got full marks
Now try it yourself
Frequently asked questions
What are the three types of percentage question?
Finding a percentage of an amount (for example 20% of 150), finding what percentage a part is of a whole (30 out of 40 is what percentage), and finding the whole when you know the part and the percentage (60 is 40% of what number). Every percentage question that exists is a variation on one of these.
How do you know which type of question it is?
Check what is given and what is asked: if you are given an amount and a percentage and asked for a result — type 1. If you are given two numbers and asked what percentage one is of the other — type 2. If you are given a part and a percentage and asked for the whole — type 3.
Can you calculate percentages without a calculator?
Yes — the simplest way is to find 10% first (move the decimal point one place to the left) and then multiply or divide as needed. For example 30% of 90: first 10% of 90 = 9, then 9 × 3 = 27. GCSE Paper 1 is non-calculator, so this is a skill worth practising.
Is there a free percentage calculator that does all three types?
Yes — the MathsUK percentage calculator solves all three types and shows the formula and the explanation for every calculation. The link is at the bottom of the page.
✍️ Written by the MathsUK teamChecked against the National Curriculum and GCSE specificationsLast updated: