GCSE Maths Tool

Percentage CalculatorQuickly calculate percentages with step-by-step GCSE explanations.

Solve 'What percent of X is Y?', 'X is what percent of Y?', and percentage increase/decrease with detailed working.

Percentage Calculator

Calculate what percentage Y is of X

Quick Examples

What percent of 80 is 32?
32 is 40.00% of 80
25 is what percent of 200?
25 is 12.50% of 200
Price increase from £50 to £65
30.00% increase from 50 to 65
20% of 150
20% of 150 is 30.00

How to Calculate Percentages

Percentages are a fundamental part of GCSE Maths. They represent parts of a whole, where the whole is divided into 100 equal parts. Understanding percentages is crucial for topics like finance, statistics, and proportional reasoning.

Finding a Percentage of an Amount

Calculate what a certain percentage of a number is

Amount × (Percentage ÷ 100)

Example: 25% of 200 = 200 × (25 ÷ 100) = 200 × 0.25 = 50

Expressing One Number as a Percentage of Another

Find what percentage one number is of another

(Part ÷ Whole) × 100

Example: 32 is what % of 80? (32 ÷ 80) × 100 = 0.4 × 100 = 40%

Percentage Increase

Calculate how much a value has increased by as a percentage

((New - Old) ÷ Old) × 100

Example: £50 to £65 = ((65 - 50) ÷ 50) × 100 = (15 ÷ 50) × 100 = 30%

Percentage Decrease

Calculate how much a value has decreased by as a percentage

((Old - New) ÷ Old) × 100

Example: £80 to £64 = ((80 - 64) ÷ 80) × 100 = (16 ÷ 80) × 100 = 20%

Percentage Increase and Decrease Examples

Price Increase

A shirt costs £20. It increases by 25% to £25.

Original: £20
Increase: £20 × 0.25 = £5
New price: £20 + £5 = £25

Discount

A £80 jacket has a 30% discount.

Original: £80
Discount: £80 × 0.30 = £24
Sale price: £80 - £24 = £56

VAT Calculation

Calculate 20% VAT on a £50 item.

Item: £50
VAT: £50 × 0.20 = £10
Total: £50 + £10 = £60

Why Percentages Matter in GCSE Maths

Exam Topics

  • • Percentage of amounts
  • • Percentage change (increase/decrease)
  • • Reverse percentages
  • • Compound percentages
  • • Percentage error

Real-World Applications

  • • Shopping discounts and VAT
  • • Interest rates and investments
  • • Population growth statistics
  • • Exam grade boundaries
  • • Sports statistics and polls

Frequently Asked Questions

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