What is a Percentage?
A percentage is a way of expressing a number as a fraction of 100. The word comes from the Latin per centum, meaning "by the hundred." The symbol % is shorthand for "divided by 100."
So 75% simply means 75 out of every 100 — or 0.75 as a decimal, or ¾ as a fraction. All three forms are equivalent.
To convert a percentage to a decimal, divide by 100. To convert a decimal to a percentage, multiply by 100. Example: 0.35 × 100 = 35%.
Basic Percentage Formula
The fundamental formula for calculating a percentage is:
You scored 72 marks out of 90. What is your percentage?
Percentage = (72 ÷ 90) × 100
What is 35% of 200?
Part = (Percentage ÷ 100) × Total = (35 ÷ 100) × 200
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Use this formula when a value goes up and you want to know by how much, expressed as a percentage of the original value.
Your salary increased from £2,000 to £2,300 per month. What is the percentage increase?
= ((2,300 − 2,000) ÷ 2,000) × 100 = (300 ÷ 2,000) × 100
Percentage Decrease
Use this formula when a value goes down and you want to express the drop as a percentage of the original.
A laptop dropped from £900 to £720. What is the percentage decrease?
= ((900 − 720) ÷ 900) × 100 = (180 ÷ 900) × 100
Calculating Discounts
Discounts are percentage decreases applied to a price. There are two things you might want to calculate: the discount amount, or the final price after discount.
Find the discount amount
Find the final price
A jacket costs £120 and is 25% off. What do you pay?
Discount = (25 ÷ 100) × 120 = £30
Final Price = 120 − 30
For a 25% discount, multiply the original price by 0.75. For 10% off, multiply by 0.9. This saves a step.
Reverse Percentage
A reverse percentage is used when you know the final value after a percentage change and want to find the original value. This is common in tax and VAT calculations.
A price including 20% VAT is £96. What was the price before VAT?
Original = 96 ÷ (1 + 20 ÷ 100) = 96 ÷ 1.2
Quick Reference Table
All the key percentage formulas in one place:
| What you want to find | Formula |
|---|---|
| Basic percentage of a total | (Part ÷ Total) × 100 |
| A percentage of a number | (% ÷ 100) × Number |
| Percentage increase | ((New − Old) ÷ Old) × 100 |
| Percentage decrease | ((Old − New) ÷ Old) × 100 |
| Discount amount | (Discount % ÷ 100) × Price |
| Final price after discount | Price × (1 − % ÷ 100) |
| Original price (reverse %) | Final ÷ (1 + % ÷ 100) |
Real-World Examples
Tax Calculation
If income tax is 20% and your salary is £35,000, your tax bill is: (20 ÷ 100) × 35,000 = £7,000.
Exam Grade Boundaries
If a grade A requires 70% and the exam has 80 marks, you need: (70 ÷ 100) × 80 = 56 marks.
Business Growth
Revenue grew from £50,000 to £65,000. Growth rate: ((65,000 − 50,000) ÷ 50,000) × 100 = 30%.
Sports Statistics
A basketball player made 34 shots out of 50. Shooting percentage: (34 ÷ 50) × 100 = 68%.
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Conclusion
Percentages are one of the most practical areas of everyday math. Whether you're checking a discount, calculating a grade, or tracking business growth, the same core formulas apply. Master these five — basic percentage, increase, decrease, discount, and reverse — and you'll be able to handle almost any percentage problem you encounter.
If you'd rather skip the calculation altogether, use our free Percentage Calculator for instant, accurate results on any device.
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