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Percentages explained for real life — tips, discounts, tax and grade calculations

Percentages appear in nearly every financial decision you make — sale prices, restaurant bills, exam results, tax returns, interest rates. Most people can punch them into a calculator but struggle to estimate in their head or understand which formula applies to which situation. This guide covers the four types of percentage calculation you'll actually use.

The core concept

Percent means "per hundred." 25% means 25 out of every 100. To convert a percentage to a decimal, divide by 100: 25% = 0.25. To convert a decimal to a percentage, multiply by 100: 0.72 = 72%.

Every percentage calculation comes down to one of three questions: What is X% of Y? X is what percent of Y? Y increased/decreased by what percent to reach X?

1. Finding a percentage of a number

Formula:

Mental maths shortcut: To find 10%, move the decimal one place left. 10% of £85 = £8.50. Then 15% = 10% + half of 10% = £8.50 + £4.25 = £12.75. Fast and reliable.

• 10% of any number: move decimal one place left (240 → 24)
• 5% = half of 10%
• 20% = double 10%
• 25% = divide by 4
• 50% = divide by 2

2. Calculating a discount (percentage off)

Formula:

Alternatively: find 30% (£36) and subtract from £120 = £84. Both methods give the same answer, but the multiplier method (× 0.70) is faster when you have a calculator.

Warning about stacked discounts: 20% off followed by 10% off is NOT the same as 30% off. On a £100 item: 20% off = £80, then 10% off that = £72. Combined discount = 28%, not 30%.

3. Adding tax (VAT, GST, sales tax)

Formula:

To extract tax from a tax-inclusive price (work backwards): divide by (1 + tax rate). £60 ÷ 1.20 = £50 original price. The tax amount = £60 − £50 = £10.

4. Calculating percentage change

Formula:

A positive result is an increase; negative is a decrease. This formula is also used for investment returns, price changes and any comparison between two values over time.

5. Exam and grade percentages

Formula:

To find what raw score you need to hit a target percentage: (Target% ÷ 100) × Total Marks. To pass with 60% on a 120-mark exam: (60 ÷ 100) × 120 = 72 marks needed.

Common percentage mistakes

• Confusing "percentage of" with "percentage more than." 50% of 100 = 50. But 100 is 100% more than 50, not 50% more.
• Applying percentage in the wrong direction. A 25% increase followed by a 25% decrease does not return to the original. Up 25% on £100 = £125. Down 25% on £125 = £93.75.
• Forgetting compound vs simple interest. 5% per year on £1,000 is not always £50/year. With compound interest, the percentage applies to the growing total.