Everyday Maths: Percentages, Discounts, VAT and Ratios Explained
Most of the arithmetic that comes up in daily life — checking a discount, splitting a bill, adding VAT, comparing prices — relies on a small number of operations used consistently. The maths itself is not complicated, but it is easy to make errors when working quickly or mixing up which number goes where. This guide explains the most common everyday calculations clearly, with worked examples you can follow and adapt.
How to calculate a percentage of a number
A percentage is a fraction expressed as parts per hundred. To find a percentage of a number, divide the percentage by 100 and multiply by the number.
Formula: Result = (Percentage ÷ 100) × Number
Example: What is 15% of £240? (15 ÷ 100) × 240 = 0.15 × 240 = £36.
A quick mental shortcut: 10% of any number is just the number divided by 10. 15% is 10% plus half of 10%. So 10% of £240 is £24, half of that is £12, and 10% + 5% = £36.
How to calculate a percentage increase or decrease
A percentage increase adds a proportion to the original value. A percentage decrease subtracts it.
Increase: New value = Original × (1 + Percentage ÷ 100)
Decrease: New value = Original × (1 − Percentage ÷ 100)
Example — increase: A salary of £28,000 rises by 4%. New salary = £28,000 × 1.04 = £29,120.
Example — decrease: A price of £85 is reduced by 20%. New price = £85 × 0.80 = £68.
How to work out what percentage one number is of another
To express one number as a percentage of another, divide the first number by the second and multiply by 100.
Formula: Percentage = (Part ÷ Whole) × 100
Example: You scored 43 out of 60 in a test. What percentage is that? (43 ÷ 60) × 100 = 71.7%.
Example: A product costs £14.40 and the profit is £3.60. What is the profit margin? (3.60 ÷ 14.40) × 100 = 25%.
How to calculate a discount
A discount is a percentage reduction applied to a price. There are two things you might want to know: the amount saved, and the final price after the discount.
Discount amount: Original price × (Discount % ÷ 100)
Final price: Original price × (1 − Discount % ÷ 100)
Example: A jacket costs £120 and is on sale at 35% off. Discount amount = £120 × 0.35 = £42. Final price = £120 − £42 = £78. Or directly: £120 × 0.65 = £78.
Watch out for stacked discounts — "an extra 10% off the sale price" does not mean 10% off the original price. It means 10% off the already-discounted price, which is a smaller saving than it might sound.
How to add VAT
In the UK, the standard VAT rate is 20%. To add VAT to a net (ex-VAT) price, multiply by 1.20. To find the VAT amount only, multiply by 0.20.
Example: A service costs £350 plus VAT. VAT = £350 × 0.20 = £70. Total = £350 + £70 = £420. Or directly: £350 × 1.20 = £420.
How to remove VAT (reverse VAT calculation)
Removing VAT from a VAT-inclusive price requires dividing by 1.20, not subtracting 20%. This is a common mistake. Subtracting 20% from a VAT-inclusive price gives the wrong answer because 20% of the gross price is not the same as 20% of the net price.
Formula: Net price = Gross price ÷ 1.20
VAT amount: Gross price − Net price, or Gross price × (0.20 ÷ 1.20) = Gross price × 0.1667
Example: A receipt shows £96 including VAT. Net price = £96 ÷ 1.20 = £80. VAT = £96 − £80 = £16.
Reduced-rate VAT (5%, applied to domestic energy and some other goods) follows the same logic: divide by 1.05 to remove it, multiply by 1.05 to add it.
How to split a bill or share a cost
Dividing a total equally between people is straightforward division. But shared costs are often not equal — one person has more items, or someone is not contributing to a shared element.
Equal split: Amount per person = Total ÷ Number of people
Example: A restaurant bill of £137.60 split between four people: £137.60 ÷ 4 = £34.40 each.
For unequal splits based on consumption, calculate each person's individual total first, then sum them to check against the overall bill.
How ratios work
A ratio expresses the relative sizes of two or more quantities. A ratio of 2:3 means for every two parts of the first quantity, there are three parts of the second. Ratios are used in recipes, map scales, mixing instructions and many other practical contexts.
To divide a quantity in a given ratio, first find the total number of parts, then divide the quantity by that total, and finally multiply by each part.
Example: Divide £500 in the ratio 2:3. Total parts = 5. Each part = £500 ÷ 5 = £100. First share = 2 × £100 = £200. Second share = 3 × £100 = £300.
Common questions about everyday maths
What is the difference between percentage and percentage points?
Percentage points measure the arithmetic difference between two percentages. If an interest rate rises from 3% to 5%, it has risen by 2 percentage points, but by 66.7% in relative terms. The distinction matters when discussing changes in rates, poll figures or statistics.
Why do stacked discounts not add up to their sum?
Each discount applies to the price after the previous discount. A 20% discount followed by a 10% discount gives an 28% overall reduction, not 30%, because the second 10% is 10% of the already-reduced price.
How do I calculate a tip?
To add a 10% tip, divide the bill by 10. For 12.5% (common in UK restaurants), divide by 8. For 15%, find 10% and add half of it. For any percentage, multiply the bill by (percentage ÷ 100).
What is the difference between gross and net?
Gross means before deductions (before tax, before VAT). Net means after deductions. Gross profit includes overheads; net profit does not. Gross pay includes tax and National Insurance; net (take-home) pay does not.
How do I calculate compound interest?
Compound interest applies to both the original amount and the previously accumulated interest. The formula is: Final amount = Principal × (1 + Rate ÷ 100)^Years. For everyday savings calculations, the Goal Saver tool applies compound interest to savings goal estimates.
Related tools and guides
Use Figure It for quick percentage, discount and VAT calculations. For budgeting your income and outgoings, try Budget Wise. To plan how long it will take to save a target amount, use Goal Saver. Browse all LibraireStudios guides for more practical help.
LibraireStudios tools are designed for everyday planning and general information. VAT rates and rules are subject to change — always verify current rates with HMRC for business or contractual purposes.