Guide · Everyday Finance
Percentage Calculations: A Quick Reference for Personal Finance
Three formulas cover almost every percentage problem you will encounter—from VAT and salary rises to investment returns and inflation. Master these and the maths of personal finance becomes straightforward.
The three core percentage formulas
Every percentage calculation in personal finance reduces to one of three problems:
(1) What is X% of Y? → Y × X ÷ 100. Used for: calculating VAT, interest on a loan, a percentage of your salary, or a discount. Example: 20% of £450 = £450 × 20 ÷ 100 = £90.
(2) X is what percentage of Y? → (X ÷ Y) × 100. Used for: expressing a share of budget, finding what percentage a pay rise represents, or calculating an expense ratio. Example: £35 is what percentage of £140? (35 ÷ 140) × 100 = 25%.
(3) Percentage change from X to Y → (Y − X) ÷ X × 100. Used for: investment returns, salary increases, inflation impact, or price changes. Example: price rose from £180 to £225 → (225 − 180) ÷ 180 × 100 = +25%.
Finance applications: worked examples
| Scenario | Calculation | Answer |
|---|---|---|
| VAT on £1,000 net purchase | £1,000 × 20% | £200 VAT → £1,200 gross |
| Remove VAT from £120 gross | £120 ÷ 1.20 | £100 net |
| £35 spending vs £140 budget | (35 ÷ 140) × 100 | 25% used |
| Price from £180 to £225 | (225 − 180) ÷ 180 × 100 | +25% change |
| 15% pay rise on £32,000 | £32,000 × 1.15 | £36,800 new salary |
| 4.75% rate on £250,000 mortgage | £250,000 × 4.75% | £11,875 annual interest |
Note the VAT removal calculation: dividing by 1.20 is not the same as multiplying by 0.80. Multiplying by 0.80 gives 80% of the gross price (£96 on £120)—which is wrong. Dividing by 1.20 correctly reverses the addition of 20% of the net price and gives £100.
The surprising impact of percentages in everyday finance
The inflation figure is the most surprising to many people. A 3% annual inflation rate on a £30,000 salary means you need a £900 pay rise just to maintain your current purchasing power—before any real increase in living standards. Over five years of 3% inflation with a frozen salary, purchasing power falls by 14%. Understanding this is essential for salary negotiations and for evaluating savings rates.
Percentage points vs percentage change is a distinction finance commentators frequently blur. If the Bank of England raises its base rate from 0.5% to 1.0%, that is a 0.5 percentage point rise but a 100% increase in the rate itself. When your bank says “we've increased the savings rate by 0.5%”—that is almost certainly 0.5 percentage points (from, say, 4.0% to 4.5%), not 0.5% of 4.0% (which would be 0.02 percentage points).
Compound percentage changes do not add up. A 10% gain followed by a 10% loss leaves you at 99% of your starting value, not 100%. Start with £1,000; gain 10% → £1,100; lose 10% on £1,100 → £990. A 50% loss requires a 100% gain to recover. This asymmetry means volatility in investment returns always reduces long-run compound growth compared to the same arithmetic average return achieved smoothly.
Tip calculation shortcut: to calculate a 15% tip on £68, find 10% (£6.80) and half of that for 5% (£3.40); add them together for 15% (£10.20). For 20%, just divide by 5: £68 ÷ 5 = £13.60.
Frequently asked questions
What is the difference between percentage points and percentage change?
A percentage point is an absolute difference between two percentage figures. A percentage change is the relative change expressed as a percentage of the starting value. If a mortgage rate rises from 3% to 5%, that is a 2 percentage point increase—but it is a 66.7% increase in the rate itself ((5 − 3) ÷ 3 × 100). Politicians and media often conflate the two deliberately or by accident. In finance, the distinction matters: a 1 percentage point rise in a 2% interest rate doubles your interest cost.
How do I calculate a percentage increase in salary?
New salary = current salary × (1 + percentage increase ÷ 100). For a 5% rise on £35,000: £35,000 × 1.05 = £36,750. To find the percentage increase when you know both figures: ((new − old) ÷ old) × 100. If you moved from £35,000 to £38,000: ((38,000 − 35,000) ÷ 35,000) × 100 = 8.57%. When negotiating, always verify whether the percentage offered is applied to your base salary only or includes bonus and benefits.
How do I remove VAT from a price?
To remove 20% UK VAT from a VAT-inclusive price, divide by 1.20 (not multiply by 0.80—that is a different calculation). A price of £120 including VAT: £120 ÷ 1.20 = £100 net. Dividing by 1.20 correctly reverses the addition of 20% because the VAT was calculated on the net price, not the gross. To add VAT to a net price: net × 1.20 = gross. At the 5% reduced rate (domestic fuel, children's car seats): divide by 1.05 to remove, or multiply by 1.05 to add.
Why does a 10% gain followed by a 10% loss not break even?
Because the 10% loss is applied to a larger base than the original amount. Start with £1,000; a 10% gain gives £1,100; a 10% loss on £1,100 gives £990—a net loss of 1%. The formula is: final value = start × (1 + gain) × (1 − loss) = £1,000 × 1.10 × 0.90 = £990. This asymmetry is why recovering from investment losses is harder than it looks: a 50% fall requires a 100% gain just to break even. It also explains why low-volatility returns can outperform high-volatility returns with the same arithmetic average.