How to calculate percentages: the three types explained

Three questions, one idea: a percentage is just a fraction out of 100.

A percentage is nothing more exotic than a fraction with a fixed denominator of 100. The word comes from the Latin per centum — “per hundred” — and the symbol % is shorthand for /100. So 25% means 25/100, which is the same as the decimal 0.25 or the fraction 1/4. Almost every percentage problem you will ever meet is one of just three questions, and once you can spot which one you are looking at, the arithmetic is mechanical.

The three questions at a glance

Most people freeze on percentages not because the maths is hard, but because the wording hides which calculation is needed. Here are the three shapes, side by side:

Type 1: What is P% of X?

This is the “take a slice” question, and it is the one behind tips, tax, commission and any “percent off” deal. Convert the percentage to a decimal by dividing by 100, then multiply by the total. Suppose a restaurant bill is £80 and you want to leave a 15% tip:

15% of 80  =  15 / 100 × 80  =  0.15 × 80  =  12

So the tip is £12, and the full payment is £92. The same recipe handles sales tax (what is 8% of £50?) and interest (what is 3% of a £10,000 balance?). A handy shortcut: 10% of any number is just that number with the decimal point moved one place left, so 10% of £80 is £8 — and you can scale from there to estimate in your head.

Type 2: X is what percent of Y?

Here you already have the part and the whole, and you want the percentage that connects them. Divide the part by the whole, then multiply by 100. If you answered 18 questions correctly out of 24 on a test:

18 is what percent of 24?  =  18 / 24 × 100  =  0.75 × 100  =  75%

The order matters: the number after “percent of” is always the whole (the denominator). A common slip is to divide the wrong way round, which would give 133% here and should immediately look wrong, because a part can never be more than 100% of its whole. Use this type for scores, conversion rates, survey results, and “what fraction of my budget did I spend?” questions.

Type 3: Percent change from A to B

Growth and decline are measured as percent change: the difference between the new and old values, expressed as a percentage of the original. The formula is (B − A) / A × 100, where A is the starting value and B is the new one. If a subscription rises from £40 to £50:

(50 − 40) / 40 × 100  =  10 / 40 × 100  =  25% increase

A negative result is a decrease. If website traffic falls from 5,000 to 4,000 visitors, the change is (4000 − 5000) / 5000 × 100 = −20%. Two cautions are worth remembering. First, always divide by the starting value, not the new one. Second, percentage changes do not simply cancel: a 50% drop followed by a 50% rise does not return you to where you started — 100 → 50 → 75 leaves you 25% down.

Percent vs percentage points: the trap

This is the distinction that catches out journalists, students and even economists, so it is worth slowing down for. When you compare two percentages, you can describe the gap in two completely different ways:

Both statements describe the exact same change in an interest rate, a tax band or an approval rating — but “up 2 points” and “up 40%” sound wildly different, and one is often used to make a story more dramatic than the other. When you read that something “rose by 40%,” always check whether the figure is a relative change or a change in percentage points; the two can differ by an order of magnitude. As a rule, use percentage points when both numbers are themselves percentages (rates, shares, probabilities), and reserve percent change for the growth of an ordinary quantity like price, population or revenue.

Where this shows up every day

These three formulas quietly run a lot of ordinary life. Discounts are Type 1 in reverse — a “30% off” tag means you pay 70% of the list price, so a £60 jacket costs 0.70 × 60 = £42. Tips and tax are straight Type 1 calculations layered on top of a bill. Exam scores and conversion rates are Type 2. And growth rates — pay rises, inflation, investment returns, year-on-year sales — are Type 3. Knowing which question you are answering is most of the battle; the multiplication and division are the easy part.

When the numbers get awkward or you just want a quick sanity check, reach for the percentage calculator for the general cases and the discount calculator when you are working out a sale price. Both run entirely on your device, so nothing you type is sent anywhere.

Related tools: Percentage calculator · Discount calculator