How to Calculate Percentages: The Complete Guide
Maths guide · Updated June 2026
Almost every percentage question you will ever face is one of three problems wearing a disguise. Once you can spot which of the three you are looking at, the maths is short and the same every time. This guide walks through all three — finding a percentage of a number, working out one number as a percentage of another, and measuring a percentage change — with the kind of examples you actually meet: tips, discounts, test scores, and pay. If you only need an answer, the percentage calculator handles all three; but understanding the method means you will never be at the mercy of a dead phone battery.
First, what a percentage actually is
"Percent" comes from per centum — Latin for "per hundred." A percentage is simply a fraction with 100 on the bottom. So 25% means 25 out of 100, which is the fraction 25/100, which is the decimal 0.25. Those three are the same value written three ways. The single most useful habit in all of percentage maths is converting the percent to a decimal before you do anything: drop the % sign and move the decimal point two places left. 7% becomes 0.07, 60% becomes 0.6, 150% becomes 1.5. Everything below rests on that one move.
Problem 1: finding a percentage of a number
This is the "what is 20% of 60?" shape — a tip, a discount, a deposit, a commission. Convert the percentage to a decimal and multiply.
Example. A £60 meal, and you want to leave a 20% tip.
- 20% as a decimal is 0.20
- 0.20 × £60 = £12
The mental shortcut is to build the number from 10% pieces. 10% of £60 is £6, so 20% is just double that — £12 — and you never touched a calculator. This is the engine behind the tip calculator and the what is X percent of Y calculator, and it is exactly how a shop works out the saving on a sale item.
Problem 2: one number as a percentage of another
This is the reverse direction — you have two amounts and want to know what proportion one is of the other. "I got 38 out of 50, what percent is that?" Divide the part by the whole, then multiply by 100.
Example. A test marked 38 out of 50.
- 38 ÷ 50 = 0.76
- 0.76 × 100 = 76%
The order matters: it is always part over whole, the thing you have divided by the thing it is a slice of. Get those upside down and the answer is nonsense. The X is what percent of Y calculator does this directly, and it is the same logic that turns a fraction into a percentage — see the fraction to percent calculator if your numbers start life as a fraction.
Problem 3: percentage change
A price went from £80 to £100; a salary, a temperature, a follower count moved. Percentage change measures the size of that move relative to where it started. Take the difference, divide by the original value, and multiply by 100.
Example. A price rose from £80 to £100.
- Difference: £100 − £80 = £20
- £20 ÷ £80 = 0.25
- 0.25 × 100 = a 25% increase
A positive result is an increase, a negative one a decrease. The word that catches people out is original: you always divide by the starting figure, not the new one. The percentage change calculator handles both directions, while the percentage increase calculator is handy when you know you are going up.
The trap: percentages don't reverse
A 50% fall and a 50% rise do not cancel out. Drop £100 by 50% and you have £50. Raise that £50 by 50% and you gain only £25, landing at £75 — not back at £100. Each percentage is taken from a different base, so a rise and a fall of the same percent never undo each other. To get back from £50 to £100 you actually need a 100% increase.
The same trap appears when you want to undo a percentage — finding the price before a discount, or the figure before VAT was added. You cannot just add the percentage back on; you have to divide. If a coat costs £72 after 20% off, that £72 is 80% of the original, so the original was £72 ÷ 0.80 = £90. That is the job of the reverse percentage calculator, and the same maths underpins working out the price before a sale on the discount calculator.
Percent vs. percentage points
One last distinction worth owning, because it is everywhere in the news. If an interest rate moves from 5% to 7%, that is a rise of 2 percentage points — but a 40% increase in relative terms (2 is 40% of 5). "Points" measure the gap between two percentages; "percent" measures the proportional change between them. A headline that blurs the two can make a small change sound enormous, or vice versa. When the underlying figures are themselves percentages, reach for the percentage points calculator to keep the two ideas apart.
Which problem am I looking at?
| If the question sounds like… | Do this |
|---|---|
| "What is 15% of 200?" | Multiply: 0.15 × 200 |
| "30 out of 40 is what percent?" | Divide, ×100: (30 ÷ 40) × 100 |
| "It went from 40 to 50 — what's the rise?" | Change ÷ original: (10 ÷ 40) × 100 |
| "£72 after 20% off — what was it before?" | Divide back: 72 ÷ 0.80 |
Skip the arithmetic
Knowing the method is what stops you being fooled by a bad statistic or a too-good-to-be-true sale. But for the day-to-day numbers, let a tool do the lifting: the general percentage calculator covers all three problems on one screen, and if your value starts as a decimal you can flip it with the decimal to percent calculator. Bookmark the one you reach for most.
Frequently asked questions
What's the fastest way to find a percentage in my head?
Break it into 10% and 1% chunks. 10% of any number is that number with the decimal point moved one place left; 1% moves it two places. To get 15% of 80, take 10% (8) plus half of that for the 5% (4), which gives 12. Most everyday percentages can be built from 10%, 5%, and 1% pieces.
Is "percent of" the same as multiplying by a decimal?
Yes. "Percent" means "out of 100," so 25% is just 25/100 = 0.25. Finding 25% of a number is the same as multiplying it by 0.25. Converting the percentage to a decimal first is usually the cleanest way to do it on a calculator.
Why do a 50% drop and a 50% rise not cancel out?
Because each percentage is taken from a different starting point. If £100 falls 50% you have £50; a 50% rise on £50 is only £25, taking you back to £75, not £100. Percentage changes always apply to the current value, not the original, so they don't reverse symmetrically.
How do I reverse a percentage to find the original amount?
Divide rather than subtract. If £72 is the price after a 20% discount, that £72 represents 80% of the original, so the original was £72 ÷ 0.80 = £90. Working backwards from a total that already includes (or excludes) a percentage is the one case where people most often go wrong.
What's the difference between percentage points and percent?
A move from 5% to 7% is a rise of 2 percentage points, but a 40% increase in relative terms. "Points" describe the gap between two percentages; "percent" describes the proportional change. Mixing them up is a classic source of misleading statistics.