To calculate a percentage, divide the part by the whole and multiply by 100 — that is the only formula you really need. And to find X% of a number, flip it around: multiply the number by X ÷ 100, so 20% of 250 is 250 × 0.20 = 50. Almost every percentage problem you will ever meet — a shop discount, an exam score, a tip, a pay rise — is one of these two moves in disguise. This guide breaks percentages down into the three questions people actually ask, with real examples and mental shortcuts for each. If you'd rather skip the arithmetic entirely, our free percentage calculator answers all three instantly — just type in your two numbers.
The one formula behind every percentage
"Percent" simply means "out of 100" — a fraction with 100 on the bottom. The master formula is:
Percentage = (part ÷ whole) × 100
If you scored 42 marks in a test marked out of 60, your score is (42 ÷ 60) × 100 = 70%. Going the other way — finding a percentage of a number — uses the mirror-image formula:
X% of Y = Y × (X ÷ 100)
So 15% of 80 is 80 × 0.15 = 12. Every example in this guide is one of these two formulas; the only skill is recognising which question you're being asked.
Quick check: percentages above 100% are perfectly possible. Savings growing from 200 to 260 means you now hold 130% of the starting amount — the formula handles it with no special rules.
Question 1: What is X% of Y?
This is the most common percentage question in daily life — it sits behind every discount, tip, tax and commission. Turn the percentage into a decimal (divide by 100), then multiply:
| Question | Working | Answer |
|---|---|---|
| What is 15% of 80? | 80 × 0.15 | 12 |
| What is 25% of 240? | 240 × 0.25 | 60 |
| Sales tax of 8% on a 250 bill | 250 × 0.08 | 20 (total bill 270) |
| What is 12.5% of 64? | 64 × 0.125 | 8 |
| A 20% tip on a 45 restaurant bill | 45 × 0.20 | 9 (total 54) |
The chart below shows the pattern: percentages scale in a straight line, so doubling the percentage doubles the result.
Percentages of 200 — hover or tap each bar for details.
Question 2: X is what percent of Y?
Here you already have the two numbers and want the percentage — exam grades, survey results, how much of a budget you've spent. Use the master formula: divide the smaller part by the whole, then multiply by 100.
| Question | Working | Answer |
|---|---|---|
| 42 marks out of 60 is what percent? | (42 ÷ 60) × 100 | 70% |
| 18 correct answers out of 24 | (18 ÷ 24) × 100 | 75% |
| 45 out of 50 survey replies | (45 ÷ 50) × 100 | 90% |
| 7 litres used from a 35-litre tank | (7 ÷ 35) × 100 | 20% |
The common slip here is dividing the wrong way round. If your answer tops 100 but the part is smaller than the whole, you've flipped the fraction — part always goes on top.
Question 3: What is the percentage increase or decrease?
When a price, salary or follower count changes, the question becomes: by what percent did it move? The formula has one extra step — find the change first, then divide by the original value:
Percentage change = ((new − old) ÷ old) × 100
| Change | Working | Answer |
|---|---|---|
| Price rises from 80 to 100 | ((100 − 80) ÷ 80) × 100 | +25% |
| Salary rises from 2,000 to 2,200 | ((2,200 − 2,000) ÷ 2,000) × 100 | +10% |
| A jacket falls from 50 to 40 | ((40 − 50) ÷ 50) × 100 | −20% |
| Followers grow from 400 to 500 | ((500 − 400) ÷ 400) × 100 | +25% |
| A rent bill drops from 120 to 96 | ((96 − 120) ÷ 120) × 100 | −20% |
Dividing by the original value is what makes the answer meaningful: a 20 rise matters far more on a price of 80 than on one of 800. For this question type specifically, our percentage change calculator shows the direction and the difference in one step.
Percentage change examples — hover or tap each bar for details.
Step by step: using the free percentage calculator
For anything beyond mental arithmetic, the calculator is the honest answer — it cannot drop a decimal point. Here's the routine:
- Open the percentage calculator and pick the question type that matches your problem.
- Type in your two numbers — for "what is X% of Y", that's the percentage and the amount.
- Read the result, then sanity-check it against a rough estimate (for example, 10% of the amount) so a typing slip can't sneak through.
Shopping maths has its own shortcut: our discount calculator goes straight from was/now prices to the percent saved, and our wider blog covers more everyday money topics in the same plain style.
Mental maths shortcuts: the 10% anchor
Most everyday percentages can be built from 10% — just move the decimal point one place left. For 340, 10% is 34. From that anchor:
- 5% is half of 10% → 17
- 15% is 10% + 5% → 34 + 17 = 51
- 20% is double 10% → 68
- 1% is the decimal point moved two places → 3.4, so 7% is 7 × 3.4 = 23.8
- 50% is simply half the number, and 25% is half again
These anchors handle restaurant tips, quick discounts and rough tax estimates with no phone required.
Common percentage mistakes to avoid
Percentage points are not percent. If an interest rate rises from 3% to 4%, that is a rise of 1 percentage point — but a relative increase of about 33%. News reports mix the two up constantly, and so do adverts.
The second classic trap is adding percentages that happen in sequence. Two successive 10% discounts do not make 20% off: 100 falls to 90 after the first, then to 81 after the second — a total saving of 19%, because the second discount applies to the already-reduced price. The same logic applies to successive rises: two 10% increases compound to 21%, not 20%.
Finally, watch the base: "50% more" and "50% of" are different claims, and a 50% fall needs a 100% rise to undo it — a 200 investment that halves to 100 must double to recover.
Doing the same percentage sums repeatedly? Bookmark the free percentage calculator — no sign-up, and it handles all three question types in this guide.
Frequently Asked Questions
What is the formula to calculate a percentage?
Percentage = (part ÷ whole) × 100. To find X% of a number instead, multiply the number by X ÷ 100 — for example, 30% of 150 is 150 × 0.30 = 45.
How do I calculate a percentage increase?
Subtract the old value from the new value, divide the result by the old value, and multiply by 100. A rise from 80 to 100 is ((100 − 80) ÷ 80) × 100 = 25%.
How do I work out what percent one number is of another?
Divide the first number by the second and multiply by 100. For example, 45 out of 60 is (45 ÷ 60) × 100 = 75%.
What is the difference between percent and percentage points?
"Percent" is a relative measure; a "percentage point" is the plain difference between two percentages. A rate moving from 3% to 4% rises by 1 percentage point, which equals a relative rise of about 33%.
Can a percentage be more than 100%?
Yes. Whenever the part is bigger than the original whole, the percentage exceeds 100 — growing from 200 to 260 means you now hold 130% of the starting amount.
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