A percentage is just a way of expressing a number as a fraction of 100 — "50%" literally means "50 out of every 100." Once that clicks, every percentage problem becomes one of three basic calculations.
Type 1: Find What Percentage One Number Is of Another
This answers questions like "42 is what percent of 50?" Divide the part by the total, then multiply by 100.
Percentage = (Part ÷ Total) × 100
Example: you scored 42 out of 50 on a test. (42 ÷ 50) × 100 = 84%.
Another example: you have finished 18 of the 24 tasks on a project. (18 ÷ 24) × 100 = 75% complete. The order matters — the number after "of" is always the total, so it goes on the bottom of the division.
Type 2: Find a Percentage of a Number
This answers "what is 20% of 120?" Turn the percentage into a decimal and multiply.
Result = (Percentage ÷ 100) × Total
Example: a $120 jacket is 20% off. The discount is (20 ÷ 100) × 120 = $24, so the sale price is $96.
Another example: a company sets aside 15% of a $340 monthly budget for software. 0.15 × 340 = $51.
Type 3: Find the Total When You Know a Part and Its Percentage
This is the "reverse" calculation: you know a piece and what share it represents, and you need the whole.
Total = Part ÷ (Percentage ÷ 100)
Example: 15 people is 30% of a class. The full class size is 15 ÷ (30 ÷ 100) = 50 students.
Another example: you paid a $36 deposit, which the shop says is 12% of the total. 36 ÷ 0.12 = $300, so the full price is $300.
Which Formula Do I Need?
Most confusion comes from picking the wrong formula, not from the arithmetic. Match the wording of your question to this table:
| Question you are asking | Formula | Example |
|---|---|---|
| What is X% of Y? | X ÷ 100 × Y | 25% of 80 = 20 |
| X is what % of Y? | X ÷ Y × 100 | 20 is 25% of 80 |
| X is P% of what? | X ÷ (P ÷ 100) | 20 is 25% of what? 20 ÷ 0.25 = 80 |
| By what % did A change to B? | (B − A) ÷ |A| × 100 | 80 → 100 = +25% |
The last row is percentage change, which has its own rules and pitfalls. It is covered in detail in Percentage Increase and Decrease Formula & Examples.
Real-World Examples
- Restaurant tip: 18% tip on a $64 bill →
(18 ÷ 100) × 64 = $11.52. - Sales tax: 8% tax on a $250 purchase →
(8 ÷ 100) × 250 = $20, total $270. - Grade weighting: if homework is 30% of your grade and you scored 90% on it, that contributes
(30 ÷ 100) × 90 = 27points toward your final grade.
Exam Marks Across Several Subjects
A common trap is averaging percentages that come from different totals. Suppose you scored:
| Subject | Marks | Percentage |
|---|---|---|
| Math | 45 / 50 | 90% |
| English | 60 / 80 | 75% |
| Science | 70 / 100 | 70% |
| Total | 175 / 230 | ≈ 76.1% |
Your overall percentage is 175 ÷ 230 × 100 ≈ 76.1%. If you simply averaged the three percentages you would get (90 + 75 + 70) ÷ 3 ≈ 78.3%, which overstates the result because the small 50-mark paper counts as much as the 100-mark paper. Add the raw marks first, then convert — unless your school explicitly weights each subject equally.
Reverse Percentages: Removing Tax or a Markup
Prices that already include tax trip people up. Say a receipt shows £120 including 20% VAT, and you want the price before tax. It is tempting to take 20% of £120 (£24) and subtract it, giving £96 — but that is wrong, because the 20% was added to the pre-tax price, not to £120.
The correct approach: the £120 represents 120% of the original price, so divide by 1.20.
120 ÷ 1.20 = £100. Check: 20% of £100 is £20, and £100 + £20 = £120. ✔
The same idea works for any "after" value. If something is now worth 80% of its original value and that is $640, the original was 640 ÷ 0.80 = $800.
Common Fractions as Percentages
Knowing a few equivalents by heart makes estimates much faster:
| Fraction | Decimal | Percentage |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/3 | 0.333… | ≈ 33.33% |
| 1/4 | 0.25 | 25% |
| 1/5 | 0.2 | 20% |
| 1/8 | 0.125 | 12.5% |
| 3/4 | 0.75 | 75% |
A Faster Way to Think About It
Converting the percentage to a decimal first often makes mental math faster: 20% = 0.20, so "20% of 120" is just 0.20 × 120. Move the decimal two places left on the percentage number, then multiply — no need to divide by 100 as a separate step.
A few more shortcuts worth knowing:
- Start from 10%: move the decimal point one place left. 10% of $64 is $6.40, so 5% is half of that ($3.20) and 15% is
6.40 + 3.20 = $9.60. - Use 1% for odd numbers: 1% of 250 is 2.5, so 7% is
7 × 2.5 = 17.5. - Swap the numbers: X% of Y always equals Y% of X. 8% of 50 is awkward, but 50% of 8 is obviously 4 — and they are the same.
- Sanity-check the size: a percentage under 100% must give a result smaller than the original number. If 30% of 90 comes out bigger than 90, something went wrong.
Common Mistakes to Avoid
- Dividing the wrong way round: "15 is what percent of 60" is
15 ÷ 60(25%), not60 ÷ 15. - Subtracting a percentage of the final value to undo tax or a markup, as in the VAT example above. Divide instead.
- Adding percentages that apply in sequence. A 20% discount followed by another 10% discount is 28% off in total, not 30%, because the second discount applies to a smaller price.
- Confusing percent with percentage points. A rate moving from 4% to 5% is a rise of 1 percentage point, but a 25% increase in the rate itself.
For anything more complex than mental math, our Percentage Calculator handles all three calculation types instantly. Working out a sale price specifically? See How to Calculate a Discount Percentage.
Frequently Asked Questions
Can a percentage be more than 100%?
Yes. A percentage above 100% simply means the part is larger than the reference value. If a plant grew from 10 cm to 25 cm, its new height is 250% of the original. What cannot exceed 100% is a share of a fixed whole — you cannot answer 110% of the questions on a test.
How do I calculate a percentage in Excel or Google Sheets?
For "A is what percent of B", enter =A1/B1 and format the cell as a percentage; the spreadsheet does the ×100 for you. For "X% of Y", use =Y1*X1 where X1 is already formatted as a percentage (for example 15%), or =Y1*15/100.
Is "percent" the same as "percentage"?
They describe the same idea. "Percent" usually follows a number ("15 percent"), while "percentage" is used without one ("a large percentage of users"). The symbol % stands for "percent".
How many decimal places should I round to?
It depends on the context. One or two decimal places is normal for money and grades. Keep full precision during intermediate steps and round only the final answer, otherwise small rounding errors can add up.
Try it yourself: pick a number from your own week — a bill, a test score, a pay slip — and work out one of the three calculations above by hand, then check your answer in the Percentage Calculator. Comparing two values with no clear "before" and "after"? Use the Percentage Difference Calculator instead.