How to Calculate Percentage
To calculate a percentage, divide the part by the whole and multiply by 100. For example, if you scored 30 out of 120, that is 30 ÷ 120 × 100 = 25%. That one formula, turned around in different ways, answers almost every percentage question you will meet, from test scores and discounts to pay rises and tax.
This guide shows each type of percentage question with a worked example, so you can do the sum yourself. If you just want the answer, the percentage calculator does it instantly and shows the same working.
The Percentage Formula
“Per cent” means “per hundred”, so a percentage is a number out of 100. 25% is 25 out of 100, or 0.25.
Percentage = (Part ÷ Whole) × 100
- The whole is the total, or the amount you are comparing against.
- The part is the piece of the total you are interested in.
The same formula can be rearranged to find the part or the whole:
- Part = (Percentage ÷ 100) × Whole
- Whole = Part ÷ (Percentage ÷ 100)
How to Calculate a Percentage in 3 Steps
- Find the part and the whole. In “18 out of 24 people said yes”, the part is 18 and the whole is 24.
- Divide the part by the whole. 18 ÷ 24 = 0.75.
- Multiply by 100. 0.75 × 100 = 75%.
How to Find a Percentage of a Number
To find a percentage of a number, turn the percentage into a decimal by dividing it by 100, then multiply.
Example: what is 15% of 80? 15 ÷ 100 = 0.15, and 0.15 × 80 = 12.
You can do it in either order. 15% of 80 gives the same answer as 80% of 15, which is sometimes easier to work out in your head.
How to Find the Whole When You Know the Percentage
Sometimes you know the part and the percentage it represents, and need the total.
Example: 18 is 30% of what number? 30 ÷ 100 = 0.30, and 18 ÷ 0.30 = 60.
Check it: 30% of 60 is 0.30 × 60 = 18.
How to Calculate Percentage Increase and Decrease
To find how much something has gone up or down in percentage terms:
Percentage change = (New − Original) ÷ Original × 100
Increase example: a price rises from $50 to $65. (65 − 50) ÷ 50 × 100 = 30% increase.
Decrease example: a value falls from 80 to 60. (60 − 80) ÷ 80 × 100 = −25%, a 25% decrease.
Always divide by the original value, not the new one. The percentage change calculator also shows the percentage you would need to get back to where you started, which is never the same as the drop.
How to Calculate the Percentage of Marks
Exam results work the same way: marks scored are the part, and total marks are the whole.
Example: 68 out of 80. 68 ÷ 80 = 0.85, and 0.85 × 100 = 85%.
For several subjects, add up all the marks scored and all the marks available first, then divide. Averaging the separate percentages gives the wrong answer when the papers are out of different totals. The marks percentage calculator does this for you.
How to Reverse a Percentage
If a percentage has already been added or taken off, divide to get back to the original. Do not just add or subtract the percentage again.
Example: a jacket costs $54 after 10% off. What was the original price? After 10% off, you pay 90% of the price, so 54 ÷ 0.90 = $60.
Adding 10% to $54 gives $59.40, which is wrong, because the 10% was taken from $60, not from $54. The reverse percentage calculator handles increases and decreases both ways.
Percentage Change vs Percentage Difference
Use percentage change when one value clearly came first, such as last year’s price and this year’s price.
Use percentage difference when neither value is the starting point, such as comparing two quotes. It divides by the average of the two values:
Percentage difference = |A − B| ÷ ((A + B) ÷ 2) × 100
Example: two quotes of $40 and $60. The gap is 20, the average is 50, and 20 ÷ 50 × 100 = 40%.
The percentage difference calculator gives this figure along with the change in each direction.
How to Calculate Percentages in Your Head
Most percentages can be built from a few easy ones:
| To find | Do this | Example with 240 |
| 10% | Move the decimal point one place left | 24 |
| 5% | Halve the 10% figure | 12 |
| 1% | Move the decimal point two places left | 2.4 |
| 50% | Halve the number | 120 |
| 25% | Halve it, then halve again | 60 |
Then combine them. 35% of 60 is 30% (3 × 6 = 18) plus 5% (3), which is 21.
Converting Percentages, Decimals and Fractions
| Percentage | Decimal | Fraction |
| 1% | 0.01 | 1/100 |
| 10% | 0.1 | 1/10 |
| 12.5% | 0.125 | 1/8 |
| 20% | 0.2 | 1/5 |
| 25% | 0.25 | 1/4 |
| 33.33% | 0.333… | 1/3 |
| 50% | 0.5 | 1/2 |
| 75% | 0.75 | 3/4 |
| 100% | 1 | 1/1 |
- Percentage to decimal: divide by 100. 12.5% = 0.125.
- Decimal to percentage: multiply by 100. 0.6 = 60%.
- Decimal to fraction: write it over 10, 100 or 1,000 and simplify. The decimal to fraction calculator shows each step, including repeating decimals.
How to Calculate a Percentage in Excel or Google Sheets
Spreadsheets use the same formula. If the part is in cell A2 and the whole is in B2:
- Percentage of a total: type =A2/B2, then click the % button to format the cell as a percentage.
- Percentage of a number: to find 15% of the number in B2, type =B2*15%.
- Percentage change: with the old value in A2 and the new value in B2, type =(B2-A2)/A2, then format as a percentage.
If you see 0.25 instead of 25%, the formula is right and only the cell format needs changing.
Common Percentage Mistakes
- Dividing by the wrong number. The whole always goes on the bottom. “What percent of 80 is 20?” is 20 ÷ 80, not 80 ÷ 20.
- Adding percentage changes. A 20% rise followed by a 20% fall does not bring you back to the start: 100 becomes 120, then 96.
- Mixing up percent and percentage points. A rate going from 4% to 5% is a rise of 1 percentage point, but a 25% increase in the rate.
- Stacking discounts. 20% off and then a further 10% off is 28% off in total, not 30%, because the second discount is taken from the lower price.
Frequently Asked Questions
What is the formula for percentage?
Percentage = (Part ÷ Whole) × 100. For example, 45 out of 60 is 45 ÷ 60 × 100 = 75%.
How do I calculate 20% of a number?
Multiply the number by 0.20, or find 10% by moving the decimal point one place left and double it. 20% of 350 is 70.
How do I work out what percentage one number is of another?
Divide the first number by the second and multiply by 100. 12 is 12 ÷ 48 × 100 = 25% of 48.
Can a percentage be more than 100?
Yes. Anything above 100% means the part is larger than the whole you are comparing it to. A value that grows from 50 to 150 is 300% of its original size, which is a 200% increase.
Check Your Answer
Once you know the method, a calculator is the fastest way to check your work. The percentage calculator covers percent of a number, what percent one number is of another and finding the whole, with every step shown. For more percentage tools, browse all percentage calculators, or see more formulas in our list of basic math formulas.