How to Calculate a Percentage: Formulas, Examples and Excel
Quick answer: percentage = (part ÷ whole) × 100. To find a percentage of a number, multiply: X% of Y = X ÷ 100 × Y. For change over time: (new − old) ÷ old × 100.
"Per cent" means "per hundred", so a percentage is just a fraction out of 100. Almost every percentage question is one of six types. Here's the formula for each, a worked example, and how to do it in Excel or Google Sheets.
1. What is X% of a number?
Formula: X ÷ 100 × number.
Example: what is 20% of 150? → 20 ÷ 100 × 150 = 30.
Mental shortcut: 10% is the number with the decimal point moved one place left (10% of 150 = 15). Double it for 20%, halve it for 5%. So 15% of 64 = 6.4 + 3.2 = 9.6.
2. X is what percent of Y?
Formula: X ÷ Y × 100.
Example: 30 is what percent of 120? → 30 ÷ 120 × 100 = 25%.
The same formula works out your marks: 445 marks out of 550 is 445 ÷ 550 × 100 = 80.91%.
Calculate percentages easily: X% of Y, what percent X is of Y, percentage increase or decrease and marks percentage.
3. Percentage increase or decrease
Formula: (new value − old value) ÷ old value × 100. A positive result is an increase; a negative result is a decrease.
- Increase: from 80 to 100 → (100 − 80) ÷ 80 × 100 = 25% increase.
- Decrease: from 100 to 80 → (80 − 100) ÷ 100 × 100 = 20% decrease.
Notice the two answers differ: going up 25% and then down 20% gets you back where you started, because each change is measured from a different starting value.
4. Adding a percentage (tax, tips, raises)
Formula: number × (1 + X ÷ 100).
Example: add 15% to 200 → 200 × 1.15 = 230. A 5% pay rise on 3,000 → 3,000 × 1.05 = 3,150.
5. Subtracting a percentage (discounts)
Formula: number × (1 − X ÷ 100).
Example: 25% off 80 → 80 × 0.75 = 60. Two discounts multiply rather than add: 20% off and then a further 10% off is 0.8 × 0.9 = 0.72, so 28% off in total — not 30%. The discount calculator handles extra discounts and sales tax for you.
6. Reverse percentage (finding the original number)
Formula: final value ÷ (1 + X ÷ 100) for an increase, or ÷ (1 − X ÷ 100) for a decrease.
- A price of 120 includes 20% tax. Original price = 120 ÷ 1.20 = 100.
- After a 25% discount you paid 60. Original price = 60 ÷ 0.75 = 80.
A very common mistake is to take the percentage of the final price (20% of 120 = 24, giving 96). That's wrong, because the 20% was calculated on the original price, not the final one.
Percentage error
Used in science classes: |measured − actual| ÷ actual × 100. If you measure gravity as 9.6 m/s² and the accepted value is 9.81 m/s², the error is |9.6 − 9.81| ÷ 9.81 × 100 ≈ 2.14%.
Percentages in Excel and Google Sheets
| Task | Formula (A1 and B1 are cells) |
|---|---|
| A1 percent of B1 | =A1/100*B1 (or =A1*B1 if A1 is formatted as %) |
| A1 as a percent of B1 | =A1/B1, then format the cell as Percentage |
| Percentage change from A1 to B1 | =(B1-A1)/A1, formatted as Percentage |
| Add 15% to A1 | =A1*1.15 |
| Remove 20% tax from A1 | =A1/1.2 |
Tip: when a cell is formatted as Percentage, Excel stores 25% as 0.25 — so don't multiply by 100 as well, or you'll see 2500%.
Percent vs percentage points
If an interest rate rises from 4% to 5%, it went up by 1 percentage point — but that's a 25% increase in the rate (1 ÷ 4 × 100). News reports mix these up often, so check which one is meant.
Everyday percentage questions
- Tips: 18% of a 45 bill = 0.18 × 45 = 8.10.
- Grades: 42 out of 50 = 84%. For weighted coursework, use the grade calculator.
- Savings: saving 600 of a 3,000 monthly income = 20%.
- Battery or progress: 3.2 GB downloaded of 8 GB = 40% done.
- Averages: to find the mean of several percentages or scores, add them and divide by how many there are — or paste them into the average calculator.
- Prices abroad: work out the discount first, then convert the final price with the currency converter calculator.
Frequently asked questions
What is the formula for percentage?
Percentage = (part ÷ whole) × 100. For example, 30 out of 120 is 30 ÷ 120 × 100 = 25%.
How do I calculate a percentage increase?
Subtract the old value from the new value, divide by the old value and multiply by 100. From 80 to 100 is (100 − 80) ÷ 80 × 100 = 25% increase.
How do I work out 15% of a number quickly?
Find 10% by moving the decimal point one place left, then add half of that. 15% of 64 is 6.4 + 3.2 = 9.6.
How do I remove a percentage to get the original price?
Divide by (1 + the percentage as a decimal). If a price including 20% tax is 120, the price before tax is 120 ÷ 1.20 = 100. Don't subtract 20% of 120 — that gives the wrong answer.
What is the difference between percent and percentage points?
Percentage points measure the simple difference between two percentages. Going from 10% to 15% is a rise of 5 percentage points, but a 50% increase.
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