"Percent" means "per hundred": 25% is 25 out of every 100, which is the fraction 25/100 or the decimal 0.25. Almost every percentage question you meet (discounts, exam marks, tax, growth, interest) is one of the seven formulas below. Each one comes with a worked example you can check with a calculator.
1. What is X% of Y?
Turn the percentage into a decimal by dividing by 100, then multiply.
X% of Y = (X ÷ 100) × Y
Example: 18% of 250 = 0.18 × 250 = 45.
This is the formula behind "how much is the tip", "how much tax will I pay" and "how much will I save with 30% off".
2. X is what percent of Y?
Divide the part by the whole, then multiply by 100.
Percentage = (X ÷ Y) × 100
Example: you scored 42 out of 60 in a test. 42 ÷ 60 = 0.7, and 0.7 × 100 = 70%.
3. Percentage increase or decrease
Subtract the old value from the new one, divide by the old value, and multiply by 100. A positive result is an increase; a negative result is a decrease.
% change = (New − Old) ÷ Old × 100
Example: a price rises from 80 to 92. (92 − 80) ÷ 80 × 100 = +15%.
Now reverse it: the price falls from 92 back to 80. (80 − 92) ÷ 92 × 100 = −13.04%, not −15%. The change is the same 12 units, but it is measured against a bigger starting value. This asymmetry explains why a 50% loss needs a 100% gain to get back to where you started.
4. Reverse percentages: find the original value
When you know the value after a percentage was added or removed, divide by the multiplier instead of subtracting the percentage.
Original = Final ÷ (1 + p/100) after an increase, or Final ÷ (1 − p/100) after a decrease
- Discount: a jacket costs 64 after 20% off. 64 ÷ 0.8 = 80 was the original price.
- Sales tax (GST or VAT): a bill of 1,180 includes 18% GST. 1,180 ÷ 1.18 = 1,000 before tax, so the tax is 180. With 5% VAT, a price of 105 is 100 before tax.
The common mistake is to take 20% of the final price and add it back: 64 + 20% of 64 = 76.80, which is wrong. The 20% was taken from the original price, not from 64.
5. Percentage difference between two values
Use percentage difference when neither value is the "before": for example, comparing two shops' prices or two measurements. It divides by the average of the two values.
% difference = |A − B| ÷ ((A + B) ÷ 2) × 100
Example: one shop charges 40 and another charges 50. The difference is 10, the average is 45, and 10 ÷ 45 × 100 = 22.22%. Because it uses the average, you get the same answer whichever value you put first.
6. Successive percentage changes
Percentages applied one after another multiply; they do not add. Convert each change into a multiplier (a 10% increase is × 1.10, a 10% decrease is × 0.90) and multiply them together.
- +10% then −10%: 1.10 × 0.90 = 0.99, so you end 1% below where you started.
- Two 10% increases in a row: 1.10 × 1.10 = 1.21, a total rise of 21%, not 20%.
- A 20% discount followed by a 20% price rise: 0.80 × 1.20 = 0.96, so the final price is still 4% lower.
7. Percent vs percentage points
When the thing being measured is itself a percentage, such as an interest rate, an exam pass rate or an election result, be careful with the wording. If a loan rate goes from 4% to 5%:
- it rose by 1 percentage point (5 − 4), and
- it rose by 25 percent ((5 − 4) ÷ 4 × 100).
Both statements are true. They describe the change in different ways, and headlines often mix them up. On a loan, even one percentage point makes a big difference to the total you repay, as our EMI guide shows.
Mental maths shortcuts
- 10%: move the decimal point one place left. 10% of 340 is 34.
- 5%: half of 10%. 5% of 340 is 17.
- 15%: 10% plus 5%. 15% of 340 is 34 + 17 = 51.
- 1%: move the decimal point two places. 1% of 340 is 3.4, so 3% is 10.2.
- 25% and 50%: a quarter and a half.
- Swap trick: X% of Y always equals Y% of X. 8% of 50 is awkward, but 50% of 8 is obviously 4.
Percentages in Excel and Google Sheets
- X% of a value in A2:
=A2*18% - What percent A2 is of B2:
=A2/B2, then format the cell as a percentage. - Percentage change from A2 (old) to B2 (new):
=(B2-A2)/A2, formatted as a percentage. - Remove 18% tax from a price in A2:
=A2/1.18
Skip the formulas
Our free Percentage Calculator handles five of these directly: X% of Y, X as a percentage of Y, percentage increase or decrease, "X is Y% of what?" (reverse percentages) and the percentage difference between two values. Type the two numbers and the answer appears instantly.
Frequently asked questions
How do I calculate 20% of a number?
Multiply the number by 0.2. For example, 20% of 150 is 150 × 0.2 = 30.
How do I add 15% to a number?
Multiply by 1.15. For example, 200 plus 15% is 200 × 1.15 = 230.
How do I remove VAT or GST from a price?
Divide by 1 plus the tax rate. For a price that includes 18% GST, divide by 1.18; for 5% VAT, divide by 1.05.
What is the difference between percentage change and percentage difference?
Percentage change compares a new value with an old one and divides by the old value. Percentage difference compares two values of equal standing and divides by their average.