Percentage formulas
| Question | Formula | Example |
|---|---|---|
| What is X% of Y? | X ÷ 100 × Y | 20% of 150 = 30 |
| X is what % of Y? | X ÷ Y × 100 | 30 is 20% of 150 |
| X is Y% of what? | X ÷ (Y ÷ 100) | 30 is 20% of 150 |
Everyday uses
Discounts: a $80 jacket at 25% off saves 0.25 × 80 = $20, so you pay $60.
Tips: an 18% tip on a $65 bill is 0.18 × 65 = $11.70.
Test scores: 42 correct out of 50 is 42 ÷ 50 × 100 = 84%.
Sales tax backwards: if $7.20 of tax is 8% of the price, the price was 7.20 ÷ 0.08 = $90.
Tips: an 18% tip on a $65 bill is 0.18 × 65 = $11.70.
Test scores: 42 correct out of 50 is 42 ÷ 50 × 100 = 84%.
Sales tax backwards: if $7.20 of tax is 8% of the price, the price was 7.20 ÷ 0.08 = $90.
Mental math shortcuts
- 10%: move the decimal point one place left (10% of 340 = 34).
- 5%: half of 10% (5% of 340 = 17).
- 1%: move the decimal two places (1% of 340 = 3.4).
- Swap the numbers when it’s easier: 16% of 25 = 25% of 16 = 4.
How to use the calculator
- Pick the type of question: “What is X% of Y?”, “X is what percent of Y?”, or “X is Y% of what?”.
- Enter the two numbers you know.
- Read the answer and the formula used. For increases and decreases between two values, use the percentage change calculator.
The three percentage questions
- Part = Percent × Whole: 15% of 240 = 0.15 × 240 = 36.
- Percent = Part ÷ Whole × 100: 36 is what percent of 240? 36 ÷ 240 × 100 = 15%.
- Whole = Part ÷ Percent: 36 is 15% of what? 36 ÷ 0.15 = 240.
Almost every percentage problem is one of these three, rearranged.
Adding or removing a percentage
To add a percentage, multiply by (1 + rate): $80 plus 8% sales tax = 80 × 1.08 = $86.40. To remove a percentage that was already added, divide — don’t subtract. If $86.40 includes 8% tax, the pre-tax price is 86.40 ÷ 1.08 = $80, not 86.40 − 8% = $79.49. The same applies to VAT-inclusive prices and to “before discount” prices.
Stacked discounts
A 20% discount followed by an extra 10% off is not 30% off. The price becomes 0.80 × 0.90 = 0.72 of the original, a 28% discount. On a $100 item that is $72, not $70.
Tips and splitting a bill
- 10%: move the decimal point one place left — 10% of $64.50 is $6.45.
- 15%: 10% plus half of that — $6.45 + $3.23 = $9.68.
- 20%: double the 10% figure — $12.90.
- Percent of a percent: 50% of 30% is 15% (0.5 × 0.3).
- Swap trick: x% of y equals y% of x — 8% of 50 is the same as 50% of 8, which is 4.
Frequently asked questions
How do I calculate a percentage of a number?
Convert the percentage to a decimal by dividing by 100, then multiply. 20% of 150 = 0.20 × 150 = 30.
How do I find what percent one number is of another?
Divide the part by the whole and multiply by 100. 30 out of 150 = 30 ÷ 150 × 100 = 20%.
How do I find the whole when I know the part and the percentage?
Divide the part by the percentage as a decimal. If 30 is 20% of a number, the number is 30 ÷ 0.20 = 150.
Is X% of Y the same as Y% of X?
Yes — multiplication works in either order. 8% of 50 equals 50% of 8, which is 4. This trick makes some mental math much easier.
How do I calculate a percentage increase?
Use the percentage change calculator: (new − old) ÷ old × 100.
How do I calculate a percentage of a total in Excel?
Use =part/total and format the cell as a percentage. For X% of Y, use =Y*X% or =Y*X/100.
How do I find the original price before a discount?
Divide the sale price by (1 − discount). A $60 item that was 25% off originally cost 60 ÷ 0.75 = $80.