Percentage Calculator
Solve any percentage problem: percent of a number, percentage change, and what percent one number is of another.
Percentage Calculator — input your values
What does this math calculator do?
The percentage calculator solves the three most common percentage problems in one place: finding a percentage of a number (e.g. 25% of 200), finding what percent one number is of another (e.g. 40 is what percent of 160?), and percentage increase or decrease (e.g. from 80 to 100).
Percentages mean 'per hundred' — a fraction with a denominator of 100. Every result includes the step-by-step arithmetic so you can see exactly how the answer is derived and learn to do it by hand.
Formula and variables
| Symbol | Meaning |
|---|---|
| X | The percentage to find |
| Y | The base number |
| % change | (new − old) ÷ old × 100 |
Worked example
A jacket that cost $80 is on sale with a 25% discount. What is the sale price?
- Discount = 25% of $80 = 0.25 × 80 = $20.
- Sale price = $80 − $20 = $60.
Answer: The jacket costs $60 after the discount.
Tips and common mistakes
Tips
- To compute 10% of a number, just move the decimal point one place left — great for mental math with tips.
- Percentage change is always relative to the starting value, so a 50% increase followed by a 50% decrease does not return to the original number.
- When adding percentages that come from the same base (e.g. taxes), add the rates first, then apply once.
- Beware of double-discount tricks: '50% + 20% off' is not 70% off — the second discount applies to the reduced price.
Common mistakes to avoid
- Dividing by the new value instead of the original when calculating percentage change.
- Confusing percentage points with percentages — a rate rising from 4% to 6% is a 50% increase, not 2%.
- Using 0 as the base in 'what percent of Y' problems, which makes the result undefined.
Percentage Calculator — frequently asked questions
How do I calculate a percentage of a number?
Divide the percentage by 100 to get a decimal, then multiply by the number. For example, 15% of 200 = 0.15 × 200 = 30.
What is the formula for percentage increase?
Percentage increase = (new value − old value) ÷ old value × 100. A rise from 80 to 100 is (100 − 80) ÷ 80 × 100 = 25%.
How do I convert a fraction to a percentage?
Divide the numerator by the denominator and multiply by 100. The fraction 3/4 becomes 0.75 × 100 = 75%.
What does 'percentage points' mean?
A percentage point is the arithmetic difference between two percentages. Moving from 4% to 6% is an increase of 2 percentage points — but a 50% relative increase.
How is percentage used in discounts?
A discount of D% reduces the price by D% of the original price: sale price = original × (1 − D/100). A 25% discount on $80 gives $60.
How do I find what percent A is of B?
Divide A by B and multiply by 100. For example, 40 ÷ 160 × 100 = 25%, so 40 is 25% of 160.
Why do banks and stores use percentages differently?
Financial institutions often use annual percentage rates and compounding, while stores use simple discounts. Always check whether a rate compounds or is simple before comparing.