Three ways to work with percentages
A percentage is just a fraction expressed out of one hundred — the word literally comes from the Latin per centum, “by the hundred”. Almost every everyday percentage question reduces to one of three calculations: finding a slice of a number, turning a ratio into a percentage, or measuring how much something grew or shrank. This calculator handles all three live as you type.
How the math works
Each mode uses a single, short formula:
- Percentage of a number:
result = (P / 100) × X - X is what percent of Y:
result = (X / Y) × 100 - Percentage change:
result = ((B − A) / A) × 100
The first divides the percentage by 100 to get a decimal multiplier. The second reverses that —
it turns a part-to-whole ratio back into a value out of 100. The third compares an ending value
B against a starting value A: a positive answer is an increase, a
negative answer is a decrease. Because dividing by zero is undefined, the last two modes need a
non-zero denominator, and the tool shows a friendly note instead of an error when one is missing.
A worked example
Suppose a jacket priced at $80 goes on sale for $60. To find
the discount as a percentage change, plug the numbers into the third formula:
((60 − 80) / 80) × 100 = (−20 / 80) × 100 = −25%. The negative sign tells you it is a
25% decrease — exactly the discount on the tag. Want the dollar saving directly?
Use the first mode: (25 / 100) × 80 = $20 off.
Quick reference
| Question | Formula | Example |
|---|---|---|
| What is 20% of 150? | (P / 100) × X | 0.20 × 150 = 30 |
| 30 is what % of 120? | (X / Y) × 100 | 0.25 × 100 = 25% |
| Increase 50 → 65 | ((B − A) / A) × 100 | (15 / 50) × 100 = +30% |
| Decrease 200 → 150 | ((B − A) / A) × 100 | (−50 / 200) × 100 = −25% |
Tips & discounts
Work out a 18% tip on a bill, or the real saving on a “40% off” deal, in one tap.
Grades & scores
Turn “42 out of 50” into a percentage to compare results on a common scale.
Growth & trends
Measure how much a price, audience or metric rose or fell between two points in time.