Percentage Calculator
Three calculators in one: find a percentage of a number, find what percentage one number is of another, and calculate percentage change between two values.
What is X% of Y?
e.g. What is 15% of 80?
X is what % of Y?
e.g. 12 is what percent of 80?
Percentage Change
What is the percentage increase or decrease from X to Y?
The Three Percentage Formulas
1. What is X% of Y?
$$\text{Result} = Y \times \frac{X}{100}$$
Example: What is 15% of 80?
$$80 \times \frac{15}{100} = 80 \times 0.15 = 12$$
15% of 80 is 12.
2. X is what percent of Y?
$$\text{Percentage} = \frac{X}{Y} \times 100$$
Example: 12 is what percent of 80?
$$\frac{12}{80} \times 100 = 0.15 \times 100 = 15%$$
12 is 15% of 80.
3. Percentage change from X to Y
$$\text{Change} = \frac{Y - X}{|X|} \times 100$$
A positive result is a percentage increase; a negative result is a percentage decrease.
Example: From 50 to 75:
$$\frac{75 - 50}{50} \times 100 = \frac{25}{50} \times 100 = 50%$$
That's a 50% increase.
Example: From 80 to 60:
$$\frac{60 - 80}{80} \times 100 = \frac{-20}{80} \times 100 = -25%$$
That's a 25% decrease.
Common Percentage Problems
| Problem | Formula | Example |
|---|---|---|
| Tip on a bill | bill × (tip% / 100) |
20% of $45 = $9 |
| Sale discount | price × (discount% / 100) |
30% off $120 = $36 off |
| Tax on purchase | price × (tax% / 100) |
8% tax on $50 = $4 |
| Grade percentage | (score / max) × 100 |
42/50 = 84% |
| Pay raise | ((new − old) / old) × 100 |
$55k from $50k = 10% raise |
| Population change | ((new − old) / old) × 100 |
1,050 from 1,000 = 5% increase |
Frequently Asked Questions
How do I calculate 20% of a number quickly in my head?
Find 10% by moving the decimal point one place left, then double it. 20% of 85: 10% = 8.5, doubled = 17.
How do I calculate a tip?
Multiply the bill by the tip percentage divided by 100. For an 18% tip on a $60 bill: 60 × 0.18 = $10.80. A quick mental trick: find 10% (move decimal left), halve it to get 5%, then add to reach your target percentage. If you're splitting the bill between multiple people, the Tip Calculator handles the split math automatically.
What's the difference between percentage change and percentage points?
They're often confused. If an interest rate goes from 4% to 6%, that's a 2 percentage point increase, but a 50% percentage change (because 2 is 50% of 4). Percentage points measure an absolute difference between two percentages; percentage change measures the relative increase or decrease.
Can the percentage change be more than 100%?
Yes. If something doubles, that's a 100% increase. If it triples, that's a 200% increase. There's no upper limit on percentage increase, but percentage decrease is capped at 100% (something can only fall to zero).
What does "per cent" mean?
Per cent comes from the Latin per centum, meaning "for each hundred." A percentage expresses a number as a fraction of 100 — 45% means 45 out of every 100.
