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Percentage Calculator

Three percentage calculators in one. Each section handles a different type of percentage problem. Results update as you type.

What is X% of Y?

% of

X is what % of Y?

is what % of

Percentage Change from X to Y

to

How to Calculate Percentages

The word percent comes from the Latin per centum, meaning "by the hundred." Every percentage problem is ultimately a question about a ratio scaled to 100. There are three core problem types that cover the vast majority of real-world percentage calculations, and each has a direct formula.

Understanding which type of problem you are solving is the first step. Once you identify whether you need to find a part, a rate, or a change, the arithmetic is straightforward.

What is X% of Y? Formula

This is the most common percentage question. You have a percentage rate and a base number, and you want to find the actual value that the percentage represents.

Formula:

Result = (X / 100) × Y

The logic: X% means X per 100, so dividing X by 100 converts the percentage to a decimal multiplier. Multiplying by Y then scales that multiplier to the base number.

Worked example: What is 15% of 80?

Step 1 — Convert the percentage to a decimal: 15 / 100 = 0.15
Step 2 — Multiply by the base number: 0.15 × 80 = 12

So 15% of 80 is 12. You can verify this mentally: 10% of 80 is 8, and 5% of 80 is 4, so 15% = 8 + 4 = 12. Correct.

This calculation appears constantly in everyday life: sales tax on a purchase, a tip on a restaurant bill, a discount on a sale item, interest on a savings balance, or a commission on a transaction.

X is What Percent of Y? Formula

Here you have both the part and the whole, and you want to express the relationship as a percentage. This is the inverse of the first problem type.

Formula:

Percent = (X / Y) × 100

Dividing X by Y gives a decimal between 0 and 1 (assuming X ≤ Y). Multiplying by 100 rescales that decimal to a "per hundred" figure — a percentage.

Worked example: 30 is what percent of 120?

Step 1 — Divide the part by the whole: 30 / 120 = 0.25
Step 2 — Convert to a percentage: 0.25 × 100 = 25%

So 30 is 25% of 120. A quick check: 25% is one quarter, and one quarter of 120 is 30. Correct.

Use cases include: what grade did you score on a test (35 correct out of 40 questions), what share of a budget one item represents, what fraction of a goal has been reached, or what proportion of a population fits a particular category.

Percentage Change Formula

Percentage change measures how much a value has grown or shrunk relative to its original size. The absolute difference alone is not enough — a change of 10 means something very different if the original value was 20 versus 10,000.

Formula:

Change% = ((New − Old) / |Old|) × 100

The vertical bars around Old indicate absolute value, which handles the case where the original value is negative (common in financial contexts such as losses or temperatures below zero). A positive result means an increase; a negative result means a decrease.

Increase example: from 50 to 75

Step 1 — Find the difference: 75 − 50 = 25
Step 2 — Divide by the original: 25 / 50 = 0.50
Step 3 — Convert to percentage: 0.50 × 100 = +50%

Decrease example: from 100 to 80

Step 1 — Find the difference: 80 − 100 = −20
Step 2 — Divide by the original: −20 / 100 = −0.20
Step 3 — Convert to percentage: −0.20 × 100 = −20%

Percentage change is used everywhere in reporting: year-over-year revenue growth, stock price movement, population change, price inflation, and test score improvement.

One common mistake is confusing percentage change with percentage point change. If an interest rate rises from 2% to 3%, the percentage point change is 1 (3 − 2), but the percentage change is 50% ((3 − 2) / 2 × 100). Both statements are technically correct but describe different things.

Common Percentage Shortcuts

For quick mental arithmetic, certain percentages have simple calculation shortcuts because they correspond to clean fractions.

Percentage Fraction equivalent Quick method Example (of 200)
10% 1/10 Move decimal one place left 20
25% 1/4 Divide by 4 50
50% 1/2 Divide by 2 100
75% 3/4 Divide by 4, multiply by 3 150
100% 1/1 The number itself 200
1% 1/100 Move decimal two places left 2
5% 1/20 Find 10%, then halve it 10
20% 1/5 Divide by 5 (or find 10% × 2) 40

Combining shortcuts speeds up estimation. For example, 15% of a number = 10% + 5% (move decimal left, then add half of that). 30% = 3 × 10%. 35% = 25% + 10%.

Frequently Asked Questions

What is the formula for finding X% of a number?

To find X% of Y, multiply Y by X/100. The formula is: Result = (X ÷ 100) × Y. For example, 20% of 150 = (20 ÷ 100) × 150 = 0.20 × 150 = 30.

How do I calculate what percentage one number is of another?

To find what percent X is of Y, divide X by Y and multiply by 100. Formula: Percent = (X ÷ Y) × 100. For example, 45 is what percent of 180? = (45 ÷ 180) × 100 = 0.25 × 100 = 25%.

How do I calculate percentage increase or decrease?

Percentage change = ((New Value − Old Value) ÷ |Old Value|) × 100. A positive result is an increase; a negative result is a decrease. Example: from 200 to 250 = ((250 − 200) ÷ 200) × 100 = 25% increase.

What is the difference between percentage and percentage points?

A percentage is a ratio expressed per 100. A percentage point is the arithmetic difference between two percentages. If a rate rises from 5% to 8%, that is a 3 percentage point increase, but a 60% relative increase ((8−5)/5 × 100).

How do I reverse a percentage — find the original number before a percent was applied?

If a value after applying X% is known, divide by (1 + X/100) to get the original. For example, if a price after a 20% increase is $120, the original price = 120 ÷ 1.20 = $100.

Can percentage change be more than 100%?

Yes. If a value doubles, the percentage increase is 100%. If it triples, the increase is 200%. There is no upper limit on percentage increase. Percentage decrease, however, cannot exceed 100% (a value cannot fall below zero in most real-world contexts).

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