Last updated: April 2026 · Reviewed by Calculatormatics Editorial Team

Percentage Calculator

A free percentage calculator that solves the three most common percentage questions in one place: finding X% of Y, working out what percent X is of Y, and calculating a percentage increase or decrease between two values. Each section accepts your numbers and shows the full step-by-step working — multiplications, divisions, intermediate values, and the final answer — so you can check the math, learn the method, and reuse it confidently in future problems. The calculations follow the standard formulas taught in school: Result = (X ÷ 100) × Y for "X% of Y"; Percent = (X ÷ Y) × 100 for "X is what % of Y"; and Change% = ((New − Old) ÷ |Old|) × 100 for percentage change. Whether you are checking a discount in a shop, calculating a tip, working out a tax bracket, or converting test scores, this tool removes the guesswork. Enter your numbers in any of the three sections below and the answer updates as you type.

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.

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%.

When to Use This Calculator

Use this whenever you need to quickly calculate a percentage in any of its three forms — finding a value, finding a rate, or finding the change. All three types live on the same page so you do not need to remember which formula to use.

Common use cases:

• Calculating sales tax, tip, or discount on a purchase
• Working out what percentage mark you scored on a test (35/40 = what %)
• Calculating the percentage change in a stock price, salary, or metric
• Reversing a percentage to find the original price before a discount was applied

For discount calculations with double discounts and final price, use our Discount Calculator.

Frequently Asked Questions