📊 Percentage Calculator

Need to figure out a percentage? Our free percentage calculator handles all three common scenarios: find X% of a number, determine what percentage one number is of another, or calculate the percentage change between two values. Just pick the operation, enter your numbers, and get an instant answer with a step-by-step breakdown.

Percentages come up everywhere—discounts, tips, tax rates, grade scores, investment returns, and more. Bookmark this page so you always have a reliable calculator one click away.

What Is a Percentage?

A percentage is a way of expressing a number as a fraction of 100. The word itself comes from the Latin per centum, meaning “by the hundred.” When you see 45%, it simply means 45 out of every 100, or 0.45 as a decimal, or 45/100 as a fraction.

Percentages make it easy to compare quantities of different sizes on a common scale. Whether you are looking at a 7% sales tax rate or a 20% off coupon, the concept is the same: a proportional relationship expressed relative to 100.

How to Calculate Percentages

There are three fundamental percentage calculations. Mastering these covers the vast majority of real-world situations.

1. Find X% of a Number

Formula: Result = Number × Percentage ÷ 100

This is the most common operation. You use it to calculate tips, discounts, tax amounts, and commissions.

2. What Percentage Is A of B?

Formula: Percentage = (A ÷ B) × 100

Use this when you know two numbers and need to express their ratio as a percentage—for example, finding out what share of your budget goes to rent, or what fraction of students passed an exam.

3. Percentage Change From A to B

Formula: Change = ((B − A) ÷ A) × 100

This tells you how much a value has increased or decreased relative to its starting point. A positive result means an increase; a negative result means a decrease. It is widely used in finance, economics, and everyday price comparisons.

Practical Examples

Example 1 — Restaurant tip: Your bill is $85.00 and you want to leave a 20% tip. Tip = $85.00 × 20 ÷ 100 = $17.00. Total with tip = $102.00.

Example 2 — Sale discount: A jacket is priced at $120.00 with a 35% discount. Discount = $120.00 × 35 ÷ 100 = $42.00. You pay $78.00.

Example 3 — Grade score: You answered 42 out of 50 questions correctly. Percentage = (42 ÷ 50) × 100 = 84%.

Example 4 — Price increase: Gas was $3.20 per gallon last month and is $3.52 now. Change = (($3.52 − $3.20) ÷ $3.20) × 100 = +10%.

Percentage vs. Percentage Points

This distinction trips people up regularly. If an interest rate moves from 5% to 7%, it increased by 2 percentage points but by 40% in relative terms ((7 − 5) ÷ 5 × 100). News headlines often mix the two, so understanding the difference helps you interpret data correctly.

Tips and Common Uses

Quick mental math for tips: To find 10%, just move the decimal point one place to the left. Double that for 20%. For 15%, add half of the 10% figure.

Markup vs. margin: In business, markup is the percentage added to cost to get the selling price, while margin is the percentage of the selling price that is profit. A 50% markup on a $10 item means you sell it for $15, but the profit margin is only 33.3% ($5 ÷ $15).

Compound percentages: Successive percentage changes do not simply add up. A 10% increase followed by a 10% decrease does not return you to the starting value—it leaves you 1% lower (110 × 0.9 = 99).

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Frequently Asked Questions

How do you calculate a percentage of a number?
Multiply the number by the percentage and divide by 100. For example, 15% of 200 is 200 × 15 / 100 = 30. You can also convert the percentage to a decimal first: 200 × 0.15 = 30.
How do you calculate percentage change?
Use the formula ((New Value − Old Value) / Old Value) × 100. A positive result means an increase, a negative result means a decrease. For example, going from 80 to 100 is a +25% change.
What is the difference between percentage and percentage points?
Percentage points measure the absolute difference between two percentages (e.g., 5% to 8% is 3 percentage points). Percentage measures the relative change (that same move is a 60% increase). Confusing the two is a common mistake.
How do you calculate a tip quickly?
For a 20% tip, find 10% by moving the decimal one place left, then double it. On a $65 bill: 10% = $6.50, so 20% = $13.00. For 15%, add half of the 10% amount: $6.50 + $3.25 = $9.75.
How do you reverse a percentage (find the original number)?
If you know that a number after a percentage increase is Y, the original is Y / (1 + rate/100). For example, if a price after a 25% markup is $50, the original was $50 / 1.25 = $40.
Why doesn't a 10% increase followed by a 10% decrease return to the original?
Because the decrease applies to the already-increased value. Start at 100, +10% = 110, then −10% of 110 = 11, so you end at 99. The net effect is a 1% loss. This is why compound percentage changes don't simply add up.