Percentage Calculator

What is a Percentage?

A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, ”%”. For example, 45% (read as “forty-five percent”) is equal to 45/100, 45:100, or 0.45.

Percentages are used to express how large/small one quantity is, relative to another quantity.

How to use this calculator

Our free percentage calculator provides three different modes to solve the most common percentage problems:

1. What is X% of Y?

Use this mode to find a specific percentage of a number.

• Example: You want to calculate a 15% tip on a $60 restaurant bill.
• Calculation: 15% of 60 = 9. The tip is $9.
• Formula: $\frac{X}{100} \times Y$

2. X is what percent of Y?

Use this mode to find the ratio of one number to another, expressed as a percentage.

• Example: You scored 45 out of 60 on a test. What is your grade percentage?
• Calculation: 45 is what % of 60 = 75%. Your grade is 75%.
• Formula: $\frac{X}{Y} \times 100$

3. Percentage Increase / Decrease

Use this mode to find the percentage change from one value to another. This is highly useful for calculating discounts, markups, or financial growth.

• Example: A shirt that originally cost $50 is now on sale for $40. What is the discount percentage?
• Calculation: From 50 to 40 = -20%. It’s a 20% decrease (discount).
• Formula: $\frac{Y - X}{|X|} \times 100$

Real-World Examples

Shopping discounts A $120 jacket is marked 30% off. How much do you save? → 30% of 120 = $36 off, final price $84.

Investment returns You bought a stock at $45 and it’s now $63. What’s your return? → From 45 to 63 = +40% gain.

Grade calculation You got 87 out of 120 points on a final exam. → 87 is what % of 120 = 72.5%.

Salary raise Your annual salary increased from $52,000 to $55,640. → From 52,000 to 55,640 = +7% raise.

Loan down payment A car costs $28,000 and the dealer requires 15% down. → 15% of 28,000 = $4,200 down payment required.

Key Tips

Increase vs decrease — direction matters A 50% increase followed by a 50% decrease does NOT get you back to the original. $100 → +50% = $150 → -50% = $75. Be careful with the base value.

Quick mental math To find 10% of any number, just move the decimal point one place left. 10% of 250 = 25. Then 5% = half of that = 12.5, and 15% = 25 + 12.5 = 37.5.

Percentage points vs percentages “Interest rate rose from 3% to 5%” — that’s a 2 percentage point increase, but a 66.7% percentage increase. These are not the same thing.

Percentages in Daily Life

Percentages appear in nearly every aspect of everyday decisions. Here are some of the most common situations where percentage calculations matter.

Tax

Sales tax is expressed as a percentage of the purchase price. If your local sales tax is 8.5%, an item priced at $50 will cost $50 + (8.5% of $50) = $50 + $4.25 = $54.25 at the register. Income tax brackets also use percentages — knowing which bracket you fall into helps you estimate how much of your next dollar of income goes to taxes.

Tips

Tipping at restaurants typically ranges from 15% to 20% of the pre-tax bill. A quick way to calculate a 15% tip: find 10% (move the decimal point left), then add half of that amount. For a $80 bill: 10% = $8, half = $4, so 15% = $12.

Grades

Academic grading systems rely heavily on percentages. A score of 42 out of 50 equals 84%. Understanding how each assignment’s percentage weight contributes to your final grade can help you prioritize study time where it matters most.

Inflation

Inflation is reported as an annual percentage change in the price of goods and services. If inflation is 3% per year, something that costs $100 today would cost approximately $103 next year. Over 10 years at 3% annual inflation, that same item would cost about $134 — a cumulative increase of 34%.

Frequently Asked Questions

What is the difference between “percent” and “percentage”?

“Percent” means “per hundred” and is used with a specific number (e.g., “50 percent”). “Percentage” refers to the general concept or an unspecified portion (e.g., “a large percentage of users”). In everyday use, they are often interchangeable, but technically “percent” follows a number and “percentage” stands alone.

Can percentages be greater than 100%?

Yes. A percentage over 100% simply means the value exceeds the reference amount. For example, if a company’s revenue grew from $1 million to $2.5 million, that is a 150% increase. In Mode 2, entering a partial value larger than the total will naturally return a result above 100%.

Why does the calculator show negative percentages?

In Mode 3 (% Change), a negative result means a decrease. If the new value is smaller than the original, the change is negative. For example, going from 80 to 60 gives -25%, indicating a 25% decrease.

How do I convert a fraction to a percentage?

Divide the numerator by the denominator, then multiply by 100. For example, 3/8 as a percentage: 3 / 8 = 0.375, then 0.375 x 100 = 37.5%. You can use Mode 2 of this calculator by entering 3 as X and 8 as Y to get the same result.

How do I convert a decimal to a percentage?

Multiply the decimal by 100 and add the percent sign. For example, 0.72 becomes 72%, and 1.35 becomes 135%. Conversely, to convert a percentage to a decimal, divide by 100: 45% becomes 0.45.

What is the difference between percentage change and percentage points?

This distinction trips up many people. If an interest rate moves from 5% to 8%, the increase is 3 percentage points. But the percentage change is 60%, because (8 - 5) / 5 x 100 = 60%. News headlines often mix these up, which can be misleading. Percentage points describe the absolute difference between two percentages, while percentage change describes the relative size of that shift.