Percentage Calculator

How to Calculate Percentages

A percentage is a way of expressing a number as a fraction of 100. The word comes from the Latin "per centum," meaning "by the hundred." Percentages are used everywhere -- from shopping discounts to statistics, finance, and everyday math.

To calculate a percentage of a number, multiply the number by the percentage and divide by 100. For example, to find 15% of 80: multiply 80 by 15, then divide by 100. The result is 12.

To find what percentage one number is of another, divide the first number (the part) by the second number (the whole) and multiply by 100. For example, 45 is what percent of 180? Divide 45 by 180 to get 0.25, then multiply by 100 to get 25%.

Percentage Formulas

Finding X% of Y

Result = Y x X / 100

Example: 20% of 150 = 150 x 20 / 100 = 30

Finding what % X is of Y

Percentage = (X / Y) x 100

Example: 36 is what % of 144? (36 / 144) x 100 = 25%

Percentage change from X to Y

Change = ((Y - X) / |X|) x 100

Example: From 80 to 100: ((100 - 80) / 80) x 100 = 25% increase

Percentage Change vs Percentage Difference

These two concepts are often confused, but they serve different purposes:

• Percentage change measures how much a value has increased or decreased relative to an original value. It has a direction -- the result is either an increase or a decrease. Use this when you have a "before" and "after" value.
• Percentage difference compares two values relative to their average, without implying that one came before the other. The formula is: |A - B| / ((A + B) / 2) x 100. Use this when comparing two independent values, such as prices from two stores.

For example, comparing a price of $80 and $100: the percentage change from 80 to 100 is 25% (increase), but the percentage difference between them is about 22.2%.

Frequently Asked Questions

How do I calculate a discount percentage?

To find the discounted price, use the "What is X% of Y?" calculator. Enter the discount percentage and the original price. Subtract the result from the original price to get the sale price. For example, a 30% discount on a $60 item: 30% of 60 = 18, so the sale price is $42.

Can percentage change be negative?

Yes. A negative percentage change means the value decreased. For example, going from 200 to 150 is a -25% change, which means a 25% decrease.

What if the original value is zero?

Percentage change from zero is undefined because you would be dividing by zero. In practice, if you start from zero, you would describe the change in absolute terms rather than as a percentage.