Percentage Calculator

How it works

A percent is a fraction of 100, so 15% is 15 out of every 100, or 0.15 as a decimal. Every percentage question is one of three rearrangements of the same relationship: part = percent × whole.

"What is X% of Y" multiplies: convert X to a decimal and multiply by Y. This is the discount, tip or tax question.

"X is what percent of Y" divides: X over Y, then times 100. This is the share-of-the-total or test-score question.

"Percent change from X to Y" measures the move from X to Y relative to where you started: the difference divided by X, times 100. A positive answer is an increase, a negative one a decrease.

Formula

X% of Y            = X ÷ 100 × Y
X is what % of Y   = X ÷ Y × 100
% change X → Y     = (Y − X) ÷ |X| × 100

Example

15% of 200 is 15 ÷ 100 × 200 = 30. A 15% tip on a $200 bill is $30.

30 is what percent of 200? 30 ÷ 200 × 100 = 15, so 30 is 15% of 200.

The percent change from 200 to 230 is (230 − 200) ÷ 200 × 100 = 15, a 15% increase. Going the other way, from 200 to 150, is (150 − 200) ÷ 200 × 100 = −25, a 25% decrease.

Assumptions and limitations

• Percentages are entered and shown as ordinary numbers: type 15 for 15%, not 0.15.
• Percent change is measured relative to the starting value X. Going from 200 to 230 is +15%, but going from 230 back to 200 is −13.04%, because the base is different.
• When X is negative, percent change divides by its absolute value so that a positive result always means Y is larger than X.
• Results are rounded to two decimal places for display only.

Frequently asked questions