What does percentage actually mean?
A percentage is a fraction out of 100, so 25% means 25 out of every 100, or one quarter. Almost every percentage question reduces to one of three forms, and this page has a separate panel for each.
The first is finding a part of a number: X% of Y equals (X / 100) x Y. The second is finding what share one number is of another: X is (X / Y) x 100 percent of Y. The third is finding how much something changed: (new - old) / old x 100.
The percentage change panel shows a plus sign for increases and displays the figure in green, or in red for decreases.
Everyday situations that need these three calculations
Shopping is the obvious one: working out 15% off a price, or 20% of a bill as a tip. The same arithmetic covers a commission rate, a deposit, or the share of a budget that goes to rent.
"X is what percent of Y" is the one to reach for with test scores, completion rates, or survey results, such as 42 correct answers out of 60.
Percentage change is what you want when comparing a number across two points in time: this month's website visits against last month's, a salary before and after a raise, or a price that moved from one value to another. For discounts specifically, the discount calculator gives the sale price directly, and the GST calculator handles adding or removing tax.
How to use the three panels
- For "What is X% of Y?", type the percentage in the first box and the total in the second. The answer appears below, rounded to two decimals.
- For "X is what percent of Y?", enter the part first and the whole second. The result is shown with a percent sign.
- For percentage change, enter the starting value under From and the ending value under To.
Worked examples using the numbers on the page's default panels: 20% of 150 is 0.20 x 150 = 30.00. 30 out of 120 is 30 / 120 x 100 = 25.00%. A move from 50 to 75 is (75 - 50) / 50 x 100 = +50.00%.
A drop works the same way: from 80 to 60 gives (60 - 80) / 80 x 100 = -25.00%.
Tips and edge cases
Percentage change is always measured against the starting value, so it is not symmetric. A rise from 50 to 75 is +50%, but the fall from 75 back to 50 is only about -33.33%. Mixing up which number goes in From is the most common mistake.
If you enter 0 as the second number in "X is what percent of Y", or 0 in From, the tool shows a dash instead of a number, because dividing by zero has no meaningful percentage.
Results are rounded to two decimal places for display, so very small differences may disappear. For loan interest rather than simple percentages, try the loan calculator.