Scope
Assumptions and limits
This universal maths tool does not apply country-specific rules. Results depend only on your inputs and the formula displayed.
Results use the values you enter and the conventions described in the methodology below. After calculating, review the result-specific assumptions and warnings shown with the estimate.
Explore everyday utility tools for related tasks in this collection.
01
How to calculate a percentage
To find X percent of Y, divide X by 100 and multiply by Y. To find what percentage one number is of another, divide the part by the whole and multiply by 100.
For example, 45 is 75% of 60 because 45 ÷ 60 × 100 = 75.
02
Percentage change versus percentage difference
Percentage change has a starting value: (new − old) ÷ |old| × 100. It is undefined when the starting value is zero.
Percentage difference is symmetric: |A − B| divided by the average of |A| and |B|, then multiplied by 100. Use it when neither value is the starting point.
03
Reverse percentages and discounts
To reverse an increase, divide the final value by 1 plus the percentage rate. To recover a price before a discount, divide by 1 minus the discount rate.
A value of 120 after a 20% increase started at 100. A price of 75 after a 25% discount also started at 100.
04
Common percentage mistakes
Do not confuse percentage points with percentage change, and do not divide by zero. Keep full precision until the final display step to reduce rounding error.
FAQ
Frequently asked questions
How do I calculate X percent of a number?
How do I find what percentage one number is of another?
What is percentage difference?
How do I reverse a percentage increase?
What happens when the starting value is zero?
Can a percentage be more than 100%?
Sources
Method references and scope
Method: results come from tested code using the documented method and assumptions shown on this page.
Review owner: Great Future Product Engineering.
Method and content last reviewed: . Next review due: .