Percentage calculator
Find a percentage, compare a part to a whole, or explore percentage changes with a live equation.
How it works & useful details
How it works & limits
Choose a percentage mode and enter two values. Percentage change is (new − starting) ÷ |starting| × 100; it is undefined for a zero starting value. Negative starting values use their absolute magnitude.
Inputs are finite numbers from −1e12 to 1e12. Decimal results use floating-point arithmetic and are rounded to 12 significant digits.
Your working space
Change the values to explore the preview. Use the action below to create a copyable, downloadable result. All calculations stay on this device; refreshing clears your work.
About this tool
Percentage calculator handles three everyday questions in one place: what a percentage of a number is, what part one number is of another, and how much a value changed. The live equation shows the arithmetic rather than only the answer.
Percentage change is calculated as (new minus starting) divided by the magnitude of the starting value, and is undefined when the starting value is zero. Results are rounded to 12 significant digits.
How to use it
- Choose the percentage mode you need.
- Enter the two values for that mode.
- Read the result and the equation that produced it.
- Use the preset buttons to compare common scenarios.
Worked examples for each mode
- Percentage of a number: 20% of 150 = 0.20 × 150 = 30.
- What percentage one number is of another: 45 is 45 ÷ 60 × 100 = 75% of 60.
- Percentage change: from 80 to 100 is (100 − 80) ÷ 80 × 100 = +25%.
- Percentage change in the other direction: from 100 to 80 is −20%, not −25%.
The last two examples show why the direction matters. Percentage change is always measured against the starting value, so a rise followed by an equal fall does not return you to where you started.
Percent vs. percentage points
When a rate moves from 4% to 5%, it has risen by one percentage point, but by 25 percent. Reports that mix these up can make a change look far larger or smaller than it is. Use percentage change on the two rates to get the relative change, and simple subtraction to get the change in points.
To reverse a percentage increase, divide instead of subtracting. A price of 120 after a 20% increase came from 120 ÷ 1.2 = 100. Subtracting 20% of 120 would give 96, which is wrong.
Frequently asked questions
How is percentage change calculated for negative values?
The magnitude of the starting value is used as the denominator, and the direction of the change is preserved by the sign of the result.
Why is my change undefined?
A starting value of zero has no meaningful base for a relative change, so the result is reported as undefined rather than infinite.
What input range is accepted?
Finite numbers from minus one trillion to one trillion.