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Percentage Calculator
Choose the question you want answered, enter two numbers, and get the result with the working shown. Covers percent of, percent change, and increasing or decreasing by a percentage.
The five percentage formulas
Percent means "per hundred", so every percentage problem is a version of one relationship: part = percent ÷ 100 × whole. Rearranged, it gives the five questions this calculator answers.
| Question | Formula |
|---|---|
| X% of Y | X ÷ 100 × Y |
| X is what % of Y | X ÷ Y × 100 |
| Percentage change from X to Y | (Y − X) ÷ |X| × 100 |
| Increase X by Y% | X × (1 + Y ÷ 100) |
| Decrease X by Y% | X × (1 − Y ÷ 100) |
Percentage change: the part people get wrong
Percentage change always uses the starting value as the base. A price that rises from 50 to 65 has changed by 30%. A price that falls from 65 back to 50 has changed by about −23.1%, not −30%, because the base is now 65. This asymmetry is why a 50% loss needs a 100% gain to break even.
The same idea explains stacking: a 20% increase followed by a 20% decrease does not return you to the start. 100 becomes 120, and 20% of 120 is 24, leaving 96.
Everyday uses
- Discounts: use "decrease X by Y%" to get a sale price, and "X is what % of Y" to check the percentage off an advertised price.
- Tax and tips: use "X% of Y" for the amount, or "increase X by Y%" for the total including it.
- Exam marks: score ÷ maximum × 100 gives the percentage.
- Growth: use percentage change for salary, sales or price movements between two periods.
Tips for accurate answers
Check which number is the base before you start: it is the "whole" in the first two formulas and the starting value in percentage change. Percentage points are not the same as percent: a rate rising from 4% to 6% is a rise of 2 percentage points, but a 50% relative increase. Results are shown to up to four decimal places with trailing zeros removed, so round to the precision your task needs.
Worked check: to test your own answer, reverse it. If 15% of 80 is 12, then 12 ÷ 80 should give back 0.15. If a price of 200 reduced by 10% is 180, then 180 ÷ 200 should give 0.9. Reversing takes a few seconds and catches the most common slip, which is using the wrong number as the base.
Worked example
A price rises from 50 to 65. What is the percentage change?
Inputs
| What do you want to find? | Percentage change from X to Y |
|---|---|
| Number X | 50 |
| Number Y | 65 |
Result
Change from 50 to 65 (increase)
| Absolute change | 15 |
|---|---|
| Working | (65 − 50) ÷ |50| × 100 |
Accuracy note: Results use standard double-precision arithmetic, so very large or very small values may be rounded. Check important results by another method.
Frequently asked questions
How do I calculate a percentage of a number?
Divide the percentage by 100 and multiply by the number. For example, 15% of 80 is 0.15 × 80 = 12.
How do I find what percent one number is of another?
Divide the first number by the second and multiply by 100. For example, 12 out of 80 is 12 ÷ 80 × 100 = 15%.
Why is a 50% drop followed by a 50% rise not back to the start?
Each percentage applies to a different base. Starting at 100, a 50% drop gives 50, and a 50% rise on 50 gives only 75.
What is the difference between percent and percentage points?
Percentage points describe the arithmetic gap between two percentages, while percent change describes the relative change. Going from 10% to 15% is 5 percentage points or a 50% increase.
How do I calculate a discount?
Choose "Decrease X by Y%" with X as the original price and Y as the discount percentage. The result is the sale price.