How it works
A percentage is a share of 100. The calculator covers the three questions people ask most often, and each one uses a single formula:
- X% of Y — how much is a given percentage of a value?
- X is what % of Y — what share does one value make up of another?
- % change — by how much did a value grow or shrink?
The change formula divides by the absolute value of the starting point, so a rise always shows as a positive percentage and a drop as a negative one — even when the starting value is negative.
Example
A jacket costs $150 and is 20% off. 20% of 150 is 150 × 20 ÷ 100 = 30, so you save $30 and pay $120.
You answered 30 of 150 questions. 30 ÷ 150 × 100 = 20%.
Your rent went from $1,000 to $1,200. (1,200 − 1,000) ÷ 1,000 × 100 = +20%. If it had dropped to $800, the change would be −20%.
Notes and assumptions
- Calculations use exact decimal arithmetic, so results such as 0.1 + 0.2 never turn into 0.30000000000000004. Very long results are rounded for display only.
- Percentage change is not symmetric: going from 100 to 120 is +20%, but going back from 120 to 100 is about −16.67%.
- A change from 0 has no defined percentage, and neither does a share of a total of 0. The calculator tells you instead of showing a misleading number.
- Percentage points are not the same as percent. An interest rate moving from 4% to 5% rose by 1 percentage point, which is a 25% increase.
Frequently asked questions
How do I add a percentage to a number?
Multiply the number by 1 plus the percentage as a decimal. Adding 8% sales tax to $50 is 50 × 1.08 = $54. You can also calculate 8% of 50 (which is 4) and add it.
How do I find the original price before a discount?
Divide the sale price by 1 minus the discount. A $120 price after 20% off came from 120 ÷ 0.80 = $150.
Why does my percentage change look different from my friend’s?
Check which value you start from. The change is always measured against the old value, so swapping the two numbers gives a different result.
Can a percentage be more than 100%?
Yes. If a value more than doubles, it grew by more than 100%. Going from 50 to 150 is a +200% change.