Percentage Calculator
Five everyday percentage operations
Understand the result
About the Percentage Calculator
How do you calculate a percentage?
A percentage expresses a number as a share of 100. The everyday calculations are finding X% of a number, finding what percentage one number is of another, and working out a percentage increase or decrease between two values — for marks, discounts, price changes, salary hikes and returns.
This percentage calculator handles all five: X% of Y, X is what percent of Y, percentage change, and adding or subtracting a percentage, and shows the working.
How this calculator works
All five operations come from one idea: a percentage is a fraction out of a hundred. “X% of Y” multiplies, “X is what percent of Y” divides, and increase and decrease apply the percentage to the original number before adding or subtracting.
Percentage change is the one that trips people up, because it is always measured against the starting value. Going from 50 to 75 is a 50% increase, but going back from 75 to 50 is a 33.3% decrease — the same absolute change measured against a different base.
Formula
X% of Y = X ÷ 100 × Y X is what % of Y = X ÷ Y × 100 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)
Worked example
- 15% of 2,500 = 0.15 × 2,500 = 375.
- 375 is what percent of 2,500? 375 ÷ 2,500 × 100 = 15%.
- Change from 2,500 to 2,875 = 375 ÷ 2,500 × 100 = a 15% increase.
Recovering from a fall needs a bigger rise
| If a value falls by | It must then rise by | To get back to the start |
|---|---|---|
| 10% | 11.1% | Yes |
| 20% | 25% | Yes |
| 30% | 42.9% | Yes |
| 50% | 100% | Yes |
| 75% | 300% | Yes |
Because each percentage is measured from a different starting value, falls and rises are not symmetrical. This matters for investments: avoiding large losses is worth more than chasing large gains.
Assumptions & important notes
Important notes
- A percentage increase followed by the same percentage decrease does not return you to the start: +10% then −10% leaves you 1% down.
- Percentage points and percent are different. Moving from 5% to 7% is a rise of 2 percentage points, but a 40% increase.
Frequently asked questions
Why do a 50% rise and a 33% fall cancel out?
Because each is measured against a different base. Rising from 50 to 75 is 25 on a base of 50 (50%); falling from 75 to 50 is 25 on a base of 75 (33.3%).
How do I calculate a percentage in reverse?
Use “X is what percent of Y”. To find the original before a known increase, divide by (1 + rate ÷ 100) rather than subtracting the percentage.
How do I calculate percentage of marks?
Divide marks obtained by total marks and multiply by 100. 432 out of 500 is 86.4%.
What is the difference between percent and percentage points?
If an interest rate rises from 8% to 10%, it rises by 2 percentage points, which is a 25% increase in the rate itself.
PaiseWise runs entirely in your browser — the figures you enter are never sent anywhere. Results are estimates for planning only, not financial, tax or investment advice.