Percentage Calculator: X% of Y, Percent Of and Percentage Change
Calculate any percentage instantly. Free, private, no sign-up.
What is X% of Y?
Answer: —
X is what % of Y?
Answer: —
Percentage change from old to new
Change: —
How to use the percentage calculator
- Pick the question you need: X% of Y, X is what % of Y, or percentage change from an old value to a new one.
- Type the two numbers into that card. Decimals and negative numbers are accepted.
- Read the answer as you type, or press Calculate. Results are rounded to 4 decimal places.
- For percentage change, green means an increase and red means a decrease.
Percentage formulas with worked examples
1. X% of Y
Answer = (X × Y) ÷ 100
Example: a coaching fee of ₹48,000 with 18% GST. GST = (18 × 48,000) ÷ 100 = ₹8,640, so the total is ₹56,640.
2. X is what percent of Y
Percent = (X ÷ Y) × 100
Example: you scored 132 out of 200 in a UPSC Prelims mock test. (132 ÷ 200) × 100 = 66%.
3. Percentage change
% change = ((New − Old) ÷ |Old|) × 100
Example: a petrol price moves from ₹96 to ₹104 a litre. ((104 − 96) ÷ 96) × 100 ≈ 8.33% increase. Going back from ₹104 to ₹96 is a 7.69% decrease, because the base is now ₹104.
Shortcuts for CSAT, SSC and bank exams
Most percentage questions in UPSC CSAT, SSC CGL and banking papers become faster when you swap the percentage for a fraction.
| Percent | Fraction | Increase by it | Decrease by it |
|---|---|---|---|
| 50% | 1/2 | × 3/2 | × 1/2 |
| 33.33% | 1/3 | × 4/3 | × 2/3 |
| 25% | 1/4 | × 5/4 | × 3/4 |
| 20% | 1/5 | × 6/5 | × 4/5 |
| 16.67% | 1/6 | × 7/6 | × 5/6 |
| 14.29% | 1/7 | × 8/7 | × 6/7 |
| 12.5% | 1/8 | × 9/8 | × 7/8 |
Common mistakes
- Dividing by the new value instead of the old value when finding percentage change.
- Adding successive percentages. Two 10% hikes give 21%, not 20%.
- Mixing up percent and percentage points when comparing rates such as inflation or pass percentages.
- Reversing a change with the same percent. After a 25% rise, you need a 20% fall to get back.
Key facts
- A percentage is a ratio expressed out of 100; 1% equals 1/100 or 0.01.
- X% of Y always equals Y% of X, so 8% of 50 is the same as 50% of 8, which is 4.
- Percentage change is undefined when the old value is zero.
Frequently asked questions
How do I calculate X percent of Y?
Multiply Y by X and divide by 100. For example, 20% of 150 = (20 × 150) ÷ 100 = 30, and 18% GST on ₹2,500 = ₹450.
How do I find what percent one number is of another?
Divide the part by the whole and multiply by 100. For example, 45 out of 180 = (45 ÷ 180) × 100 = 25%.
How do I calculate percentage increase or decrease?
Subtract the old value from the new value, divide by the old value, and multiply by 100. A positive answer is an increase and a negative answer is a decrease, so ₹80 to ₹100 is a 25% increase.
What is the difference between percent and percentage points?
Percentage points measure the plain gap between two percentages, while percent change measures that gap relative to the starting value. If a pass rate moves from 10% to 12%, it rose by 2 percentage points, which is a 20% increase.
Why does a 20% rise followed by a 20% fall not return to the original value?
Because the second change is calculated on a bigger base. ₹100 rises to ₹120, and 20% of ₹120 is ₹24, so the price falls to ₹96, a net 4% loss. The net effect of successive changes a% and b% is a + b + (a × b ÷ 100).
Is this percentage calculator free and private?
Yes. It is completely free with no sign-up, and every calculation runs in your browser, so nothing you type is sent to a server.