Solve any common percentage question here — what is X% of Y, what percent X is of Y, and the percentage increase or decrease between two numbers.
A percentage is just a part out of 100, so 25% is the same as 0.25.
For percentage change, always divide the difference by the original (old) number, not the new one.
A positive answer means an increase. A negative answer means a decrease.
X% of Y: Y × X ÷ 100
X as a % of Y: X ÷ Y × 100
% change: (New − Old) ÷ Old × 100
The percentage calculator handles the three percentage questions people meet most often, each in its own box. What is X% of Y? What percent is X of Y? And by what percentage did a value change from an old number to a new one? The answers update as you type, so you can move between marks, prices, salaries and statistics without rearranging formulas each time.
Percentages are everywhere in India: board exam results, GST and discounts, salary hikes, loan interest, election swings and cricket strike rates. Most errors come not from arithmetic but from choosing the wrong base, for example dividing a price change by the new price instead of the old one. Keeping the three question types separate makes the base clear in each case.
1. Decide which question you are asking: a part of a whole, a part as a share of a whole, or a change between two values.
2. X% of Y: multiply Y by X and divide by 100. Result = Y × X ÷ 100.
3. X as a percentage of Y: divide X by Y and multiply by 100. Percentage = X ÷ Y × 100.
4. Percentage change: subtract the old value from the new value, divide by the old value and multiply by 100. Change = (New − Old) ÷ Old × 100.
5. Read the sign of a change: positive means an increase, negative a decrease.
6. Check the answer roughly: 10% is one-tenth, 25% one-quarter, 50% one-half.
A percentage is a fraction with 100 as the denominator. 18% means 18/100, or 0.18. So finding 18% of 2,450 is multiplying 2,450 by 0.18. Going the other way, finding what percent 345 is of 460 means writing 345/460 as an equivalent fraction over 100, which is the same as multiplying the decimal by 100. Every percentage question is one of these two moves: multiply by the fraction, or turn a fraction into a number over 100.
Percentage change always divides by the old value, because the question is 'how big is the change compared with where we started?' That makes changes asymmetric. A rise from 100 to 150 is +50%, but a fall from 150 back to 100 is −33.3%, since the base is now 150. This is why a 50% gain followed by a 50% loss leaves you at 75. When the old value is zero, the change is undefined, and the calculator flags it instead of dividing by zero.
When the values themselves are percentages, two kinds of change are possible. If a bank's FD rate moves from 6.5% to 7%, it rose by 0.5 percentage points, the simple difference. As a percentage change, it rose by 0.5 ÷ 6.5 × 100, about 7.7%. Both statements are correct but they answer different questions. News reports and marketing often pick whichever sounds bigger, so check which one is being quoted.
Ravi uses all three boxes in one evening. He checks 18% GST on a ₹2,450 service bill, works out his daughter's score of 345 out of 460 as a percentage, and compares his salary rising from ₹42,000 to ₹46,200 a month.
GST rate and bill: 18% of ₹2,450
Marks scored and total: 345 out of 460
Old and new monthly salary: ₹42,000 to ₹46,200
18% of 2,450 = 2,450 × 18 ÷ 100 = 44,100 ÷ 100 = 441, so the GST is ₹441.
345 as a percentage of 460 = 345 ÷ 460 × 100 = 0.75 × 100 = 75%.
Salary change: difference = 46,200 − 42,000 = 4,200.
Percentage change = 4,200 ÷ 42,000 × 100 = 10%. The sign is positive, so it is an increase.
Answer: GST is ₹441, the score is 75%, and the salary rose by 10%.
Dividing a change by the new value instead of the old value.
Adding percentage changes over several years instead of compounding them.
Reporting a change in a rate as percent when it is in percentage points, or the reverse.
Averaging percentages from groups of different sizes without weighting them.
Assuming a percentage decrease cancels an equal percentage increase.
Working out GST, tips and discounts on bills.
Converting exam marks into percentages.
Measuring salary hikes, price rises and sales growth.
Reading election results, surveys and business reports.
Why isn't a 50% increase cancelled out by a 50% decrease?
Because each percentage is worked out on a different starting number. 100 increased by 50% becomes 150. But 150 decreased by 50% becomes 75, not 100 — because the decrease is worked out on the bigger number, 150.
What is the difference between percentage points and percent?
If a rate goes from 5% to 7%, that is a rise of 2 percentage points, but it is also a 40% increase. Mixing up these two is a common mistake in news reports.