How to Calculate Percentage: Formulas, Examples and Shortcuts

Almost every percentage question is one of three: what is X% of Y (multiply Y by X and divide by 100), X is what per cent of Y (divide X by Y and multiply by 100), or what is the percentage change from an old value to a new one (divide the difference by the old value and multiply by 100). So 18% of ₹2,500 is ₹450, 432 marks out of 600 is 72%, and a salary rising from ₹40,000 to ₹52,000 is a 30% hike.

The free percentage calculator answers all three at once: enter two numbers, X and Y, and it shows X% of Y, X as a percentage of Y, and the percentage change from X to Y. Below is how to pick the right row, plus reverse percentages, chained percentages and shortcuts you can do in your head.

The formulas in one table

How to read the percentage calculator

Because the tool shows three answers for the same two numbers, the only skill is choosing the line that matches your question. Enter X = 18 and Y = 2500 and you get:

• 18% of 2500 = 450 (the large figure at the top);
• 18 is what % of 2500 = 0.72%;
• % change 18 → 2500 = 13,788.89%.

All three are correct answers, but only the first answers "what is 18% GST on ₹2,500". If you divide by zero (Y = 0 in the second row, or X = 0 in the third), the tool says "Not defined (division by 0)" instead of showing a misleading number.

Type 1: What is X% of Y?

"Per cent" means "per hundred", so X% is X ÷ 100. Multiply that by Y.

• 18% of 2,500 = 2,500 × 18 ÷ 100 = 450. This is the GST on a ₹2,500 bill at 18%.
• 12.5% of 880 = 880 × 12.5 ÷ 100 = 110.
• 33% of 720 = 720 × 33 ÷ 100 = 237.6.

Discounts, tips, commission and simple interest are all this type. For a bill split, the tip guide shows the same idea done in your head.

Type 2: X is what percentage of Y?

Divide the part by the whole, then multiply by 100. The number after "out of" always goes at the bottom.

• 432 out of 600: 432 ÷ 600 = 0.72, so 72%.
• 52 out of 65: 52 ÷ 65 = 0.8, so 80%.

For marks across several subjects, add the marks first and then divide. Scoring 45 out of 50 in one paper (90%) and 60 out of 100 in another (60%) gives 105 out of 150, which is 70%, not the 75% you get by averaging 90 and 60. Averaging percentages only works when every paper has the same maximum marks.

The exam marks percentage calculator does this for one total (432 out of 600 shows 72%) and adds a letter grade from its own fixed bands, which may not match your board's grading. The percentage of marks guide shows how to add up marks across subjects.

Type 3: Percentage increase and decrease

Subtract the old value from the new, divide by the old value, and multiply by 100. A positive answer is an increase; a negative one is a decrease.

• Salary ₹40,000 → ₹52,000: (52,000 − 40,000) ÷ 40,000 × 100 = 30% increase.
• Price ₹200 → ₹150: (150 − 200) ÷ 200 × 100 = 25% decrease.

The base is always the starting value, which is why rises and falls are not symmetrical. A share that falls from ₹100 to ₹50 has lost 50%, but it must rise 100% to get back to ₹100.

Watch the difference between per cent and percentage points. If a loan rate goes from 8% to 9%, it has risen by 1 percentage point, but by 12.5% in relative terms (1 ÷ 8 × 100). News reports mix these up often. The percentage change calculator labels the result as an increase or decrease and shows the difference; 8 → 9 gives "Increase 12.5%, difference 1".

Reverse percentages: finding the original number

When you know the value after a percentage was added or taken off, divide; don't add or subtract the percentage back.

• After a discount: a jacket costs ₹2,550 after 15% off. Original = 2,550 ÷ (1 − 0.15) = 2,550 ÷ 0.85 = ₹3,000. Adding 15% to ₹2,550 gives ₹2,932.50, which is wrong, because the 15% was taken off the larger original price.
• After tax: a bill of ₹1,180 includes 18% GST. Base = 1,180 ÷ 1.18 = ₹1,000. The GST guide explains this in detail.
• After a hike: a salary of ₹52,000 after a 30% hike was 52,000 ÷ 1.30 = ₹40,000 before it.

A shortcut with the percentage calculator: put the final amount in X and the remaining percentage in Y (85 for a 15% discount, 118 for 18% GST). The second row, "X is what % of Y", then shows the original amount with a % sign after it. X = 2550, Y = 85 shows 3000%, meaning ₹3,000; X = 1180, Y = 118 shows 1000%, meaning ₹1,000. It works because X ÷ Y × 100 is the same calculation as final ÷ 0.85.

Successive percentages don't simply add

When one percentage is applied after another, the second one works on the new value, not the original.

• A 10% rise followed by a 10% fall: 100 → 110 → 99. The fall is 10% of 110, which is 11, so you end up 1% lower.
• A 20% discount plus an extra 10% off: 100 → 80 → 72. The total discount is 28%, not 30%.

The quick method is to multiply the factors: 1.10 × 0.90 = 0.99 and 0.80 × 0.90 = 0.72. Interest that compounds year after year works the same way, which the compound interest calculator shows over many periods.

Mental maths shortcuts

Most everyday percentages can be built from 10%, 5% and 1%.

Two more tricks. First, some percentages are simple fractions: 50% is a half, 25% a quarter, 20% a fifth, 12.5% an eighth (12.5% of 880 is 880 ÷ 8 = 110) and 33⅓% a third. Second, X% of Y always equals Y% of X, so 4% of 75 is the same as 75% of 4, which is obviously 3. The calculator confirms both give 3.

Five mistakes that give wrong answers

1. Using the new value as the base for a percentage change. Always divide by the starting value.
2. Subtracting a percentage from a total that already includes it, as with GST-inclusive prices and discounted prices. Divide instead.
3. Averaging percentages from papers or groups of different sizes. Add up the raw numbers first.
4. Adding successive percentages. Multiply the factors instead.
5. Mixing up per cent and percentage points when rates change.

For grade-point conversions rather than marks, the CGPA to percentage guide explains which formula applies to CBSE and to universities.

Frequently asked questions

How do I calculate the percentage of my marks?

Add the marks you scored, divide by the total maximum marks, and multiply by 100. 432 out of 600 is 432 ÷ 600 × 100 = 72%.

How do I calculate a percentage increase in salary?

Subtract the old salary from the new one, divide by the old salary and multiply by 100. From ₹40,000 to ₹52,000 is 12,000 ÷ 40,000 × 100 = 30%. The salary hike calculator works the other way, from a hike percentage to the new salary.

How do I find the original price before a discount?

Divide the sale price by (1 − discount ÷ 100). A ₹2,550 price after 15% off was 2,550 ÷ 0.85 = ₹3,000. The discount calculator works forwards: ₹3,000 with 15% off shows a final price of ₹2,550.

How do I convert a fraction or decimal to a percentage?

Divide the top by the bottom to get a decimal, then multiply by 100. 3/8 = 0.375 = 37.5%. To go back, divide the percentage by 100.

Can a percentage be more than 100?

Yes, when you compare or measure change. 250 is 125% of 200, and a rise from 50 to 100 is a 100% increase. A score out of a fixed total can't exceed 100%, though.

Is X% of Y the same as Y% of X?

Always. Both equal X × Y ÷ 100, so pick whichever is easier: 8% of 50 is the same as 50% of 8, which is 4.