Percentage Calculator

Percentages made simple: formulas, examples and everyday uses

A percentage expresses a number as a part of 100. The word comes from the Latin "per centum", meaning "by the hundred". We use percentages for marks, discounts, interest, taxes, profit and growth. The same three ideas cover almost every case, and this calculator handles each of them.

The three basic questions

• What is X% of Y? Multiply Y by X and divide by 100. Example: 15% of 2,400 = 2,400 × 15 ÷ 100 = 360.
• X is what percent of Y? Divide X by Y and multiply by 100. Example: 45 out of 60 is 45 ÷ 60 × 100 = 75%.
• Percentage change from A to B: (B − A) ÷ A × 100. Example: a price rising from 800 to 920 is a 15% increase.

Percentage points versus percent

If an interest rate rises from 6% to 8%, it has gone up by 2 percentage points, but by 33.3 per cent in relative terms (2 ÷ 6). News reports often mix these up, so be careful when comparing rates.

Why a 20% rise and 20% fall do not cancel out

Take 100 and increase it by 20% to get 120. A 20% decrease on 120 is 24, leaving 96. The base changes each time, so the second percentage applies to a different number. To return to 100 from 120 you need a fall of 16.67%.

Everyday applications

• Marks: total marks obtained ÷ maximum marks × 100. If you scored 438 out of 500, your percentage is 87.6%.
• Discounts: a 30% discount on ₹1,999 saves ₹599.70, so you pay ₹1,399.30.
• Tips and service charge: 10% of a ₹850 bill is ₹85.
• Profit and loss: profit % = (selling price − cost price) ÷ cost price × 100. Note that it is based on cost, not on selling price.
• Salary hike: a hike from ₹40,000 to ₹44,000 is 10%.

Reverse percentages

If a price after a 25% discount is ₹750, the original price is 750 ÷ 0.75 = ₹1,000. Many people wrongly add 25% to 750 and get ₹937.50. Always divide by the remaining fraction.

Successive percentages

When two changes happen in a row, multiply the factors. A 10% increase followed by a 10% decrease is 1.10 × 0.90 = 0.99, a net fall of 1%. This idea is useful for compound growth, chained discounts and tax on tax.

Quick mental tricks

• 10% of a number: move the decimal point one place left.
• 5%: take half of 10%. 15%: add 10% and 5%.
• 1%: move the decimal point two places left.
• x% of y equals y% of x, so 8% of 50 is the same as 50% of 8, which is 4.

Check your answers

Estimate first. If you are finding 19% of 520, it should be a little under 20% of 520, which is 104. The exact answer is 98.8, which fits. Estimation catches typing mistakes before they reach a bill, a form or an exam answer sheet.

Percentages in exams and interviews

Competitive exams often test percentage shortcuts: fractions such as 1/8 = 12.5%, 1/6 = 16.67% and 3/8 = 37.5% save time. Memorise a few and you can answer many questions without a calculator. In data-interpretation questions, always check which base the percentage uses (previous year, total, or another group) before computing. When you present figures in a report, state the base, for example "up 12% over last quarter", so readers do not misinterpret a bare percentage.