Percentage Calculator

Understanding Percentages

The word "percent" comes from the Latin per centum, meaning "by the hundred." A percentage is simply a way of expressing a number as a fraction of 100. When we say "25%", we mean 25 out of every 100, or the fraction 25/100, or the decimal 0.25. Percentages make it easy to compare ratios of different sizes — is 37 out of 150 better than 42 out of 200? Converting both to percentages (24.7% vs 21%) gives you an instant answer.

Percentage Formulas Explained

Markup vs Margin — The Difference That Matters

These two concepts are frequently confused in business, but they calculate very differently:

• Markup is the percentage added to the cost price to get the selling price. If you buy for ₹100 and sell for ₹150, markup = (50/100) × 100 = 50% markup.
• Margin (profit margin) is the percentage of the selling price that is profit. Same example: margin = (50/150) × 100 = 33.3% margin.

A 50% markup always gives a 33.3% margin. A 100% markup gives a 50% margin. To convert between them: Margin = Markup ÷ (1 + Markup), and Markup = Margin ÷ (1 − Margin).

Common Percentage Use Cases

Finance and Tax

• GST Calculation: Add 5%, 12%, 18%, or 28% GST to the base price of goods and services in India.
• Income Tax: Tax slabs apply progressively — the first ₹3 lakh at 0%, ₹3–6 lakh at 5%, ₹6–9 lakh at 10%, and so on under the new regime.
• Interest Rates: Loan EMI, fixed deposit returns, and credit card charges are all expressed as annual percentages.
• Investment Returns: CAGR (Compound Annual Growth Rate) expresses multi-year investment performance as a single percentage.

Education

• Exam Scores: 425 out of 500 = 85%. Percentage cutoffs determine admission eligibility in India.
• CGPA to Percentage: Many Indian universities use the formula Percentage = CGPA × 9.5 (varies by institution).
• Attendance: Most colleges require 75% minimum attendance, calculated as (classes attended ÷ total classes) × 100.

Shopping and Discounts

• Successive Discounts: A 20% discount followed by a 10% discount is NOT the same as a 30% discount. The effective discount is 28% because the second discount applies to the already-reduced price.
• Price Before Discount: If an item costs ₹700 after a 30% discount, the original price = 700 ÷ (1 − 0.30) = ₹1,000.

Percentage Tricks for Quick Mental Math

• 10% of any number: Move the decimal point one place left. 10% of 4,500 = 450.
• 5% of any number: Find 10%, then halve it. 5% of 4,500 = 225.
• 15%: Find 10% + 5%. 15% of 4,500 = 450 + 225 = 675.
• 20%: Find 10% and double it. 20% of 4,500 = 900.
• 25%: Divide by 4. 25% of 4,500 = 1,125.
• 1% of any number: Move the decimal two places left. 1% of 4,500 = 45.
• X% of Y = Y% of X: 8% of 50 = 50% of 8 = 4. Use whichever is easier to compute mentally.

Percentage vs Percentage Points — a Crucial Difference

These two are constantly confused, often in news headlines. If an interest rate rises from 4% to 6%, that is an increase of 2 percentage points, but a 50% increase in relative terms (because 2 is half of 4). Saying “rates went up 2%” is wrong — they went up 2 percentage points. Keeping this distinction clear prevents serious misunderstandings in finance, statistics, and reporting.

Markup vs Margin — the Common Business Mistake

Many small businesses lose money by confusing markup and margin. Markup is profit as a percentage of cost, while margin is profit as a percentage of the selling price. If you buy an item for ₹100 and sell it for ₹150, your markup is 50% (₹50 ÷ ₹100) but your margin is only 33.3% (₹50 ÷ ₹150). A 50% markup never equals a 50% margin — assuming so can quietly erode your profits. To convert, margin = markup ÷ (1 + markup).

Worked Examples You'll Actually Use

• Tip: 18% tip on a ₹1,250 bill = 1,250 × 0.18 = ₹225.
• Exam score: 63 correct out of 80 = (63 ÷ 80) × 100 = 78.75%.
• Salary hike: A 12% raise on ₹65,000 = 65,000 × 1.12 = ₹72,800.
• Percentage change: Sales rose from 400 to 520 units → (520 − 400) ÷ 400 × 100 = 30% growth.