Percentage Calculator: Everyday Math Everyone Should Know

Mode 1: Finding what percentage X is of Y. Formula: (X/Y) x 100. Example: you scored 67 out of 85 on a test. What percentage is that? (67/85) x 100 = 78.8%. Mode 2: Finding X% of Y. Formula: (X/100) x Y. Example: what is 15% of 2,400? (15/100) x 2400 = 360. Mode 3: Percentage change between two values. Formula: ((New-Old)/Old) x 100. Example: salary increased from 45,000 to 52,000. Percentage increase = ((52000-45000)/45000) x 100 = 15.6%.

The confusion usually happens when people mix up Mode 1 and Mode 2. Our calculator clearly labels each mode so you input the right numbers in the right places. If you need to find the original price before a discount was applied, that is Mode 3 in reverse - a calculation the calculator handles automatically.

Calculating a sale price uses Mode 2: Sale Price = Original Price - (Discount% / 100 x Original Price). A 2,500 item with 30% discount costs 2,500 - 750 = 1,750. Finding the original price from the sale price is the reverse: Original = Sale Price / (1 - Discount%/100). If an item costs 1,750 after 30% off, the original price is 1,750 / 0.70 = 2,500.

The stacked discount trap is worth understanding. A product with 40% off followed by an additional 20% off is NOT 60% off total. It gives: first 40% off (100 becomes 60), then 20% off the reduced price (60 becomes 48). Total effective discount is 52%, not 60%. The formula for combined discounts is: 1 - (1-d1) x (1-d2). Retailers deliberately use this language. Always calculate the effective price rather than adding the percentages together.

When a salary increases from 60,000 to 72,000, the hike percentage is ((72000-60000)/60000) x 100 = 20%. To calculate expected salary after a 15% hike: 60,000 x 1.15 = 69,000. Percentage change normalizes different salary bases - a hike from 50,000 to 60,000 (20%) is a better percentage increase than from 80,000 to 94,000 (17.5%), even though the absolute increase is higher in the second case.

In investing, percentage change is the universal language. A mutual fund NAV moving from 45 to 52 in a year generated ((52-45)/45) x 100 = 15.6% returns. For comparing investments across different time horizons, use CAGR (Compound Annual Growth Rate): CAGR = ((Final/Initial)^(1/years) - 1) x 100. A fund that grew from 1,00,000 to 2,15,000 in 8 years generated approximately 10.1% CAGR per year - a useful number for comparing with fixed deposit rates or other benchmarks.

Converting raw marks to percentages is Mode 1: (Marks Obtained / Total Marks) x 100. For aggregate percentages across multiple subjects with different maximum marks, add all marks obtained and divide by the sum of all maximum marks. Five subjects with maximums of 100, 100, 100, 100, 50 (total 450) and scores of 75, 82, 68, 91, 43 gives aggregate = 359/450 x 100 = 79.8%.

Percentile versus percentage is a crucial distinction for competitive exams like JEE and CAT. Your percentage is your score relative to the maximum marks. Your percentile is your position relative to other test takers. A 70% score might put you in the 95th percentile if the exam was difficult and most students scored poorly. Percentile rank tells you what fraction of students scored below you - a 99th percentile means you outperformed 99% of test takers regardless of your actual marks.