➗ Mathematics — Free Online Calculators & Tools

Compound interest earns interest on interest — your money grows exponentially, not linearly. A = P(1 + r/n)^(nt). At 10% annually: ₹1L grows to ₹2.59L in 10 years (compound) vs ₹2L (simple interest). This difference compounds dramatically over 20–30 years, making it the most important concept in personal finance.

% of X = (percent/100) × X. X is what % of Y = (X/Y) × 100. % change = ((new–old)/old) × 100. Add P% to X = X × (1 + P/100). Remove P% from X = X × (1 – P/100). Note: adding 20% and removing 20% does NOT cancel out: 100 + 20% = 120, 120 – 20% = 96 (not 100).

Divide both numerator and denominator by their GCD (Greatest Common Divisor). Example: 18/24 → GCD(18,24)=6 → 3/4. To find GCD: use Euclidean algorithm — divide larger by smaller, replace larger with remainder, repeat until remainder=0. The last non-zero remainder is the GCD.

A ratio compares two quantities (3:4 means for every 3 of A there are 4 of B). A proportion states that two ratios are equal: 3:4 = 6:8. Proportions are used to solve "find the missing value" problems. If A:B = C:D, then A×D = B×C (cross-multiplication rule).

Exact age = years completed + months completed (in the current year) + days completed (in the current month). Month borrowing: if current day < birth day, borrow from previous month. Year borrowing: if current month < birth month, borrow from previous year. This matches how official documents calculate age.