A2 · Derivations
Formula derivations
Competitors publish formulas. Almost nobody publishes derivations, which is why, when your bank's figure differs from a calculator's by a few hundred, you usually have no way to tell which is right. Each page below derives its formula, checks it at the limits where the answer is obvious, works one verified example, and says plainly where the formula stops being valid.
Each derivation is stored once and included by reference from every calculator that uses it. DRV-001 backs every loan and mortgage tool on the site; the India and US pages differ in currency, examples and citations, and this section is byte-identical.
DRV-001The annuity payment, derived from scratchWhere the EMI formula comes from. Six steps of algebra, no calculus, and three checks that prove it is right.Serves 8 calculatorsDRV-004Why an 8% flat loan is really a 14.13% loanA flat rate charges interest on money you have already repaid. Converting it to an honest reducing-balance rate needs a numerical solve, and the common shortcut is too crude to publish.Serves 3 calculatorsDRV-005Why two SIP calculators give you different answersA ₹23,004 discrepancy on identical inputs, caused by a convention that neither provider states. Here is the algebra and which one is right for an actual SIP.Serves 4 calculatorsDRV-013BMI, and where the 703 comes fromNearly every US site quotes 703 without explaining it. It is a pure unit conversion, and explaining it costs two lines.Serves 3 calculatorsDRV-017Concrete quantities, and where the 1.54 comes fromThe familiar "about eight bags per cubic metre for M20" has a provenance. Here it is, along with why dry volume exceeds wet.Serves 3 calculatorsDRV-018Why steel weight is d² ÷ 162Every Indian site quotes the rule; almost none derives it. Two lines of algebra, and the page becomes the one an engineer bookmarks.Serves 3 calculatorsDRV-019Subnetting, and the two addresses you cannot useWhy usable hosts is 2^(32−p) − 2, and the two prefix lengths where that rule is wrong.Serves 3 calculatorsDRV-022Why your A/B test needs so many visitorsThe inverse-square relationship, which is the actual answer to the question behind almost every sample-size search.Serves 3 calculators