Calculation Methodology & Mathematical Rigor
A transparent, open-source review of the equations, floating-point precision models, and statutory benchmark datasets powering AllYouTools.
1. Financial Calculation Engine
Our financial calculation suite (EMI, SIP, Compound Interest, and GST) operates on standard actuarial and quantitative finance mathematics:
Loan Amortization (Reducing-Balance EMI):
EMI = [P × r × (1 + r)^n] / [((1 + r)^n) − 1]
Where P is principal, r is the monthly rate (annual / 1200), and n is total monthly installments. Verified against standard banking amortisation schedules.
Future Value of Systematic Investment Plan (SIP Annuity Due):
FV = M × [((1 + i)^n − 1) / i] × (1 + i)
Where M is the periodic payment, i is periodic monthly rate, and (1 + i) represents beginning-of-period investment timing.
Reverse GST Extraction (Inclusive Pricing):
Base Amount = Inclusive Price / (1 + Rate / 100)
Ensures zero arithmetic drift when isolating pre-tax base cost and exact CGST/SGST components.
2. Floating-Point Precision & Rounding Standards
JavaScript uses IEEE-754 double-precision 64-bit binary floating-point representation. To eliminate binary representation artifacts (such as 0.1 + 0.2 = 0.30000000000000004), our calculation kernels apply integer scaling and banker's half-up rounding conventions before displaying final currency and unit figures.
3. Cryptographic Security & CSPRNG Standards
For security utilities like the Password Generator, we strictly prohibit pseudo-random generators (e.g. Math.random()). Instead, we enforce the W3C Web Cryptography API (window.crypto.getRandomValues()), ensuring all entropy is harvested directly from hardware OS kernels. Shannon entropy calculations adhere to NIST SP 800-63B standards.
Statutory Benchmark Reference Bodies
Reserve Bank of India (RBI) & Fed
Standard retail loan amortization schedules and 0% prepayment penalty frameworks.
World Health Organization (WHO)
Adult BMI classification cutoffs and Asian-specific adiposity risk thresholds.
IETF & ECMA International
RFC 8259 JSON grammar and ECMAScript Unicode case folding specifications.
BIPM & NIST Metrology
International yard, pound, and thermodynamic temperature conversion constants.