Calculation Methodology

ToolFlux Lab mathematical calculators adhere strictly to standard algebraic conventions, order of operations (PEMDAS/BODMAS), and exact analytical definitions:

• Percentage Calculations: P = (Part / Total) × 100. Percentage increase uses Original × (1 + Rate/100); percentage decrease uses Original × (1 - Rate/100).
• Arithmetic Mean (Average): x̄ = (Σ xᵢ) / n. Sum of all dataset values divided by the total count of elements n, excluding non-numeric values.
• Ratios & Simplification: Ratios are simplified via the Euclidean algorithm to find the Greatest Common Divisor (GCD), dividing both terms by GCD to determine simplest whole-number form.
• Fraction Arithmetic: Addition and subtraction determine the Least Common Multiple (LCM = |a × b| / GCD(a,b)) for denominators before cross-multiplying numerators and simplifying.
• Powers & Roots: Evaluated via double-precision IEEE 754 floating-point standards for real roots.

Financial computations apply standardized banking formulas for amortized repayment schedules and interest compounding:

• Equated Monthly Installment (EMI): EMI = P × [ r(1 + r)ⁿ ] / [ (1 + r)ⁿ - 1 ]
  Where P = principal loan balance, r = periodic monthly interest rate (Annual Rate / 12 / 100), and n = total payment count in months.
• Compound Interest: A = P × (1 + r / m)^(m × t)
  Where A = final balance, m = compounding frequency per year, and t = duration in years.
• Return on Investment (ROI): ROI (%) = [ (Net Profit) / Cost of Investment ] × 100
• Profit Margin vs Markup: Gross Margin (%) = [ (Revenue - Cost) / Revenue ] × 100
Markup (%) = [ (Revenue - Cost) / Cost ] × 100

Our health utilities reference established epidemiological guidelines from the World Health Organization (WHO) and clinical physiology literature:

• Body Mass Index (BMI): BMI = Weight (kg) / [ Height (m) ]²
  Classified per WHO thresholds: Underweight (< 18.5), Normal (18.5–24.9), Overweight (25.0–29.9), and Obese (≥ 30.0).
• Basal Metabolic Rate (BMR — Mifflin-St Jeor):
  For Men: BMR = 10 × weight(kg) + 6.25 × height(cm) - 5 × age(y) + 5
  For Women: BMR = 10 × weight(kg) + 6.25 × height(cm) - 5 × age(y) - 161
• Total Daily Energy Expenditure (TDEE): TDEE = BMR × Activity Factor
  Activity multipliers: Sedentary (1.2), Light (1.375), Moderate (1.55), Very Active (1.725), Extra Active (1.9).

Engineering calculators implement foundational electromagnetic and physical laws codified by international IEEE and IEC standards:

• Ohm’s Law: V = I × R, I = V / R, R = V / I
  Where V = Potential difference in Volts, I = Current in Amperes, and R = Resistance in Ohms.
• Electrical Power (Joule’s Law): P = V × I = I² × R = V² / R
• Resistor Color Codes: Adheres strictly to IEC 60062:2016 specifications for 4-band, 5-band, and 6-band color bands, TCR coefficients, and IEC 60063 preferred resistance series (E12, E24, E96).

All unit conversion factors utilize exact defined constants maintained by the International Bureau of Weights and Measures (BIPM) and the National Institute of Standards and Technology (NIST):

• Length & Distance: 1 inch = exact 0.0254 m (1959 International Yard and Pound Agreement); 1 foot = 0.3048 m; 1 mile = 1609.344 m.
• Mass & Weight: 1 pound (lb) = exact 0.45359237 kg; 1 ounce (oz) = 28.349523125 g.
• Temperature Scales: Exact formulas: °F = (°C × 9/5) + 32; K = °C + 273.15.
• Digital Storage: Clear differentiation between SI decimal prefixes (1 KB = 1,000 B) and IEC binary prefixes (1 KiB = 1,024 B).