worldlytic
Transparent Mathematics

Calculation Methodology & Formulas

Worldlytic does not rely on opaque estimates. Every result across our calculators is generated by deterministic, transparent, and reproducible mathematical algorithms. Below is how each engine operates.

Engines Documented
1. Progressive Statutory Tax Engine 2. Standardized 9-Category Cost of Living Engine 3. Tax-Aware Equivalent Salary Inversion 4. Remote Destination & Nomad Scoring Engine 5. Freelance Rate & Contractor Inversion Engine 6. Potential Savings & Financial Milestone Engine
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1. Progressive Statutory Tax Engine

Calculates take-home pay by iterating through progressive statutory income tax brackets and mandatory social security contributions.

// Marginal Bracket Algorithm
Tax = Σ (max(0, min(TaxableIncome, UpperLimit_i) - LowerLimit_i) × Rate_i)
  • Deductions: Subtracts standard personal allowances and pre-tax employee social security contributions.
  • Multi-Tier Systems: Supports regional and state income taxes (e.g. US state taxes, Canadian provincial taxes, Swiss cantonal multipliers).
  • Social Contributions: Calculates statutory pension, healthcare, and unemployment withholdings with official statutory ceiling caps.
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2. Standardized 9-Category Cost of Living Engine

Evaluates living costs using a standardized basket across 9 essential categories benchmarked to New York City (Index = 100).

// Expenditure Basket Formula
TotalMonthlyCost = Σ (CategoryMedian × HouseholdMultiplier × LifestyleFactor)
  • Household Scaling: Single (1.0x), Couple (1.65x), Family of 4 (2.6x).
  • Lifestyle Tiers: Budget (0.75x), Moderate (1.0x), Comfortable (1.45x), Premium (2.1x).
  • Categories: Housing & Rent, Groceries, Transportation, Utilities, Internet/Mobile, Healthcare, Dining, Childcare, and Miscellaneous.
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3. Tax-Aware Equivalent Salary Inversion

Calculates the destination gross salary needed to match the purchasing power and living standard of your current location.

// Equivalence Equation
TargetNet = CurrentNet × (DestinationCoLIndex / CurrentCoLIndex) DestinationGross = TaxEngine^-1(TargetNet)
  • Tax Inversion: Inverts the destination tax code using numerical root-finding (bisection) to find the exact gross salary yielding TargetNet.
  • Tax Divergence Warning: Highlights divergence when high-cost destinations push relocators into significantly higher marginal tax brackets.
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4. Remote Destination & Nomad Scoring Engine

Ranks international destinations on a 0–100 composite score based on customizable lifestyle criteria.

// Weighted Score Formula
CompositeScore = Σ (NormalizedMetric_i × NormalizedWeight_i) × 100
  • Min-Max Normalization: All metrics are scaled across the global dataset [0, 1].
  • Criteria Covered: Net Savings Potential, Cost of Living, Coworking/Internet, Safety & Healthcare, and Climate.
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5. Freelance Rate & Contractor Inversion Engine

Converts a desired net take-home salary into required hourly and day contracting rates.

// Gross Billings Formula
RequiredBillings = TaxEngine^-1(TargetNet + BusinessExpenses) HourlyRate = RequiredBillings / BillableHoursPerYear
  • Billable Time Adjustment: Accounts for unbillable administration, paid holidays, and sick days.
  • Buffer Margin: Recommends a 15–20% safety margin for business downtime and self-employed risks.
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6. Potential Savings & Financial Milestone Engine

Projects surplus cash flow and the timeline required to achieve major financial milestones.

// Monthly Surplus Formula
MonthlySavings = NetMonthlyIncome - MonthlyLivingCosts MonthsToGoal = TargetGoalAmount / MonthlySavings
  • Savings Rate: Computes the percentage of net take-home pay successfully retained as savings.
  • Relocation Delta: Compares current savings capacity against destination savings capacity in a unified display currency.

Important Methodological Note

All calculations provide estimated ranges for informational modeling and career decision-support. Actual tax withholdings, local municipal surcharges, and individual spending patterns vary. Review our complete Financial Disclaimer and inspect our Data Sources.