Tax Calculation Methodology & Sources
How Salary After Tax verifies tax brackets, social insurance formulas, and allowances.
1. Mathematical Slicing Principles
Income taxes in modern market economies are almost universally progressive. Earning more money never results in taking home less net pay, because higher tax percentages apply only to income earned strictly above the bracket floor.
Tax = ∑ max(0, min(TaxableIncome, TierMax) - TierMin) × TierRate2. Official Statutory Sources & Regulatory Bodies
All 19 country engines are verified against published government publications and statutory regulations:
| Country | Revenue Authority | Statutory Framework |
|---|---|---|
 United States | Internal Revenue Service (IRS) | Internal Revenue Code / Rev. Proc. 2023-34 |
 United Kingdom | HM Revenue & Customs (HMRC) | Income Tax Act 2007 / Spring Budget 2024 |
 Canada | Canada Revenue Agency (CRA) | Income Tax Act / CPP2 Regulations 2024 |
 Australia | Australian Taxation Office (ATO) | Treasury Laws Amendment (Stage 3 Cuts 2024) |
 Germany | Bundesministerium der Finanzen (BMF) | Einkommensteuergesetz (EStG 2024) |
 Ireland | Revenue Commissioners | Finance Act 2023 / 2024 Budget Cut-Offs |
 France | Direction Générale des Finances Publiques | Loi de Finances / Code Général des Impôts |
 Netherlands | Belastingdienst | Wet inkomstenbelasting 2001 (Box 1 2024) |
 Singapore | Inland Revenue Authority of Singapore (IRAS) | Income Tax Act / CPFB Rates 2024 |
3. Reverse Calculation Solver (Numerical Convergence)
Because progressive tax equations involve multiple non-linear inflection points, standard personal allowance phase-outs (such as the UK £100k taper), and social insurance caps, analytical inversion is often piecewise discontinuous.
We employ a high-precision binary bisection algorithm (tolerance ±0.01) that solves for the exact gross requirement within 40 iterations, ensuring 100% mathematical consistency with our forward tax engine.