Transparency & Rigor
How DudeMath Calculators Work
DudeMath is built on a clear principle: every calculation should be fully traceable, honestly documented, and verifiable by the user.
Step 1
Formula Selection & Source Verification
How DudeMath decides which formula to implement for each calculator.
Each calculator starts from an established, cited mathematical or physical relationship. DudeMath does not invent formulas or use heuristic approximations without citation. Governing equations are drawn from widely recognized educational and technical standards:
- Standard Engineering Textbooks — e.g., Russell C. Hibbeler (Mechanics of Materials, Engineering Mechanics: Statics & Dynamics), Raymond A. Serway & John W. Jewett (Physics for Scientists and Engineers), Frank M. White / Munson et al. (Fluid Mechanics).
- Measurement Standards — NIST (National Institute of Standards and Technology) CODATA values for physical constants (e.g., standard gravity g = 9.80665 m/s², universal gravitational constant G = 6.67430 × 10⁻¹¹ N·m²/kg²) and SI metric unit mappings.
- Industry Reference Specifications — ASTM A615 / A615M specifications for reinforcement bar dimensions and CRSI (Concrete Reinforcing Steel Institute) technical guidelines.
Every calculator page cites its governing literature in its reference block. When a physical problem possesses multiple boundary configurations, DudeMath implements only the exact case stated and explicitly discloses scope boundaries.
Step 2
Defining Scope — What Each Calculator Actually Does
Every calculator has an explicitly bounded scope. DudeMath does not overstate functionality.
Scope Boundaries
Each calculator operates within explicit boundary conditions:
- • Beam Deflection: Implements simply-supported beams under uniformly distributed loads (UDL) with δ = 5wL⁴/(384EI). Does not compute cantilever or point-load configurations.
- • Matrix Determinant: Computes 2×2 linear algebra matrices using det(A) = ad − bc with step-by-step Leibniz expansion. Larger matrices are outside current scope.
- • Dynamic Pressure: Computes fluid dynamic pressure q = ½ρv² from density and velocity. Does not solve two-point Bernoulli elevation-head differential equations.
Documenting Real Limitations
Every calculator provides educational analysis documenting:
- • Idealized physical assumptions (e.g., inviscid flow, linear elasticity, small displacements).
- • Conditions where advanced structural or fluid analysis is required (such as Timoshenko shear deformation for deep beams).
- • Practical conversion factors and nominal dimension tolerances.
- • Clear distinction between serviceability limits (SLS) and ultimate capacity (ULS).
Step 3
Formula Implementation — TypeScript Pure Functions
How mathematical formulas are translated into reliable code.
Every mathematical formula is authored as an isolated pure TypeScript function located in src/lib/formulas/. Pure functions produce no side effects, maintain no global state, and require no server communication. For any given numerical inputs, they deterministically compute the exact output.
100% Client-Side Execution: All numerical evaluations execute directly within the user's web browser. No user inputs, parameters, or calculated results are ever transmitted across the network, so the calculation itself does not require a server round trip.
Dimensional Consistency: The calculation pipeline converts all user inputs (such as imperial units or non-base metric scales) into standardized SI base units prior to formula invocation. Once solved, output values are formatted into clean engineering notation with appropriate physical units.
Step 4
Automated Validation Pipeline
Mechanical verification executed on every build.
Automated Unit Tests
Automated Vitest test suites execute prior to production deployment. Tests verify formula implementations against textbook reference cases, boundary conditions, and numerical stability.
Schema Validation Scripts
Build-time validator scripts inspect all calculator metadata schemas, confirming that every catalog entry corresponds to an existing pure function, documented guide, and active route.
Worked Examples
Every calculator features authentic, step-by-step worked examples showing parameter substitution and manual calculation steps that match the calculator's runtime output.
Engineering Notice
Scope Limitations & Academic Purpose
Clear boundaries regarding professional engineering practice.
- ✕ Preliminary & Academic Use Only: DudeMath calculators are engineered for educational reference, homework checking, and preliminary engineering feasibility estimation.
- ✕ Professional Review Required: Calculations must never replace formal review and stamping by a licensed Professional Engineer (PE) or Chartered Engineer (CEng) for safety-critical, structural, or life-safety applications.
- ✕ Independent Maintenance: DudeMath is an independently created student project and is not formally certified by or affiliated with any government agency, testing laboratory, or commercial standards committee.
Community & Quality
Reporting Formula Discrepancies
How to report calculation issues or propose formula refinements.
DudeMath welcomes community feedback and formula discrepancy reports. If you identify a discrepancy, missing assumption, or edge-case error in any formula, please report it:
- 1. Contact Form: Submit details via our contact page selecting "Formula Discrepancy / Bug Report". Include formula inputs, observed result, and verified literature reference.
- 2. GitHub Issue Tracker: Open a technical issue or discussion via the DudeMath open-source profile with relevant mathematical derivations.
Verified discrepancies will be corrected immediately, covered by regression unit tests, and documented in public version control.