Mathematical Rigour: All algorithms on RoofPitchCalculator.co.uk are programmed using standard Euclidean trigonometry, ISO 80000-2 mathematical notation, and certified British Standard engineering specifications (BS 5534, BS 5250, BS 6229, and BS EN 1995-1-1 Eurocode 5).
Verification & Numerical Invariants
Every calculation is validated against five mathematical invariants:
- Trigonometric Invariant: $ an( heta) = rac{ ext{Rise}}{ ext{Run}}$, $\sec( heta) = rac{1}{\cos( heta)} = \sqrt{1 + an^2( heta)}$.
- Rafter Orthogonality: $ ext{Plumb Cut Angle} + ext{Seat Cut Angle} = 90.00^\circ \pm 0.0001^\circ$.
- Pythagorean Closure: $ ext{Rafter Line}^2 = ext{Run}^2 + ext{Rise}^2$.
- Plan Area Scaling: $ ext{True 3D Sloped Area} = ext{Plan Area} imes \sec( heta)$.
- Flat Roof Deflection Invariant: Design Fall ($1:40$) strictly accounts for maximum structural joist deflection ($ rac{L}{250}$) ensuring cleared falls exceed $1:80$.
📚 Primary Technical Sources & British Standards
- BS 5534:2014+A2:2018: Code of practice for slating and tiling for pitched roofs and vertical cladding. British Standards Institution.
- BS 5250:2021: Management of moisture in buildings — Code of practice. British Standards Institution.
- BS 6229:2018: Flat roofs with continuously supported flexible waterproof coverings — Code of practice.
- NHBC Standards Chapter 7.2: Pitched Roofs — Minimum pitches, rafter timber sizing, batten gauges and fixing specifications.
- UK Manufacturer Technical Literature: Marley Technical Handbooks, BMI Redland Fixing Guides, CUPA Pizarras Slate Technical Manuals.
Last technical audit date: 17 August 2026.