Master Reference: Below is the complete mathematical pitch conversion matrix for UK construction, covering angles from 5° to 60° in standard trade increments. All values are calculated from first principles according to Euclidean geometry.
| Pitch (Degrees) | X-in-12 Ratio | Slope Ratio | Gradient (%) | Pitch Multiplier | Rise per 1m Run | UK Classification |
|---|---|---|---|---|---|---|
| 1.0° | 0.21 : 12 | 1 : 57.29 | 1.75% | 1.0002 | 0.017 m | Flat / Ultra-Low Pitch |
| 2.0° | 0.42 : 12 | 1 : 28.64 | 3.49% | 1.0006 | 0.035 m | Flat / Ultra-Low Pitch |
| 3.0° | 0.63 : 12 | 1 : 19.08 | 5.24% | 1.0014 | 0.052 m | Flat / Ultra-Low Pitch |
| 4.0° | 0.84 : 12 | 1 : 14.3 | 6.99% | 1.0024 | 0.070 m | Flat / Ultra-Low Pitch |
| 5.0° | 1.05 : 12 | 1 : 11.43 | 8.75% | 1.0038 | 0.087 m | Flat / Ultra-Low Pitch |
| 7.5° | 1.58 : 12 | 1 : 7.6 | 13.17% | 1.0086 | 0.132 m | Flat / Ultra-Low Pitch |
| 10.0° | 2.12 : 12 | 1 : 5.67 | 17.63% | 1.0154 | 0.176 m | Low Pitch |
| 12.5° | 2.66 : 12 | 1 : 4.51 | 22.17% | 1.0243 | 0.222 m | Low Pitch |
| 15.0° | 3.22 : 12 | 1 : 3.73 | 26.79% | 1.0353 | 0.268 m | Low Pitch |
| 17.5° | 3.78 : 12 | 1 : 3.17 | 31.53% | 1.0485 | 0.315 m | Low Pitch |
| 20.0° | 4.37 : 12 | 1 : 2.75 | 36.40% | 1.0642 | 0.364 m | Low Pitch |
| 22.5° | 4.97 : 12 | 1 : 2.41 | 41.42% | 1.0824 | 0.414 m | Standard UK Pitch |
| 25.0° | 5.60 : 12 | 1 : 2.14 | 46.63% | 1.1034 | 0.466 m | Standard UK Pitch |
| 27.5° | 6.25 : 12 | 1 : 1.92 | 52.06% | 1.1274 | 0.521 m | Standard UK Pitch |
| 30.0° | 6.93 : 12 | 1 : 1.73 | 57.74% | 1.1547 | 0.577 m | Standard UK Pitch |
| 32.5° | 7.64 : 12 | 1 : 1.57 | 63.71% | 1.1857 | 0.637 m | Standard UK Pitch |
| 35.0° | 8.40 : 12 | 1 : 1.43 | 70.02% | 1.2208 | 0.700 m | Standard UK Pitch |
| 37.5° | 9.21 : 12 | 1 : 1.3 | 76.73% | 1.2605 | 0.767 m | Standard UK Pitch |
| 40.0° | 10.07 : 12 | 1 : 1.19 | 83.91% | 1.3054 | 0.839 m | Standard UK Pitch |
| 42.5° | 11.00 : 12 | 1 : 1.09 | 91.63% | 1.3563 | 0.916 m | Standard UK Pitch |
| 45.0° | 12.00 : 12 | 1 : 1 | 100.00% | 1.4142 | 1.000 m | Standard UK Pitch |
| 47.5° | 13.10 : 12 | 1 : 0.92 | 109.13% | 1.4802 | 1.091 m | Steep / Mansard Pitch |
| 50.0° | 14.30 : 12 | 1 : 0.84 | 119.18% | 1.5557 | 1.192 m | Steep / Mansard Pitch |
| 52.5° | 15.64 : 12 | 1 : 0.77 | 130.32% | 1.6427 | 1.303 m | Steep / Mansard Pitch |
| 55.0° | 17.14 : 12 | 1 : 0.7 | 142.81% | 1.7434 | 1.428 m | Steep / Mansard Pitch |
| 60.0° | 20.78 : 12 | 1 : 0.58 | 173.21% | 2.0000 | 1.732 m | Steep / Mansard Pitch |
| 65.0° | 25.73 : 12 | 1 : 0.47 | 214.45% | 2.3662 | 2.145 m | Steep / Mansard Pitch |
| 70.0° | 32.97 : 12 | 1 : 0.36 | 274.75% | 2.9238 | 2.747 m | Steep / Mansard Pitch |
How to Read the Roof Pitch Conversion Chart
Each column provides an exact mathematical equivalence for trade and architectural specifications:
- Degrees (°): The standard UK angle of inclination measured above the horizontal plane.
- X-in-12 Ratio: Rise in inches per 12 inches of horizontal run (e.g. 6.00:12 = 26.57°).
- Slope Ratio: Expressed as 1 in X (e.g. 1 in 2 gradient = 26.57°).
- Gradient (%): Vertical rise divided by horizontal run multiplied by 100.
- Pitch Multiplier (Factor): Multiplier used to scale 2D plan footprint area into true 3D sloped surface area (
Area = Plan Area × Factor). - Rise per 1m Run: The vertical height gain in millimetres for every 1.0 metre of horizontal distance.
📚 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.