Step-by-Step Summary: To calculate roof pitch manually, measure the vertical rise and horizontal run using identical units, divide rise by run to find the tangent ratio, and calculate the inverse tangent: Pitch Angle = arctan(Rise ÷ Run) × (180 ÷ π). For a rise of 1.5m and a run of 3.0m, arctan(1.5 ÷ 3.0) = arctan(0.50) = 26.57°.
The 4-Step Mathematical Calculation Process
- Step 1: Measure the Horizontal Run: Measure the horizontal baseline distance from the outer wall plate to the vertical plumb line beneath the ridge apex (for a symmetrical gable, this is half of the total building span).
- Step 2: Measure the Vertical Rise: Measure the vertical height from the top of the horizontal wall plate to the apex of the roof ridge.
- Step 3: Compute the Slope Gradient Ratio: Divide Rise by Run:
Ratio = Rise ÷ Run. Multiply by 100 for percentage slope. - Step 4: Calculate the Pitch Angle in Degrees: On any scientific calculator or smartphone, press
tan⁻¹(orarctan) of the ratio.
Trigonometric Conversion Quick Reference Table
| Rise per 1 Metre Run | Slope Ratio | Slope Percentage | Pitch Angle (Degrees) | Pitch Multiplier Factor |
|---|---|---|---|---|
| 176 mm | 1 in 5.67 | 17.63% | 10.00° | 1.0154 |
| 268 mm | 1 in 3.73 | 26.79% | 15.00° | 1.0353 |
| 364 mm | 1 in 2.75 | 36.40% | 20.00° | 1.0642 |
| 414 mm | 1 in 2.41 | 41.42% | 22.50° | 1.0824 |
| 500 mm | 1 in 2.00 | 50.00% | 26.57° | 1.1180 |
| 577 mm | 1 in 1.73 | 57.74% | 30.00° | 1.1547 |
| 700 mm | 1 in 1.43 | 70.02% | 35.00° | 1.2208 |
| 839 mm | 1 in 1.19 | 83.91% | 40.00° | 1.3054 |
| 1,000 mm | 1 in 1.00 | 100.00% | 45.00° | 1.4142 |
📚 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.