Rise over run is tan θ; rafter length is the hypotenuse.
Key formulas
Model
Strip the house drawing to a right triangle. Rise is vertical; run is half-span for a symmetric roof.
Example
Rise 2.4 m, run 6 m → tan θ=0.4 → θ≈21.8°. Rafter √(2.4²+6²)=√42.24≈6.5 m.
Units
Keep metres throughout. Mixing cm rise with m run destroys tan θ.
Worked example
Worked example
Problem. A roof rises 2.4 m over a horizontal run of 6 m. Find the pitch angle and the rafter length.
Solution. tan θ = 2.4/6 = 0.4 → θ = tan⁻¹(0.4) ≈ 21.8°. Rafter = √(2.4² + 6²) = √(5.76 + 36) = √41.76 ≈ 6.46 m.
Pitch ratio
Builders sometimes quote rise:run = 1:3, which is the same triangle.
Review quiz
Rise 3 m, run 4 m. Rafter length is:
Practice questions
- Rise 3, run 4. Find rafter and tan θ.
- Why use half the building width as run on a gable roof?
Study notes
Is pitch the angle or the ratio?
Both appear in language — clarify which the question wants.