What is roof pitch?
Roof pitch is the steepness of a roof, expressed as an angle (or as a rise-over-run ratio). It is the angle whose tangent equals the vertical rise divided by the horizontal run from the wall to the ridge.
// maths › Construction
Roof pitch and rafter length
A worked real-world example: from a roof's vertical rise and horizontal run, inverse tangent gives the pitch angle and the Pythagorean theorem gives the rafter length — the two numbers a carpenter needs — shown on an animated roof cross-section you can reshape.
pitch = tan⁻¹(rise / run), rafter = √(rise² + run²)
A mind behind this: Hipparchus of Nicaea c. 190 – c. 120 BC
Frequently asked questions
How do you find the rafter length?
The rafter is the sloping edge — the hypotenuse of the rise–run right triangle — so its length is the square root of the rise squared plus the run squared. Builders then add an overhang allowance.
Why does pitch matter for a building?
Pitch affects water and snow runoff, the materials you can use, wind resistance, and the usable space in the roof. Steeper roofs shed water and snow better; flatter roofs are cheaper but need careful waterproofing.
What is a common roof pitch?
Domestic roofs often fall between about 15° and 45°. Below roughly 10° a roof is considered low-slope or flat and needs different waterproofing; very steep roofs above 45° are used for snow shedding and architectural effect.
Where is this used in real life?
Carpenters and roofers use it to cut rafters and order timber, architects to design rooflines, solar installers to set panel tilt, and engineers to check load and runoff. The rise–run triangle underlies ramps and staircases too.