Calculating roof pitch: formulas and practical applications
Degrees, percent and rafter length – all from height and depth
The roof pitch is a key measurement in construction. It determines the roof covering, the type of roof tile, the snow load, the photovoltaic yield, and the structural load on the framework. The calculation is geometric: pitch in degrees = arctan(ridge height ÷ roof depth), where the roof depth is the horizontal projection – for a symmetrical gable roof, half the building width.
Degrees vs. percent: In building construction, pitch is usually given in degrees, while in civil engineering and road construction it is often given in percent. A 50% pitch corresponds to 26.57° – this is the common gable roof with a ridge height equal to half the building width. 100% is 45°. To convert: percent = tan(degrees) × 100; degrees = arctan(percent/100).
Rafter length for material planning: The Pythagorean theorem gives the actual length of the rafter: √(height² + depth²). This length is essential for calculating roof battens, counter battens, roof tiles and underlay membrane. For a roof with a height of 3 m and a depth of 4 m (the classic 3-4-5 triangle), the rafter length is exactly 5 m – handy for ordering timber.
Drainage and minimum pitches: Germany's ZVDH (Central Association of the German Roofing Trade) sets minimum roof pitches in its technical guidelines for each type of covering. Concrete roof tiles require at least 22° (41%), flat roof tiles 15° (27%), corrugated sheets and trapezoidal sheeting from 5° (9%). Flat roofs are brought to at least 2° (1.1°) pitch through tapered insulation to prevent puddling.