Roof pitch

In building construction, roof pitch is the steepness of a roof quantified as a ratio or as the number of angular degrees that "one" 'exposure' surface deviates from horizontal level. A roof surface may be either 'functionally flat' or pitched.
Description.
The pitch of a roof is its vertical 'rise' over its horizontal 'span'. However, most often a ratio of "pitch" (also fraction) is slang used for the (more useful) 'slope' (of rise over 'run') of just one side (half the span) of a dual pitched roof. This is the 'slope' of geometry, stairways and other construction disciplines, or the trigonometric arc tangent function of its decimal fraction. In the imperial measurement systems, "pitch" is usually expressed with the rise first and run second (in the USA, run is held to number 12). In the USA the rise is rationalized to a ratio of so many measuring units rise to each 12 measuring units of run (e.g., 3:12, 4:12, 5:12). Places that use metric measurement systems use a degree angle, or what fall there is per unit of run, and expressed as a '1 in _' slope (a '1 in 1' equals 45°). Where convenient, the least common multiple is used (e.g., a '3 in 4' slope, for a '9 in 12' or '1 in 1 1/3').
The pitch matters for a variety of reasons, including the type of roofing material used, walkability, proportions to the building as a whole (which is sometimes a critical factor in some architectural styles such as a steep pitch in Gothic architecture and a low pitch in Classical architecture), and combinations of pitches to form distinctive roof shapes such as a gambrel roof. The basic ranges of pitch are not uniformly defined, but range from "flat", which are not perfectly flat but sloped to drain water up to 1/2:12 to 2:12 (1 in 24 to 1 in 6); "low-slope" roofing, which requires special materials and techniques to avoid leaks and ranges from 1:12 (2:12) to 4:12 (1 in 3); "conventional" from 4:12 (1 in 3) to 9:12 (3 in 4); and "steep-slope" roofing, which is above 9:12 (3 in 4) (21:12) (7 in 4) and may require extra fasteners.
US convention is to use whole numbers when even (e.g. "three in twelve") or the nearest single or two-digit fraction when not (e.g. either "five and a quarter in twelve" or "five point two-five in twelve", each expressed numerically as 5.25:12).
Definitions vary on when a roof is considered pitched. In degrees, 10° (2 in 12 or 1 in 6) is considered a minimum.
The exact roof slope in degrees is given by the arctangent. For example: arctan(3/12)=14.0°
The primary purpose of pitching a roof is to redirect water and snow. Thus, pitch is typically greater in areas of high rain or snowfall. The steep roof of the tropical Papua New Guinea longhouse, for example, sweeps almost to the ground. The high, steeply-pitched gabled roofs of Northern Europe are typical in regions of heavy snowfall. In some areas building codes require a minimum slope. Buffalo, New York and Montreal, Quebec, Canada, specify 6 in 12, a pitch of approximately 26.6 degrees.
Carpenters frame rafters on an angle to "pitch" a roof. Gable and other multi-pitched roofs allow for lower primary structures with a corresponding reduction in framing and sheathing materials.
Historical pitches.
Historically, roof pitch was designated in two other ways: A ratio of the ridge height to the width of the building (span) and as a ratio of the rafter length to the width of the building.
Commonly used roof pitches were given names such as:-