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The roof's pitch is its vertical rise divided by its horizontal span (or "run"), what is called "slope" in geometry and stair construction, or the tangent function in trigonometry. It is typically expressed with the rise first and run second, with the run denominated by the number 12, giving a ratio of how many inches of incline there is to each foot of run. For example, 3:12, 4:12, 5:12, and so on.
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).
To find the exact roof slope in degrees, one takes 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 conservation of exterior framing and sheathing materials.
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