This section is from the book "Cyclopedia Of Architecture, Carpentry, And Building", by James C. et al. Also available from Amazon: Cyclopedia Of Architecture, Carpentry And Building.
The pitch of a roof is the term used to indicate the slope of the sides of the roof surface or the inclination of these sides with respect to a horizontal plane or a surface absolutely flat and parallel to the horizon. Evidently the pitch of any roof may vary to an almost infinite extent. It may be absolutely flat or it may be practically vertical, or it may be inclined at any angle between these two limits. Unfortunately there are several systems in use for indicating the pitch or the amount of the angle of the slope, so that there is likely to be some misunderstanding about it. Usually, however, some one system is in use in any one section of the country and there is a general understanding that this is the system intended when speaking of the pitch of a roof. The most simple way of indicating the pitch and at the same time the most accurate way, is to give the angle which the roof surface makes with a horizontal plane Thus the pitch of the roof may be thirty degrees, or forty-five degrees or sixty degrees. This system is much in use among civil engineers, by whom it is favored on account of its accuracy and the small probability of its being misunderstood, but it is not much in use among carpenters and architects, who generally prefer to use some other system.
Another method of indicating the slope of the roof surfaces is to take the rise of the roof at the center of the span, or the vertical distance from the top of the plate to the under side of the rafters at the center of the span, and to divide this distance by the span itself or the distance between the inside edges of two rafters which come opposite to each other in the roof frame, at the point where they intersect the top surface of the plate. The fraction thus obtained is used to express the degree of slope of the roof, or the angle that the roof surface makes with the horizontal plane, in the following way: If the span of the roof between the edges of the rafters at the level of the top of the plate is 20 feet and the rise of the roof at the center, measured vertically from the top of the plate to the under side of the rafters, is 10 feet, then the roof is of half pitch, since the fraction obtained by dividing the rise of the roof by the span of the roof is one over two or one half. The angle which this roof surface makes with the horizontal plane is forty-five degrees, since the rise at the center is equal to half the span, and the rise of the sloping rafter is equal to its run or its projection on the horizontal plane. This slope is also called a square slope or a square pitch for the reason that the rise of the rafter is equal to its run. In this roof also it will be seen that the rafter rises a distance of 12 inches for each foot of run, counting the rise always from the level of the top of the plate and the run from the point where the under side of the rafter intersects the top of the plate. Thus at the center of the roof the run is 10 feet and the rise is also 10 feet. If this same roof were one of full pitch, the rise at. the center of the span would be 20 feet, equal to the span itself, and there would be 2 feet of rise for each foot of run. This would make a very steep roof, in fact it is very seldom so steep a roof is used in ordinary work. A two-thirds pitch would be a little less steep than the full pitch, between the full pitch and the half pitch, and this roof would have a rise of 16 inches for each foot of run, so that if the span were 20 feet, as in the case of the other roofs just mentioned, the rise at the center of the span would be 160 inches or 13 feet and 4 inches. The reason why this pitch is called a two-thirds pitch is that in the case of a full pitch roof the rise for each foot of run is 24 inches, in this case the rise for each foot of run is 16 inches, and 16 inches is just two-thirds of 24 inches. Also the rise at the center of the span, 13 feet and 4 inches, is just two-thirds of the span, which is 20 feet. Whenever it is desired to give a roof a steeper pitch than the half pitch, the two-thirds pitch is generally employed.
If the roof is one of one-third pitch, the rise of the rafter for each foot of run will be one-third of the 24 inches which are required to make a full pitch, one-third of this being 8 inches. Thus a one-third pitch roof has a rise of 8 inches for each foot of run, and the rise at the center of the span is one-third of the entire span. If the span of the roof is 20 feet, the rise at the center of the span will be 6 feet and 8 inches, or just one-half as much as in the case of the roof of the same span and with a two-thirds pitch.
If the roof has a "one-quarter pitch," this means that the rise of the rafter for each foot of run is one-quarter of 24 inches, which is 6 inches, and that the rise of the roof at the center of the span is one-quarter of the entire span. If the roof has a span of 20 feet, this will make the rise in the case of a one-quarter pitch equal to 5 feet.
The pitches mentioned above are the most common pitches and those most generally used, though, of course, any pitch may be used as desired. The two-thirds pitch corresponds to an angle with the horizontal of about fifty-three degrees, and the one-half pitch corresponds exactly with an angle of forty-five degrees. The one-third pitch corresponds to an angle of thirty-three and three-quarters degrees and the one-quarter pitch corresponds with an angle twenty-six and one-half degrees. From this it will be seen that the names of the pitches, one-third, one-half, and one-quarter, do not express the relation of the angles which the various slopes make with the horizontal to the angle made by the roof of full pitch.
There are several factors which enter into the problem of determining the most suitable pitch to give a roof, and they must be carefully considered before arriving at a decision. In the first place there is to be considered the appearance of the finished roof when the building is completed. In this connection it may be said that personal preference and individual taste on the part of the designer are the determining factors, and that no hard and fast rules can be laid down. Another thing which must be thought of is the relative cost of the different slopes or pitches, as this is often of great importance and, in the case of a large number of buildings, would make considerable difference in cost. It may be said that in general a roof with a comparatively low pitch, say about thirty degrees, corresponding to a rise of approximately 6 7/8 inches per foot of run, is the most economical so far as the roof framing alone is concerned. Of course such a roof gives no accommodation in the attic portion of the building. Consideration must also be given to the question of the climate in which the proposed building is to be erected, as this will have a very decided influence upon the decision in regard to the most suitable pitch for the roof. In cold northern climates where the snowfall is great, it is best to have a roof with a steep pitch, so that it will shed the snow and rain, or melted snow as quickly and as thoroughly as is possible. In a warm southern climate where there is no snow and where the rain fall is not large, a roof of smaller pitch may safely be used and will be more economical of construction. The character of the material to be used for covering the roof surfaces must also be remembered in determining the pitch, since if this roof covering is very impervious to water the roof may be given a lower pitch than if the roof covering is more easily penetrated by rain and snow. In general it may be said that roofs covered with slates may be safely given a pitch of from 5 to 5 1/2 inches to the foot run, while a roof covered with shingles must not be flatter than thirty degrees or nearly 7 inches to the foot run. Flat roofs should be covered with some preparation of tar and gravel, or with metal, tin, copper, galvanized iron, or zinc. Any roof which has a rise of less than 3 inches to the foot may be considered to be flat.