This section is from the book "A Treatise On Architecture And Building Construction Vol3: Stair Building, Ornamental Ironwork, Roofing, Sheet-Metal Work, Electric-Light Wiring And Bellwork", by The Colliery Engineer Co.. Also available from Amazon: A Treatise On Architecture And Building Construction.

The next step is to ascertain the width of the treads, not forgetting the rules of proportion between treads and risers, and always remembering that the number of treads in each flight is one less than the number of risers; this is owing to the landing being counted as one tread.

There are several rules for determining the proportion which should exist between tread and riser for regular stairways, and upon which depends not only the appearance of the stairway, but the ease with which it may be traveled.

Three rules will be given, of which the first is the simplest, and is generally preferred.

Let the product of the tread and riser equal the number 66.

For example, assume that the riser is six inches high, then the width of the tread will be 66 ÷ 6 = 11 inches. In the same way, the width of tread may be assumed, and the height of the riser found.

To any given height of riser in inches, add a number that will make the sum equal 12; double the number added, and the result will be the width of the tread in inches.

For example, assume that the height of a riser is 7 inches; then 7 + 5 = 12, and 5 x 2 = 10, the width of the tread in inches.

Draw a right triangle, as shown in Fig. 8, with a base of 24 inches and altitude of 11 inches. Mark the width of tread from a on line a b, as a c; at c erect a perpendicular, cutting the hypotenuse at e. Then ce indicates the riser.

Fig. a.

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