Concrete Stair / Stoop Volume Takeoff
The ready-mix volume of a poured stair or stoop = the stepped wedge plus the raking waist slab: cross-section = n triangular steps (each 1/2 x riser x tread) + the throat slab (throat thickness x rake length sqrt((n x riser)^2 + (n x tread)^2)), times the width; cy = in^3 / 46656. A 4-riser stoop at 7 in rise, 11 in tread, 48 in wide on a 4 in throat is about 10.1 ft^3 (0.37 cy); a 6-riser flight at 7.5/10 in, 36 in wide, 5 in throat is 12.5 ft^3. Order a bit over -- this is the neat geometry and ignores the nosing overhang, a top landing or bottom footing, and the rebar displacement. A ready-mix ordering estimate; the structural stair detail and the finisher's forms govern the pour.
Formula and source
steps_area = n x 0.5 x riser_in x tread_in; rake_length = sqrt((n x riser_in)^2 + (n x tread_in)^2); slab_area = throat_in x rake_length; volume_in3 = (steps_area + slab_area) x width_in; volume_cy = volume_in3 / 46656.
Concrete stair / stoop volume geometry, first-principles (the waist-slab-plus-steps takeoff method); the structural stair detail and the forms govern the actual pour.
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