How this calculator works
A straight flight is modelled by a constant-thickness waist slab parallel to the pitch line and identical triangular steps above it. Nosing adds a triangular extension across the full riser height; a riser sloping inward at its top removes a triangular wedge. This explicit side-profile model does not describe a thin rectangular nosing lip, solid stairs filled to ground level, landings or support beams. Reverse volume is net, without waste.
Formula
Step wedge area = rise x (run + triangular nosing - rise x tan(riser recess angle)) / 2; carriage = steps x sqrt(run^2 + rise^2); waist area = throat x carriage; V = width x (steps x wedge area + waist area).
Worked example
Four steps with 0.3 m run and 0.4 m rise have 2 m carriage length. Each triangular step has 0.06 m2 side area. A 0.1 m waist adds 0.2 m2, giving (4 x 0.06 + 0.2) x 1 m width = 0.44 m3.
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Frequently asked questions
Where do I measure throat depth?
Measure normal to the sloping waist slab, not vertically. The model multiplies this depth by the sloping carriage length.
Does step count include the upper landing?
Enter the number of repeated wedges actually cast in the flight. Measure and add a landing as its own slab.
Can a reverse step count be fractional?
Yes. It is a volume equivalent, not a buildable stair layout. Choose an integer step count and verify the actual stair geometry separately.