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How do I calculate the length of the railing for a spiral staircase?

You need to know three things:

(1) The distance from the railing to the axis of the staircase (the radius r),

(2) The rise of the staircase in one revolution (H), and

(3) The number of revolutions (or the total height) of the staircase. What you do is envision the railing as a helical line traced out on a cylinder. If you unroll the cylinder, this becomes a sloping line (or several identical sloping lines) on a plane. This line (or each of these lines) is the hypoteneuse of a right triangle with a height of the repeat distance and a base length of the circumference of the circle. The square of the length of this hypoteneuse is equal to the sum of the squares of the other two sides. So,
L = (H^2 + C^2)^(0.5), where
L is the length of railing in one turn of the staircase,
H is the height of one turn of the staircase, and
C is the circumference of the cylinder = 2 pi r.
All you then need to get the total length of the railing is the number of turns N. The total length of the railing is NL.

Richard E. Barrans Jr., Ph.D.
Assistant Director
PG Research Foundation, Darien, Illinois

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