How To Calculate Helical Length

A helix is defined as a spiral that also has a linear dependence upon a third dimension. Found both within nature and within the man-made world, examples of helices include springs, coils and spiral staircases. The length of a helix can be calculated using a simple formula.

Step 1

Write down the quantities that define the helix. A helix can be defined by three quantities: the radius, the rise of the helix in one revolution and the number of turns. For this example, we will define the following symbols:

\(r = \text{ Radius}\)
\(H = \text{ Rise of helix in one revolution}\)
\(N = \text{ Number of turns}\)

Step 2

Calculate the length associated with one turn within the helix. To do this use the following formula:

\(L = \sqrt{H^2 + C^2}\)

In this nomenclature, H^2 means "H multiplied by H" or "H squared." C is the circumference of the circle and is equal to :

\(C = 2 × 3.145 × R\)

For example, if a spiral staircase has a radius of 1 meter, then the circumference is equal to :

\(C = 2 × 3.145 × 1 = 6.29 \text{ meters}\)

If the staircase rises by approximately 2 meters after each turn (H = 2) then the length associated with one turn around the staircase is:

\(L = \sqrt{2^2 + 6.29^2} = \sqrt{4 + 39.6} = 6.60 \text{ meters}\)

Step 3

Calculate the total helical length (T). To do this use the formula:

\(T = NL\)

Following the example, if the staircase has 10 turns:

\(T = 10 × 6.60 = 66 \text{ meters}\)