# 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:

\(T = 10 × 6.60 = 66 \text{ meters}\)

### Cite This Article

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Markings, Samuel. "How To Calculate Helical Length" *sciencing.com*, https://www.sciencing.com/calculate-helical-length-7808380/. 26 October 2020.

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Markings, Samuel. (2020, October 26). How To Calculate Helical Length. *sciencing.com*. Retrieved from https://www.sciencing.com/calculate-helical-length-7808380/

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Markings, Samuel. How To Calculate Helical Length last modified March 24, 2022. https://www.sciencing.com/calculate-helical-length-7808380/