How to Calculate Helical Length

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Updated October 26, 2020
By Samuel Markings

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.

    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}

    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}

    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}

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About the Author

Samuel Markings has been writing for scientific publications for more than 10 years, and has published articles in journals such as "Nature." He is an expert in solid-state physics, and during the day is a researcher at a Russell Group U.K. university.

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