How to Calculate a Spiral

••• real444/iStock/GettyImages

Spirals are one of nature's (and mathematics') more surprising and aesthetic phenomena. Their mathematical description may not be immediately apparent. But by counting a spiral's rings and making a few measurements, you can figure out some key properties of the spiral.

    Determine the number of rings in the spiral. This is the number of times the spiral curve wraps around the center point. Call this number of rings "​R.​"

    Determine the outer diameter of the spiral as a whole. This is the length of a straight line that runs from one point on the spiral's outer circumference to a point on the circumference's opposite end. Call this length "​D​."

    Determine the inner diameter of the spiral. This is the diameter of the circle formed by the innermost ring of the spiral. Call this length "​d​."

    Plug the numbers obtained in the first three steps into the following formula:

    L = \frac{3.14 × R × (D+d)}{2}

    For example, if you had a spiral with 10 rings, an outer diameter of 20 and an inner diameter of 5, you would plug these numbers into the formula to get:

    L = \frac{3.14 × 10 × (20+5)}{2}

    Solve for "​L​." The result is the length of the spiral. Using the example from the previous step:

    \begin{aligned} L &= \frac{3.14 × 10 × (20+5)}{2} \\ &= \frac{3.14 × 10 × 25}{2} \\ &= \frac{785}{2} \\ &= 392.5 \end{aligned}

    Tips

    • Be sure to take all measurements of the spiral in the same units.

Related Articles

How to Calculate Volume of a Circular Cylinder
How to Calculate Volume
How to Calculate the Base of a Shape
How to Find the Circumference of an Octagon
How to Construct a Rhombus With a Compass & Straight...
How to Calculate a Temperature Range
How to Calculate Volume of a Rectangular Prism
How to Calculate Helical Length
How to Calculate Electrical Winding Wires by Weight...
How to Find the Area of a Shaded Part of a Square With...
How to Calculate the Diameter of a Rectangle
How to Calculate Circumference in Inches
How to Convert Square Dimensions to Round
Characteristics of Aquatic Plants
How to Calculate Diameter From Circumference
What Kinds of Metals Do Not Stick to Magnets?
How to Convert Diameter to Square Centimeters
How to Calculate the Volume and Circumference of a...
How to Calculate Mechanical Advantage Screws
How to Calculate a 3D Perimeter