The Formula for the Circumference of a Spiral

C = 2 * Pi * R = Pi * D

This is the well-known formula for the circumfence of a circle, and it can partially be used to figure out the circumference of a spiral!

Circumference = Pi * (A + B + C +...+ Z). Each letter in the parentheses stands for the radius of an arc.

Note: you can simply remove the "2" from the formula(in terms of radii) to find out half of the circumference of a circle! A perfect, circular spiral is just a bunch of semicircles combined!

I'll show one example of an equation:

Radius of 1st arc = 5

Radius of 2nd arc = 3

Radius of 3rd & smallest arc = 1

Pi(5 + 3 + 1) = Pi * 9 = 28.2743338...

which is the circumference of the spiral!

The formula is simple enough for spirals that are perfectly circular, but what if the spiral happens to be more like an oval?

The formula gets more complicated since the circumference of an oval is quite a complex formula! C = 2 * Pi * the Square Root of (X^2 + Y^2)/2, so for an oval-like spiral, Circumference = Pi * (The Square Root of (A^2 + B^2)/2 + the Square Root of (C^2 + D^2)/2 +...+ the Square Root of (Y^2 + Z^2)/2). Each letter in parentheses stands for the longest or shortest radius of an arc.

Sometimes, if it's necessary, try multiplying the circumference of a radius' corresponding circle by a fraction! Use a protractor to measure the amount of degrees in an arc's angle, then divide the number by 360 since that's the number of degrees in a full circle! That's the fraction you should multiply by!

Of course, Derek C. Jr.'s tip will also work for the circumference of an oval!

To make things simpler, you can multiply the radius of an arc by the angle of the same arc in radians.

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© Derek Cumberbatch