Spiral Length Calculator

What Is Spiral Length?

Spiral length is the total distance along a curved spiral path. Two common cases are flat Archimedean rolls (like coiled tape or paper) and helical spirals wrapped around a cylinder (like a handrail or screw thread).

This calculator uses practical formulas for both cases. For related geometry, try our Spiral Staircase Calculator and Cylinder Calculator.

Archimedean Roll Formula

For a flat coil with outer diameter $D$, inner diameter $d$, and material thickness $t$:

$$N = \\frac{D - d}{2t}, \\quad L = \\frac{\\pi N (D + d)}{2}$$

Here $N$ is the number of turnings and $L$ is the spiral length. This approximation works well when thickness is small compared to the diameters.

Helical Spiral Around a Cylinder

When a helix wraps once around a cylinder of height $H$ and circumference $C$, unrolling gives a right triangle:

$$L = \\sqrt{H^2 + C^2}$$

The circumference relates to diameter by $C = \\pi D$.

Example

A roll with outer diameter 20, inner diameter 4, and thickness 0.5 has $N = (20 - 4)/(2 \\times 0.5) = 16$ turns and length $L = \\pi \\times 16 \\times (20 + 4) / 2 \\approx 603.2$ units.