What is the Spiral Length Calculator?
The Spiral Length Calculator estimates the total developed length of a flat spiral or coil — such as a rolled strip of metal, a coiled hose, tape on a reel, or an Archimedean spiral track. Given the outer diameter, the inner (core) diameter, and the number of complete turns, it returns the unrolled length. The tool is unit-agnostic: enter all diameters in the same unit (mm, cm, inches, etc.) and the result comes out in that same unit.
How to use it
Enter the outer diameter of the fully wound spiral, the inner diameter of the empty core or starting point, and the number of turns the material makes between them. Click calculate to see the total length, plus the average diameter and the radial spacing added per turn (the pitch).
The formula explained
An Archimedean spiral grows by a constant amount each turn. Its length is well approximated by treating it as a stack of concentric circles whose diameters increase linearly from the inner to the outer value. The average circle has diameter \((D_{\text{outer}} + D_{\text{inner}})/2\), and there are \(n\) of them, giving:
$$L \approx \frac{\pi \cdot n}{2} \times \left(D_{\text{outer}} + D_{\text{inner}}\right)$$
This is equivalent to \(n\) times the average circumference, which is accurate as long as the turns are evenly spaced and the spacing is small compared with the diameter.
Worked example
Suppose a coil has an outer diameter of 100 mm, an inner core diameter of 20 mm, and 10 turns. Then $$L \approx \frac{\pi \times 10}{2} \times (100 + 20) = 15.708 \times 120 \approx 1884.96 \text{ mm},$$ or about 1.88 metres of material.
FAQ
Do the units matter? No — just keep them consistent. If diameters are in inches, the length is in inches.
Is the answer exact? It is a very close approximation for evenly wound spirals. The error grows only if the spacing per turn is large relative to the diameter.
What is the pitch value? It is the radial distance the spiral moves outward per turn: \(\frac{D_{\text{outer}} - D_{\text{inner}}}{2 \cdot n}\).
