How this calculator works
A strip of constant thickness wound into a roll follows an Archimedean spiral: every full turn increases the radius by one thickness. The number of turns is therefore the radial build-up divided by the thickness, N = (D - d)/(2t). Each turn has a slightly larger circumference than the one before, so the total length is close to the average circumference of the roll multiplied by the number of turns. That gives L = πN(D + d)/2, which is also written as π(D² - d²)/(4t). The result is an average-circumference approximation; for a roll with many turns the difference from the exact spiral arc is negligible. The calculator can solve for either diameter, the thickness or the number of turns from the others.
Formula
N = (D - d)/(2t); L = πN(D + d)/2 = π(D² - d²)/(4t); D = d + 2tN; d = D - 2tN; t = (D - d)/(2N). D and d are the outer and inner diameters, t is the thickness and N is the number of turns.
Worked example
A roll with outer diameter 0.10 m, inner diameter 0.02 m and strip thickness 0.001 m has N = 0.08/(0.002) = 40 turns and length L = π × 40 × 0.06 ≈ 7.5398 m.
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Frequently asked questions
What does the number of turns mean?
It is the number of complete wraps between the inner and outer diameters. Each wrap adds one strip thickness to the radius, so the total is the radial difference divided by the thickness.
Is the length exact?
The formula uses the average circumference of the roll for each turn. The exact Archimedean arc is slightly different, but the difference becomes very small once a roll has more than a few turns.
Can I solve for the thickness or a diameter?
Yes. Switch the mode to the unknown you want. Include any gap between layers in the thickness, because a loose wind uses more radial space per turn.
Does the answer include a loose end or an overlap?
No. Add the length of any unwound tail, leader or overlap separately. The calculation covers only the wound part between the two diameters.