How much wire is needed for a coil?

Estimate wire length for coils

If the coiling wire is wrapped tight around the stem, the best wire length estimate should be n(d+t)𝝅, where n is the number of rotations around the stem d is the stem diameter and t is the coiling wire thickness. This experiment measures how this estimate compares to an actual coil for different combinations of d and t and determines reasonable padding p to include in a wire length estimate using n(d+t+p)𝝅.

I most often form coils around other wire such as 18ga or 20ga link stems or frame perimeters. So we'll use 18ga and 20ga wire as the coil stems and use their wire thicknesses as d. We'll test a range of coiling wire (18ga, 20ga, 22ga, 24ga, 26ga, 28ga) and use their wire thicknesses as t. Because it can be somewhat difficult to wrap a coil around a stem with the same gauge without bending the stem, we'll use softer copper wire for coiling and harder stainless steel wire as the stems to make it easier. Let n = 10 to get in enough rotations to measure a decent coil length.

First estimate an initial wire length as a little more than what you need and cut it to exact length. I added some padding p = 0.3 mm to the estimate using n(d+t+p)𝝅 and rounded the result to the nearest 1.0 mm to use as initial wire length.

Wrap the coiling wire tightly around the stem exactly n = 10 times, using chain nose pliers to push the coils together every few rotations. Let the ends stick out straight at a right angle on opposite sides of the coil. Lay the coils flat with ends face down as seen in the pictured example. Draw rectangles around the coils so that height h represents the residual length of wire and width w represents the coil length.

Calculate actual wire length used to create the coil by subtracting h from the initial wire length. Divide the actual wire length by n𝝅 to get actual wire length per rotation/𝝅. Estimated wire length per rotation/𝝅 = (d+t). The error (estimated - actual) shown in the chart is less than 0.06 mm for 18ga and 20ga coils and shrinks further for larger gauge (thinner) wire. The error spike for 24ga coiling wire around 20ga stem is caused by one coil made not quite as tight as the others and can be seen in the example picture above (4th coil from the left). The slightly negative values for the thinnest wires could be due to the limits of measurement resolution or could indicate that the thin wire was actually stretched and lengthened the tiniest bit in the process of coiling. Overall, coil wire length estimation is extremely accurate but it doesn't hurt to add a small amount of padding (0.05 or 0.1 mm) to the estimate for 18ga and 20ga wire.

Coil length can be estimated as nt. The actual coil length n(t+s) includes some space s in between each coil depending on how closely the coils can be squished together. The chart to the right shows coil length error (estimate - actual = s) per rotation (dividing coil length error by n). Overall, there is less than 0.05 mm space s in between each coil. Unlike wire length, coil length error does not necessarily diminish with thinner wire. In fact be aware that some thin wire may tend to spring back along the stem just like an actual spring. This means it will take fewer rotations and therefore less wire to achieve a desired coil length.