Spindle math

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As I anticipate another rainy weekend where I may or may not be able to finish the carpentry on the porch, I thought I would explain some of the math involved with the geometry of the spindle spacing. You might recall that the only thing I have left to build and install are the spindles for the railings over the steps. I’ve decided to go with the angled stop chamfers and I built a prototype to convince myself that they will work. However, how many spindles do I need and where should they go?

If you think about it, if there are N spindles then there are N-1 gaps between the spindles and then some room left at each end. For example, if there are two spindles then there is the one gap between them, if there are 3 spindles then we have 2 gaps, and so on. The gaps between the spindles should all be the same size per section of the railing and these gaps should also ideally be the same size for all sections of railing. As you install them you may have some small variations but you should try to minimize these as much as possible.

Given a width for the railing section, how do you calculate how many spindles you need and where they should go? A very important consideration is the space left at each end. As a rule, it should be less than or equal to the space between the spindles and it shouldn’t be smaller than half the space between the spindles (what I call the “inter-spindle gap”).

In my situation for the railing on the left side of the steps, the total width of the railing section is 35 3/8 inches. This is the level horizontal distance between the posts. My spindles are 1 1/2 inches wide and my design inter-spindle gap is 3 inches. That is, the gap between the spindles is twice the width of the spindles. Let’s do some algebra.

Let N be the number of spindles that I will use to fit in this gap. The total space taken up by the spindles themselves is 1.5N and the total space taken up by the inter-spindle gaps is 3(N-1). Remember that there is one fewer gap than number of spindles. So if 35 3/8 (or 35.375 in decimals) is the total width, we have

1.5N + 3(N – 1) ≤ 35.75

which means

1.5N + 3N – 3 ≤ 35.75

which means

4.5N – 3 ≤ 35.75

which means

4.5N ≤ 38.75

which approximately means

N ≤ 8.62

and since we don’t want a fractional part of a spindle

N ≤ 8

This means we will have 8 or fewer spindles and since we need to experiment a bit to optimize how much space we’ll have left on the ends, we’ll consider the cases where we use 7 or 8 spindles. Here’s part of a spreadsheet that shows some calculations regarding the spacing. Incidentally, the spreadsheet was created in the IBM Workplace Managed Client and was saved in OpenDocument Format.

spindle spacing calculations

Moving through the main columns from left to right, using 7 spindles with 3 inch spacing leaves more than 3 inches at each end. Too big. Using 8 spindles with 3 inch spacing leaves less than 1 1/2 inches (half of 3 inches) at each end. Too small.

We need to fudge things a bit here. People will not be able tell the difference between 3 inch spacing and alternatives that are slightly smaller or larger. How much will depend on the person, but I think we’re safe with trying to add or subtract 1/8 inch. Adding that 1/8 inch in the 7 spindle case now leaves a smaller gap at the end, and it is almost exactly 3 inches. Subtracting an 1/8 inch and going with 8 spindles leaves gaps at the ends of 1 5/8 inch.

We could go either way here. I went with the last 8 spindle option because I like having the less than full spacing of the narrow spindles next to the much larger posts. You might like the alternative. If you’re not sure, ask some people what they think. It’s good to give your spouse or significant other a strongly weighted vote, in my opinion.

The final set of calculations we need to do concern the horizontal placement of the spindles. I measured from the upper post (that is, the one on the landing) and using the above numbers got the following measurements for where to put the left/upper edge of each spindle as I move down the steps.

spindle spacing calculations

My son William helped me transfer these measurement to the upper railing this morning. We used a long level and a square to make sure things were all straight. Double check all numbers and measurements before installing anything.

Next (on the porch project): “Stair spindles – ‘C’ wins – Halfway home”

One Comment

  1. This is by far one of the most unique blog posts I have ever read. See, things like this have made this site one of my favorites.

    PS Love the spindles above. I think I am going to have to use another door. I would feel guilty walking on that porch.

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