Wednesday, June 12, 2013

Calculating stair/level depth?

Does anyone have a quick tool (or guideline) for knowing how to determine how deep a staircase takes you, or how long it would need to be in order to go down X depth?

For example, I have stairs on level 1 that go down to level 2. It's a straight set of stairs, and I'd like there to be 20' vertical distance between level 1 and the floor of level two. How long does that set of stairs need to be with a reasonable rise and run?

And then, say, I have another set of stairs on level 1 that go down to level 2, but now they stop halfway and then have a landing and then double back. How long do these need to be?

I've found some rise/run calculators on carpentry sites but I'm finding it hard to figure out how to use them. Anyone have a quick-and-easy calculator or reasonable guide, if not an easy to use tool?

I've already plotted out my dungeons, but if I can fix them depth so it's consistently correct that would be lovely.


  1. The tangent of the slope from horizontal is the rise-to-tread ratio.

    Modern American public building codes typically use a rise-to-tread of 17/29, about 30 degrees -- so 29 horizontal feet of stairway gets you down 17 feet. 45 degrees (1/1) is passable, but pretty steep. The UK currently has an absolute maximum slope of 42 degrees, which is about r-to-t 9/10. Let's assume that as a baseline.

    20 feet vertical consumes 22 feet horizontal on a straight run. (A modern American staircase would need 34 feet.) A single winder folds that to be 11 feet out and 11 feet back next to it, plus the width of the landing (which is probably the same as the width of the stairs, say 5 feet) - so 16 feet total.

    With an alternating tread stair you can go up to about 65 degrees, but it's not clear whether they existed before the late 1800s.

  2. A quick search shows these guidelines:
    "Over the years, carpenters have determined that tread width times riser height should equal somewhere between 72 to 75 inches.

    On a main stair, the maximum rise should be no more than 8 1/4 inches and the minimum run should be no less than 9 inches."

    So for anything that isn't a naval gangway, you're realistically looking at an 8" rise and 9" run, or 11.25' of run per 10' of rise for somewhat steep stairs.

    For a more comfortable 6" rise per 12" of run, it's an easy to remember 20' of run per 10' of rise.

    Scary steep stairs (think naval gangways) are going to be 12" rise per 6" of run, or a 10' rise in a 5' space. Which feels about right if you've actually toured a naval vessel.

    So in answer to your questions, assuming gentle stairs (6" rise, 12" run), you need 40' linear feet of run for a 20' rise. You can break that up with landings, in which case you just add the length of the landings to the overall length of the stairs.

    Spiral stairs are trickier, since they have a varying run per rise (much less at the center, more on the outside edges). I'd probably treat the required linear rise as the center of the stairs and figure it out that way - a 20' high spiral stair case with 5' wide steps has about 8/pi spirals, or just over 2.5 full rotations. So if you enter at the top facing north, you should come out at the bottom face south.

  3. You definitely can get away with 55 degrees in a dungeon. They have 55-degree stairs in real-world dungeons.

    (And they're really scary. Especially because they're slippery from the dripping limestone.)

  4. Thanks guys. I think the steeper stairs will take care of most of my dungeon levels.

  5. Well, as someone who lives in a country with a long history and that has seen many old dwellings, I must say that the real answer is "what do you want it to be?" Old buildings have often much steeper stairs than we soft modernlings fund comfortable. 45º stairs are not unknown, and steeper ones certainly exist. Also, remember, in a dungeon, either they re-purposed and expanded natural caves, or they dug out the whole thing. On the first case, stairs can be either cut on the rock, or built after the elevation change. On the second case, longer smoother stairs require considerable extra digging and building.

    Mind you, for playability, I would stick with 45º stairs being the norm, as it makes calculating them much easier ;)

    1. Steep, unsafe stairs are the norm in my dungeons. I just need to arrange more fights on them. ;)

  6. I was looking at this a different way myself; not for mathematical/historical accuracy, but to get an understanding of the "standard" dungeon stairs and how deep a gap there traditionally was between levels. It seems that most draw just a 10 or 20 foot stretch of steps, regardless of actual length/depth. There is often no mention of the vertical distance between the levels that I could see.

    In the end I decided on 40' from the floor of one level to the floor of the level above or below. Assuming 10' high corridors/rooms, this means normally 30 feet of solid earth/rock between levels, while leaving some "space" for high ceilings, deep pits and sublevels. I was tempted to go even deeper between levels, but then I thought the longer stairs would make it more obvious that comparatively short stairs aren't level changes. I'm also inclined to a shallow gradiant, at least for the shorter legs of the goblins and dwarves that built much of the original works of my dungeon, so I went with 30' long for 20' depth of stairs.

    I'm curious Peter, how do you arrange high ceilings and/or deep pits in your dungeon, with only 20' between?

    1. 20' was just an example so I could get the calculation right. I don't actually use 20' between all the levels. The first two are a bit less than that distance apart, though. The next one down is further down.


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