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I know it depends on the height climbed, the angle of the spiral and probably on the width of the staircase, but is there a quick way to calculate it?

Let's say we have a 10' radius spiral staircase (the steps are 9' wide) with a common angle (30 degrees), connecting two floors that are 100' apart.

How much distance would one have to travel to get to the second floor? And how many rounds would it take for a character with a walking speed of 30'(considering the stairs are not difficult terrain and without using the dash action)?

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  • \$\begingroup\$ For the round calculation, is the Dash action allowed? What class is the character? \ Also what is supporting the stairs if they are the same width as the radius (most spiral staircases have a column in the center)? \$\endgroup\$ – David Coffron Apr 12 '18 at 21:41
  • \$\begingroup\$ No dash action or whatever. I just want to know the time it takes to walk from the bottom to the top. If it's relevant, let's say we have a 24" column in the center. \$\endgroup\$ – Meta4ic Apr 12 '18 at 22:03
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    \$\begingroup\$ In all seriousness, how do you handle characters climbing straight stairs? \$\endgroup\$ – nitsua60 Apr 12 '18 at 23:35
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    \$\begingroup\$ @V2Blast This is not a physics question; solving it with physics is a possible answer but you could also use game logic to arrive at a workable approximation. Also physics is a terrible answer to this question. \$\endgroup\$ – Please stop being evil Apr 12 '18 at 23:39
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    \$\begingroup\$ I think since it is asking for a way to handle a real world situation using the game mechanics of a specified rule set, it's perfectly on topic. The OP is referencing the formula for spiral staircase length, but what they are really asking is "how can I easily approximate this in D&D 5e?" \$\endgroup\$ – keithcurtis Apr 13 '18 at 0:16
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The precise number of feet traveled probably isn't important, so handwave it and move on.

The exact number of feet that a character or group would have to travel to ascend 100 feet via spiral staircase is going to require a bunch of math, and calculating that number will probably slow down play in a session. In addition, it's probably not going to make a huge difference in play if you just handwave the number; that is, it's probably not going to hurt your players' feeling of verisimilitude that the number is off by a bit. It's important to know how many feet your players will have to travel to go between floors, but it's not important for that number to precisely match reality.

With all that said, I have two ways to handwave this number to present.

Version 1: 200 feet.

One step on a staircase is about 1 foot long. I estimate this because I'm personally a size 11 shoe, and most steps are about the size of my foot. One step up is about 6 inches. I estimate this in the same way; most steps that I travel on are about half the size of my foot. With these two numbers, we know that we have 200 steps to travel (100 feet up * 2 steps per foot) and each step is about a foot long. Thus, 200 feet to travel. This would take 7 rounds to travel, and would have 10 feet of movement left over.

Version 2: 100 feet.

This is the version I prefer. In this case, no calculation is done. It's simply assumed that 100 feet is 100 feet, and that play time is too valuable to spend on calculating the sides of a triangle. In this case, it would take 4 rounds to ascend the stairs, with 20 feet left over.

In either case, I would strongly suggest treating the stairs as difficult terrain. Walking up or down stairs is harder than walking on flat ground, and that's exactly what difficult terrain was meant to represent. If you treated the stairs as difficult terrain, then the two versions would take 14 and 7 rounds, respectively.

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    \$\begingroup\$ I agree that this is usually not that important, but I came to the same 200' number by calculating the distance on a triangle. I think calling the stairs difficult terrain is simple enough to deal with the problem. \$\endgroup\$ – Shem Apr 13 '18 at 0:02
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    \$\begingroup\$ It's simpler in engineering rules (rise/run ratio) than scientist rules (degree angle). A spiral staircase is a continuously variable staircase, so you can dial any stair pitch you want. 1:1 (1' run to 1' rise, 100% grade, 45°) would be about as steep as you'd want to go, giving 100' rise and 100' run or 200'. Done. \$\endgroup\$ – Harper - Reinstate Monica Apr 13 '18 at 19:32
  • \$\begingroup\$ Version 1 makes sense to me. It provides a quick and simple rule of thumb to estimate the distance travelled. I don't think stairs should always be treated as difficult terrain, but as you suggest, difficult terrain may apply, effectively doubling the time needed to ascend or descend. Finally, there are some instances where knowing the precise number of feet travelled is relevant : multilevel battleground, puzzle challenge, chases, dungeons with long staircases (Ravenloft Castle comes in mind), etc. \$\endgroup\$ – Meta4ic Apr 14 '18 at 12:08
  • \$\begingroup\$ @Meta4ic I added a line to address your concerns. My point isn't that the number doesn't matter at all, my point is that the number doesn't have to match reality. It matters that it's a specific number of feet from one floor to another, it doesn't matter if that matches a similar spiral staircase IRL. \$\endgroup\$ – DuckTapeAl Apr 14 '18 at 17:39
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Call the stairs difficult terrain and call it good…

Let's specify some things:

  • 100' elevation change (~10 stories on today's measurements)
  • Stairs are at 30° angle (the standard is 32° in the US, but 30° will make the math easier)

We don't actually have to deal with the circular component of this, because D&D doesn't define rotational movement any different than linear movement. So we will just picture a straight staircase. In fact it's the same distance traveled for someone going up the stairs, it just takes less horizontal space.

So, the distance traveled can be determined by the hypotenuse of a triangle. The height of this triangle is 100', and the angle opposite to this height is 30°. $$\sin(30°)=o/h$$

$$\sin(30°)=1/2=100/h$$

$$h=200$$

So the distance traveled (h) is 200', or twice the elevation change. Since this is the same as difficult terrain, it's easy to just call the stairs difficult terrain and move on.

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    \$\begingroup\$ I will say, as someone who regularly climbs spiral stairs spanning 50' and even 100' elevation change (church bell-ringing): you're absolutely right that rotational vs. linear doesn't matter. [edit: For speed, that is. I'm saying that a person who can handle spiral stairs at all handles them at roughly the same speed as they do straight stairs. PeteKirkham made a good point about vertigo setting a barrier for some, though.] \$\endgroup\$ – nitsua60 Apr 12 '18 at 23:42
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    \$\begingroup\$ Well, technically you can travel less distance by moving along the inside of the circle (this calculation assumes moving along the center of the stairs). However, you cannot run as fast around a circle like that than you can running in a straight line. So they probably come close enough to cancel out. \$\endgroup\$ – Shem Apr 12 '18 at 23:58
  • \$\begingroup\$ I find it fascinating that a person walking up a spiral staircase will require as much movement to ascend it as a person who is outside the tower climbing the wall. (Not criticizing this analysis: just pointing out that this is a really interesting coincidence to me. And one which provides the game with a surprising amount of balance, and allows for some interesting dramatic situations). \$\endgroup\$ – Gandalfmeansme Apr 13 '18 at 2:24
  • \$\begingroup\$ @nitsua60 I will say, as someone who avoids climbing spiral stairs as they give me vertigo, that the rotational aspect matters a lot. \$\endgroup\$ – Pete Kirkham Apr 13 '18 at 9:45
  • \$\begingroup\$ Are we sure the OP was referring to the angle of the staircase and not the angle of the steps with the 30 degree figure? Steps in a spiral staircase have an angular factor since they can be built to encompass a circle \$\endgroup\$ – David Coffron Apr 13 '18 at 11:56
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I think this is needless overcomplication. Fifth Edition tells us that the Pythagorean Theorem is c = the greater of b or a. Diagonals are effectively nonexistent. Trigonometry is even less relevant. The great imperative is making things quick and easy, so that no calculations get in the way of going ahead with the action.

The very simplest and most expedient thing to do would be to treat spiral stairs as difficult terrain and charge 10 feet for every 5 feet of movement (in this case elevation change) and get on with killing whatever evil thing needs killing on the second floor.

I know you don't consider stairs difficult terrain in your question, but they really should be, especially spiral stairs.

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    \$\begingroup\$ Thank you for adressing the question. However, I don't remember having asked for a judgment over the complexity of the question - nor the necessity of it. As a DM, I reckon it's my job to resolve complex questions, and then run it as simple as possible at the table. As for considering stairs difficult terrain, it's always a possibility (a DM decision, depending on the nature of the stairs), but even at half speed, the distance have to be travelled, so it must be known. \$\endgroup\$ – Meta4ic Apr 13 '18 at 18:04
  • \$\begingroup\$ Feel free to downvote the answer if you think it is not useful or misleading. You will always get a variety of answers. You asked "is there a quick way to calculate it ['How much movement is needed']?" This answer addresses that, and tries to reconcile what is actually a mathematical question with how such complexity is abstracted within the rule set (hence beginning with demonstrating the principle via the way the system ignores the calculation of the diagonal.) \$\endgroup\$ – keithcurtis Apr 13 '18 at 19:12
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This sounds like a physics problem, so let's start by simplifying it to get some intuition. The problem of ascending stairs is essentially a problem of moving one's center-of-mass along the hypotenuse of a right triangle. The height of this triangle is fixed at 100' (the vertical distance to ascend), but the horizontal distance is unspecified, and depends on the slope of the stairs.

If the stairs are not difficult terrain, I interpret that to mean that they aren't particularly steep; that they are shallow enough to climb without much effort. If we estimate a 45-degree incline, then we can easily calculate the length of the hypotenuse as approximately 140'. This is roughly 5 rounds of movement at standard 30' speed, without dashing.

For a spiral staircase, the slope varies linearly from the inside to the outside edge of the stairs. Assuming no obstacles, a climber can minimize the distance traveled by maximizing steepness; moving as close to the inside edge as possible without the steepness becoming difficult terrain. So our straight-staircase estimate stands, if we accept 45-degrees as the maximal incline that isn't difficult terrain.

In general, we can multiply the height of the stairs by 1.4 to get a reasonable estimate for distance in feet, or divide the height by 20 to get a reasonable estimate of the number of rounds to climb at speed 30'.

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  • \$\begingroup\$ As an engineer who has worked with such things, 45 degrees would even a very sharp angle, and I might define it as difficult terrain if it was that sharp. 30 degrees would be a much more accurate estimation (technically, the standard is 32 degrees, but 30 degrees makes much easier math). \$\endgroup\$ – Shem Apr 12 '18 at 23:21
  • \$\begingroup\$ @Shem thanks for the insight. I agree 45 is probably too steep, but I would guess modern building codes are a lower rise than the historical norm; the difficult-terrain threshold for D&D heroes is probably somewhere in between. Either one makes for a good enough table estimate I'd wager. \$\endgroup\$ – starchild Apr 13 '18 at 0:05
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Unfinished without specs for the steps themselves

You essentially break the movement into two sections: vertical movement and movement around the staircase. The movement around the staircase can be mapped to a straight line (horizontal movement) using geometry.

Horizontal Movement

One rotation around the staircase takes a minimum travel distance equal to the circumference of the [center column plus the gap needed for the character to move]. In 5e, the precise location of its motion is not specified, so the space between its feet and the center column is 0.

  • Center Column Radius = 1 foot
  • Character Gap (RAW) = 0
  • Movement (Circumference) = 2 * pi * (1 + 0) = 2 * pi

Then multiply this by the number of rotations based on the size of the steps.

Vertical Movement

The vertical movement is the height of the staircase which is 100 feet.

Total Movement

Pythagorean Theorem gives the total movement since we have mapped the movement around to a straight line which gives us ....

How many rounds?

Assuming the character's features and traits are not relevant, a character could scale the staircase in X rounds [CEILING(.../30)]

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  • \$\begingroup\$ This appears to assume that the character makes only one trip around the circle. At 30-degrees each, that's 12 steps totaling 100', or more than 8' vertical rise per step. That sounds like difficult terrain to me! \$\endgroup\$ – starchild Apr 12 '18 at 22:19
  • \$\begingroup\$ For a quick sanity-check, the final answer presented here is barely more than the height - the distance traveled by climbing straight up. \$\endgroup\$ – starchild Apr 12 '18 at 22:21
  • \$\begingroup\$ @starchild yes. I was modifying my original answer which had no center column and the value was 100 feet (bouncing straight up the steps). I will revise \$\endgroup\$ – David Coffron Apr 12 '18 at 22:23
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Never less than 25 feet, 200 feet in your example

On a typical battle map, spiral stairs take up 4 spaces in a square. In order to resolve travel along them, assign them whatever number feels right to you when designing the map, but never less than one more square beyond the 4 they take up. If you are using a pregen map, quickly scan for floor distance and double it to discern the required movement if none is given. If you have a spiral staircase that doesn't take up exactly 4 spaces on a battle map you should make up a different number, but I don't think I've ever seen such a staircase published without its own special rules.

This isn't a rule published anywhere as far as I'm aware, but it's how I've been GMing this for years and years across multiple iterations of D&D (including ones with 10' squares, which means no less than 50' movement on a 2X2 or 25' on a 1X1) and it's worked well.

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