Answers.Body: <p>You can derive detailed part geometry using the <a href="http://www.ldraw.org" rel="noreferrer">LDraw</a> parts library. LDraw provides freely accessibly models for nearly every part that Lego has produced. I'd recommend parsing these parts rather than rolling you own models if you're going to be using many parts.</p>
  
  <p>Here is the relevant content of <a href="http://www.ldraw.org/library/official/parts/6141.dat" rel="noreferrer">the file</a> representing a 1 x 1 round plate:</p>
  
  <pre><code>1 16 0 3 0 -1 0 0 0 -1.25 0 0 0 1 stud4.dat
  1 16 0 3 0 -6 0 0 0 -1 0 0 0 6 4-4disc.dat
  1 16 0 3 0 -2 0 0 0 -1 0 0 0 2 4-4ring4.dat
  1 16 0 0 0 10 0 0 0 3 0 0 0 10 4-4cylo.dat
  1 16 0 0 0 2 0 0 0 1 0 0 0 2 4-4ring4.dat
  1 16 0 0 0 2 0 0 0 1 0 0 0 2 4-4ring3.dat
  1 16 0 0 0 1 0 0 0 1 0 0 0 1 stud.dat
  </code></pre>
  
  <p>LDraw uses its own custom <a href="http://ldraw.org/article/218.html" rel="noreferrer">file format</a>. Units are in <a href="http://www.brickwiki.info/wiki/LDraw_unit" rel="noreferrer">LDU</a> and represent about .4mm.</p>
  
  <p>I won't try to describe the format in detail, but lines starting with <code>1</code> simply include another file that is translated, scaled, and rotated based on the included transformation matrix.</p>
  
  <h1>Base cylinder</h1>
  
  <p>We can break the part definition down to its components. The outside of the base cylinder corresponds to:</p>
  
  <pre><code>1 16 0 3 0 -1 0 0 0 -1.25 0 0 0 1 stud4.dat
  </code></pre>
  
  <p>stud4.dat represents a ring that could fit a stud inside of it. It's present in many parts (e.g. underneath 2xn bricks and plates). It looks like this:</p>
  
  <p><a href="https://i.sstatic.net/3DSUR.png" rel="noreferrer"><img src="https://i.sstatic.net/3DSUR.png" alt="stud4.dat render"></a></p>
  
  <p>Its outside is represented as (from stud4.dat):</p>
  
  <pre><code>1 16 0 -4 0 8 0 0 0 4 0 0 0 8 4-4cyli.dat
  </code></pre>
  
  <p>The primitive 4-4clyi.dat (4 fourths of a cylinder) is a basic open cylinder:</p>
  
  <p><a href="https://i.sstatic.net/Taj1w.png" rel="noreferrer"><img src="https://i.sstatic.net/Taj1w.png" alt="4-4cyli"></a></p>
  
  <p>Most LDraw primitives including this one are normalized size 1, so we start with a cylinder with height 1 and radius 1. A transformation matrix is then applied:</p>
  
  <pre><code>1 16 0 -4 0 8 0 0 0 4 0 0 0 8 4-4cyli.dat
              |               |
              +-------+-------+
                      |
  
                  8   0   0
                  0   4   0
                  0   0   8
  </code></pre>
  
  <p>Now, it's a cylinder of height 4 and radius 8. This was also transformed by the original inclusion of stud4.dat:</p>
  
  <pre><code>1 16 0 3 0 -1 0 0 0 -1.25 0 0 0 1 stud4.dat
  </code></pre>
  
  <p>We need to multiply its height by 1.25 to get a cylinder of height 5 and radius 8. Here's the final result:</p>
  
  <p><strong>Base height</strong> = 1 * 4 * 1.25 = 5 LDU * .4mm = 2.0mm</p>
  
  <p><strong>Base diameter</strong> = 2 * 8 LDU = 16 LDU * .4mm = 6.4mm</p>
  
  <h1>Middle ring</h1>
  
  <p>If you followed all of that, the middle ring is easy. It's outer wall is represented by:</p>
  
  <pre><code>1 16 0 0 0 10 0 0 0 3 0 0 0 10 4-4cylo.dat
  </code></pre>
  
  <p>So, it's a cylinder with a 10 LDU radius and 3 LDU height:</p>
  
  <p><strong>Middle ring diameter</strong> = 2 * 10 LDU * .4mm = 8mm</p>
  
  <p><strong>Middle ring height</strong> = 3 LDU * .4mm = 1.2mm</p>
  
  <h1>Checking our work</h1>
  
  <p>The height of the base and the middle ring sum to 8 LDU, which is good because this is the correct height for a plate like this.</p>
  
  <p>As you noted, you expected the outer ring to be 7.8mm, but I calculated it as 8.0mm. The reason for this is that LDraw uses the ideal sizes of bricks for its library. This is convenient for collision boxes in the theoretical world, but in reality, Lego has to make parts slightly smaller so that they fit between each other easily. As you mentioned, this tolerance is about .1mm per side, so we're in the right neighborhood with our calculations.</p>
  
  <p>In addition, most things in LDraw end up rounded to 1 LDU, so measurements have a tolerance of around +/- .2mm. Most Lego parts fit very nicely into a 1 LDU grid, so this isn't usually an issue. I'm not sure what level of precision you require, but my hunch is that the LDraw library will get you close enough for your needs.</p>
  
  <p>Good luck with your project, and let us know if we can help with anything else!</p>
  
Answers.ContentLicense: CC BY-SA 3.0
Answers.CreationDate: 2017-12-12T22:15:46.297Z
Answers.LastActivityDate: 2017-12-12T23:35:05.883Z
Answers.LastEditDate: 2017-12-12T23:35:05.883Z
Answers.UserDisplayName: jncraton
Answers.Body: <p>I have a micrometer for measuring with 0.1 mm precision. Using that I measured following lengths:</p>
  
  <ul>
  <li>diameter of top cylinder (stud): 4.9 mm</li>
  <li>diameter of lower cylinder: 6.4 mm</li>
  <li>diameter of middle ring: 7.9 mm</li>
  <li>height of middle ring: 1.0 mm</li>
  <li>total height of the plate: 5.1 mm</li>
  <li>inside diameter of lower cylinder: 4.9 mm (no surprise)</li>
  </ul>
  
  <p>Can anyone confirm or question these lengths? I would be interested in knowing whether I did it right.</p>
  
Answers.ContentLicense: CC BY-SA 3.0
Answers.CreationDate: 2017-12-12T08:03:46.033Z
Answers.Text: It's a "micrometer" in English, not to be confused with a "micrometre", which is 0.001mm
Answers.UserDisplayName: Matthew
Answers.ContentLicense: CC BY-SA 3.0
Answers.CreationDate: 2017-12-12T08:14:36.697Z
Answers.Text: Thank you. Now I also know the German word : Mikrometer
Answers.UserDisplayName: Metalbeard
Answers.ContentLicense: CC BY-SA 3.0
Answers.CreationDate: 2017-12-12T11:43:35.260Z
Answers.Text: The German word I know for this tool is "Messschieber".
  Also I'm confused: According to the graphic i linked (souce is german wikipedia) in my original Question, the diameter od the top circle should be 4.8mm instead of 4.9
Answers.UserDisplayName: IARI
Answers.ContentLicense: CC BY-SA 3.0
Answers.CreationDate: 2017-12-12T19:24:07.870Z
Answers.Text: There are several translations, as usual for highly specialised items. I measured several times the stud and also the inside of the tile. All times it was 4.9 mm or VERY close to that value.
Answers.UserDisplayName: Metalbeard
Answers.ContentLicense: CC BY-SA 4.0
Answers.CreationDate: 2021-04-28T17:06:28.267Z
Answers.Text: In stud.io, the middle ring is thicker than 2 LDU.  2.5 LDU looks about right.
Answers.UserDisplayName: crimson30
Answers.ContentLicense: CC BY-SA 3.0
Answers.CreationDate: 2017-12-11T23:25:03.443Z
Answers.LastActivityDate: 2017-12-12T16:09:04.230Z
Answers.LastEditDate: 2017-12-12T16:09:04.230Z
Answers.UserDisplayName: Metalbeard
Body: <p>What are the dimensions of the following Lego Part:</p>
  
  <p><img src="https://i.sstatic.net/MSQ99m.jpg" alt="Round Plate 1x1"></p>
  
  <p>I know of the basic dimensions shown in <a href="https://de.wikipedia.org/wiki/Lego#/media/File:Lego_dimensions.svg" rel="nofollow noreferrer">this graphic</a>.</p>
  
  <p>I believe, the diameter of the largest Ring is 7.8mm.
  However, I'm missing the following two measurements:</p>
  
  <ul>
  <li>diameter of the base-cylinder</li>
  <li>height of the base-cylinder</li>
  <li>height of the small big middle cylinder</li>
  </ul>
  
Comments.ContentLicense: CC BY-SA 3.0
Comments.CreationDate: 2017-12-11T23:31:33.783Z
Comments.Text: Is "lego-dimensions" the right tag? I think it refers to the LEGO computer game thing.
Comments.UserDisplayName: Metalbeard
Comments.ContentLicense: CC BY-SA 3.0
Comments.CreationDate: 2017-12-12T11:41:04.077Z
Comments.Text: Actually Im trying to model some lego pieces for AR-tracking, for whcih i need acurate measurements - so it has nothing to do with the computer game ;)
Comments.UserDisplayName: IARI
Comments.ContentLicense: CC BY-SA 3.0
Comments.CreationDate: 2018-02-06T13:46:24.543Z
Comments.Text: [This Bricks question](https://bricks.stackexchange.com/questions/288/what-are-the-dimensions-of-a-lego-brick) has additional information on LEGO sizes. First I thought your question is a duplicate, but it is not.
Comments.UserDisplayName: Metalbeard
Tags: <size>
Title: Round Plate 1x1 Dimension
UserDisplayName: IARI
ThreadText: # Round Plate 1x1 Dimension
  
  (Asked by: username_0 on 2017-12-07)
  
  What are the dimensions of the following Lego Part:
  
  ![Round Plate 1x1](https://i.sstatic.net/MSQ99m.jpg)
  
  I know of the basic dimensions shown in [this graphic](https://de.wikipedia.org/wiki/Lego#/media/File:Lego_dimensions.svg).
  
  I believe, the diameter of the largest Ring is 7.8mm.
  However, I'm missing the following two measurements:
  
  * diameter of the base-cylinder
  * height of the base-cylinder
  * height of the small big middle cylinder
  
  **Tags:** size
  
  > **Comments:**
  > **username_1**: Is "lego-dimensions" the right tag? I think it refers to the LEGO computer game thing.  
  > **username_0**: Actually Im trying to model some lego pieces for AR-tracking, for whcih i need acurate measurements - so it has nothing to do with the computer game ;)  
  > **username_1**: [This Bricks question](https://bricks.stackexchange.com/questions/288/what-are-the-dimensions-of-a-lego-brick) has additional information on LEGO sizes. First I thought your question is a duplicate, but it is not.  
  
  ---
  
  ## 2 answers
  
  ### Answer by username_2 on 2017-12-12. Score: 6
  
  You can derive detailed part geometry using the [LDraw](http://www.ldraw.org) parts library. LDraw provides freely accessibly models for nearly every part that Lego has produced. I'd recommend parsing these parts rather than rolling you own models if you're going to be using many parts.
  
  Here is the relevant content of [the file](http://www.ldraw.org/library/official/parts/6141.dat) representing a 1 x 1 round plate:
  
  ```
  1 16 0 3 0 -1 0 0 0 -1.25 0 0 0 1 stud4.dat
  1 16 0 3 0 -6 0 0 0 -1 0 0 0 6 4-4disc.dat
  1 16 0 3 0 -2 0 0 0 -1 0 0 0 2 4-4ring4.dat
  1 16 0 0 0 10 0 0 0 3 0 0 0 10 4-4cylo.dat
  1 16 0 0 0 2 0 0 0 1 0 0 0 2 4-4ring4.dat
  1 16 0 0 0 2 0 0 0 1 0 0 0 2 4-4ring3.dat
  1 16 0 0 0 1 0 0 0 1 0 0 0 1 stud.dat
  
  ```
  
  LDraw uses its own custom [file format](http://ldraw.org/article/218.html). Units are in [LDU](http://www.brickwiki.info/wiki/LDraw_unit) and represent about .4mm.
  
  I won't try to describe the format in detail, but lines starting with `1` simply include another file that is translated, scaled, and rotated based on the included transformation matrix.
  
  # Base cylinder
  
  We can break the part definition down to its components. The outside of the base cylinder corresponds to:
  
  ```
  1 16 0 3 0 -1 0 0 0 -1.25 0 0 0 1 stud4.dat
  
  ```
  
  stud4.dat represents a ring that could fit a stud inside of it. It's present in many parts (e.g. underneath 2xn bricks and plates). It looks like this:
  
  [![stud4.dat render](https://i.sstatic.net/3DSUR.png)](https://i.sstatic.net/3DSUR.png)
  
  Its outside is represented as (from stud4.dat):
  
  ```
  1 16 0 -4 0 8 0 0 0 4 0 0 0 8 4-4cyli.dat
  
  ```
  
  The primitive 4-4clyi.dat (4 fourths of a cylinder) is a basic open cylinder:
  
  [![4-4cyli](https://i.sstatic.net/Taj1w.png)](https://i.sstatic.net/Taj1w.png)
  
  Most LDraw primitives including this one are normalized size 1, so we start with a cylinder with height 1 and radius 1. A transformation matrix is then applied:
  
  ```
  1 16 0 -4 0 8 0 0 0 4 0 0 0 8 4-4cyli.dat
              |               |
              +-------+-------+
                      |
  
                  8   0   0
                  0   4   0
                  0   0   8
  
  ```
  
  Now, it's a cylinder of height 4 and radius 8. This was also transformed by the original inclusion of stud4.dat:
  
  ```
  1 16 0 3 0 -1 0 0 0 -1.25 0 0 0 1 stud4.dat
  
  ```
  
  We need to multiply its height by 1.25 to get a cylinder of height 5 and radius 8. Here's the final result:
  
  **Base height** = 1 \* 4 \* 1.25 = 5 LDU \* .4mm = 2.0mm
  
  **Base diameter** = 2 \* 8 LDU = 16 LDU \* .4mm = 6.4mm
  
  # Middle ring
  
  If you followed all of that, the middle ring is easy. It's outer wall is represented by:
  
  ```
  1 16 0 0 0 10 0 0 0 3 0 0 0 10 4-4cylo.dat
  
  ```
  
  So, it's a cylinder with a 10 LDU radius and 3 LDU height:
  
  **Middle ring diameter** = 2 \* 10 LDU \* .4mm = 8mm
  
  **Middle ring height** = 3 LDU \* .4mm = 1.2mm
  
  # Checking our work
  
  The height of the base and the middle ring sum to 8 LDU, which is good because this is the correct height for a plate like this.
  
  As you noted, you expected the outer ring to be 7.8mm, but I calculated it as 8.0mm. The reason for this is that LDraw uses the ideal sizes of bricks for its library. This is convenient for collision boxes in the theoretical world, but in reality, Lego has to make parts slightly smaller so that they fit between each other easily. As you mentioned, this tolerance is about .1mm per side, so we're in the right neighborhood with our calculations.
  
  In addition, most things in LDraw end up rounded to 1 LDU, so measurements have a tolerance of around +/- .2mm. Most Lego parts fit very nicely into a 1 LDU grid, so this isn't usually an issue. I'm not sure what level of precision you require, but my hunch is that the LDraw library will get you close enough for your needs.
  
  Good luck with your project, and let us know if we can help with anything else!
  
  
  ---
  
  ### Answer by username_1 on 2017-12-11. Score: 5
  
  I have a micrometer for measuring with 0.1 mm precision. Using that I measured following lengths:
  
  * diameter of top cylinder (stud): 4.9 mm
  * diameter of lower cylinder: 6.4 mm
  * diameter of middle ring: 7.9 mm
  * height of middle ring: 1.0 mm
  * total height of the plate: 5.1 mm
  * inside diameter of lower cylinder: 4.9 mm (no surprise)
  
  Can anyone confirm or question these lengths? I would be interested in knowing whether I did it right.
  
  > **Comments:**
  > **username_3**: It's a "micrometer" in English, not to be confused with a "micrometre", which is 0.001mm  
  > **username_1**: Thank you. Now I also know the German word : Mikrometer  
  > **username_0**: The German word I know for this tool is "Messschieber". Also I'm confused: According to the graphic i linked (souce is german wikipedia) in my original Question, the diameter od the top circle should be 4.8mm instead of 4.9  
  > **username_1**: There are several translations, as usual for highly specialised items. I measured several times the stud and also the inside of the tile. All times it was 4.9 mm or VERY close to that value.  
  > **username_4**: In stud.io, the middle ring is thicker than 2 LDU.  2.5 LDU looks about right.  
  
  ---
  
  