# The Brick Bakery: LEGO Dimensions.

When you are building with standard (non-Technics) LEGO, you seldom
have to worry about the dimensions of the parts - you build horizontal
rows of bricks with the studs pointing up and everything basically
"just fits". However, with Technics parts, there is greater opportunity
for placing parts so that the rows of studs run at unusual angles and
the question of the exact dimensions of parts becomes important.
Here is a picture that summarises most of the dimensions with
examples:

Referring to the numbers in the image:

- The height of 5 standard bricks equals the width of
6 studs. This is a fairly awkward number to deal with -
but that's life. Each stud is 8mm wide (about 5/16ths
of an inch) but that doesn't matter - LEGO enthusiasts
always measure things in units of 'studs'.
- Thin bricks ("Plates") are one-third of the height
of a standard brick. Hence there are 5 plate-thicknesses
for every two studs...which explains why LEGO chose to
provide 1/3rd thickness plates rather than half-thickness
as you might have expected.
- The Geometry of gear wheels seems easy at first sight.
Gear teeth are named according to the number of teeth they
have - so an 8t gearwheel has 8 teeth. The number of teeth
is always 8 times diameter of the gear (or 16 times its
radius). Hence:
- The 8t gear is 1 stud in diameter (0.5 stud radius).
- The 16t gear is 2 studs in diameter (1 stud radius).
- The 24t gear is 3 studs in diameter (1.5 stud radius).
- The 40t gear is 5 studs in diameter (2.5 stud radius).

...which is fine so long as you want to mount gear wheels
in a line along a beam - but if you want to mount them
at right angles to the rows of studs, that 5:6 relation
between the size of a stud and the height of a beam makes
life very messy. Figuring out the math is tricky - but
follow this link for more
details.
...and...
...show how the holes in a beam line up with the holes
in a vertical column of bricks. Notice that spacings of 3, 5 and 7
studs are possible with varying numbers of 1/3rd thickness
plates.
LEGO chains are designed to mesh with LEGO gears. 3 links
equals 2 studs.
This shows the relationship between the thickness of various
collars. The wide grey collar is one stud long - the narrow ones
are a half stud. The usual grey gears - and some wheels are also
one stud thick. The worm gears are actually a shade short of two
studs. Thin beams are also a half stud wide. LEGO axles are
always an exact number of studs long.
Angled components come at a variety of angles - the angled
beams bend at 45 degrees, the steep sloped bricks have a 45
degree slope on them - but the little step at the end of the
brick means that when you put them together, the total slope
is a little steeper than that (because of the 5:6 brick height
to stud size ratio). The gently sloping bricks are 25.7 degree
slopes (14 bricks make up a full circle)...but again, the slope
is a little steeper when the bricks are piled up.

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Steve Baker <steve@sjbaker.org>