The Ubiquitous1 Draw Ratio

Probably the first thing a
novice hears in thermo-
forming after he/she learns to
spell “thermoforming,” is the
phrase, “Draw Ratio.” So, this
lesson focuses on the concept of
draw ratio.

Is There More Than One

Unfortunately, yes. There are
at least three definitions. Let’s
define the common ones.

Areal Draw Ratio, often given
the symbol RA, is the ratio of the
area of the part being formed
to the area of the sheet needed
to make the part. Although I
promised not to use equations
in our TF 101 lessons, some
simple ones here won’t hurt all
that much:

RA = AreaPart/AreaSheet

A simple example, please?
Consider a cylinder one unit in
diameter by one unit high. The
area of the cylinder is (.+./4)
= 5..4. The area of the sheet
used to form the cylinder is
./4. Therefore the areal draw
ratio, RA, is 5. As an interesting
aside, the reciprocal of the
areal draw ratio is the average
reduced thickness of the formed
part, being 1/5 = 0.20. In other
words, the original sheet thickness
has been reduced by 80%,
on the average.

Linear Draw Ratio, often
given the symbol RL, is the ratio
of the length of a line scribed
on the part surface to the original
length of the line. Again, in
equation form:

RL = LinePart/LineSheet

For the same example, the length
of the line on the cylinder is
(1+1+1) = 3. The original length
of the line is 1. Therefore, the
linear draw ratio, RL, is 3. The
linear draw ratio is akin to
the way in which the plastic
is stretched in a tensile test

Height-to-Diameter Ratio,
often written as H:D, is the
height of the cylinder (1), to the
diameter of the cylinder (1). Or
H:D = 1. H:D is used primarily
for axisymmetric2 parts such as
cones or cylinders, such as drink

In summary, for the cylinder
described above, RA=5, RL = 3,
and H:D = 1. So you see, there
is no agreement between these

Are Draw Ratios of
Use? Importance?

So, which one do we use?
Depends. First, we need to
determine whether draw ratio is
a useful concept.

Let’s focus on areal draw
ratio to determine its utility.
As we have already learned,
the reciprocal of RA is the average
reduced thickness. But
where is this reduced thickness?
Somewhere down the side of
the formed part. In fact, there
is probably a line around the
periphery of the part where
the part thickness is exactly the
average reduced thickness. So,
what does this tell us about
the uniformity of the part wall
thickness? Or the degree of difficulty
in forming the part? Or
whether webs are formed somewhere
in the part? Or what the
plug needs to look like? Or …?
Really, nothing.

Having said that, areal draw
ratio is perhaps the easiest
concept to understand. Linear
draw ratio, as noted, is often
compared with extension limits
determined from tensile
testing equipment. And H:D is
often used in Europe to describe
formability of plastics for cup

At best, draw ratios represent
bragging rights rather than information
about the degree of
difficulty in forming the parts.
Many formers will tell you that
parts that have very small draw
ratios are much more difficult
to form reliably than parts with
large draw ratios. And parts
with many compartments are
far more difficult to form than
parts with single compartments,
even when the draw ratios of the
two types are identical.

[See? Those equations didn’t
hurt at all, now, did they?] ¦

Keywords: Areal draw ratio,
linear draw ratio, H:D



1 Ubiquitous: Being present everywhere
at once.

2 Axisymmetric: Having symmetry around
an axis.

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