SIMETRIUM .COM s · √2 series · ISO 128
SERIES · DRAFTING AND CAD
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Notation
GOST 2.303 denotes the weight of the continuous thick line by the letter s, and the thin line as s/2 or s/3. ISO 128 speaks of line groups: «group 0.5» means 0.5 and 0.25 mm.
Do not confuse
Line weight is the width of a stroke on paper, not in the model. It does not change with the view scale, but it shrinks together with the sheet when the drawing is copied.
On the plate is a rack of nine technical pens. Each has a ring of its own colour on the cap: under ISO 9175 this is how the width is recognised without reading the label. One by one the pens come down to the sheet and draw a line each: 0.13, 0.18, 0.25 … 2.0 mm. For clarity each one writes in the colour of its ring; the real ink is black in every pen. Each line is thicker than the previous one by almost exactly √2 — below is the live ratio of the last two lines.
Quantity passport · drafting and CAD · length on paper

Lineweight

Series 0.13 … 2.0 mm in steps of √2 · ISO 128-20 · GOST 2.303 · line groups

An A3 drawing is put on a copier and reduced to A4. All lengths become √2 times shorter — and so do the line weights. A 0.5 mm line comes out at 0.35 mm, a 0.25 line at 0.18. Both land in the standard series again, because the series of line weights is built on the same factor as the sheet sizes.

The ISO 128 series has nine values: 0.13, 0.18, 0.25, 0.35, 0.5, 0.7, 1.0, 1.4 and 2.0 mm. A thick line is twice as thick as a thin one, which is two steps of the series. The series does not go below 0.13: at the next reduction or on microfilm such a line breaks up into dots, and hatching merges into a grey patch.

Notations — continuous thick line · d — line width in ISO 128-20
ISO 128 series0.13 · 0.18 · 0.25 · 0.35 · 0.5 · 0.7 · 1 · 1.4 · 2 mm — step √2 ≈ 1.414
Line groupsthick : thin = 2 : 1 — 0.25/0.13 · 0.35/0.18 · 0.5/0.25 · 0.7/0.35 · 1/0.5
GOST 2.303continuous thick s = 0.5…1.4 mm · thin, dashed and thin chain lines — s/3…s/2
Spacingbetween parallel lines at least 0.7 mm on paper
Pen ring colour0.13 violet · 0.18 red · 0.25 white · 0.35 yellow · 0.5 brown · 0.7 blue · 1 orange · 1.4 green · 2 grey
To the plotter and copier AutoCAD tip
01 · Definition

A stroke width tied to the sheet size

Line weight is the width of the trace a pen or toner leaves on paper, in millimetres. It is an ordinary length, but its series is matched to the A sizes: the sides of an A sheet are in the ratio 1 : √2, and moving to the neighbouring size changes all dimensions by a factor of √2. If line weights go in the same step, a reduced drawing is still a drawing to standard.

Exact √2 gives 0.125, 0.177, 0.25, 0.354, 0.5, 0.707, 1, 1.414, 2. The values were rounded to hundredths, and the ratio of neighbouring weights wanders from 1.38 to 1.43. The thin line is taken two steps thinner than the thick one — exactly half. So every drawing gets its own group: the weight of the continuous thick line is chosen by sheet size and complexity, and the others are derived from it.

d — line width, mm · n — position in the series · s — continuous thick line · k — sheet reduction factor
Interactive · the drawing is reduced

What happens to the lines on smaller sheets

The buttons are the weight of the thick line and the sheet size the drawing was made on. The rows are the same drawing reduced to each next A size. The blue bar is the thick line, the green one the thin line; if the thin line drops below 0.13 mm, it turns red. The scale is logarithmic, from 0.05 to 2 mm.

Thick line s
Original size

Interactive · plotter, magnifier and copier

Five parts, four line groups, three reductions

The main action is the «Start plotting» button. The plotter draws a part on an A3 sheet: first the thick lines with a thick pen, then it changes to a thin pen and draws centre lines, threads, hatching and dimensions. A ×8 magnifier settles over a spot where a thick and a thin line run side by side. Then the sheet is reduced three times on the copier — to A4, A5 and A6, each time by a factor of √2. The lines slim down with the sheet; when the thin line drops below 0.13 mm, the toner breaks it into dots and the hatching turns grey. Each line on the sheet is coloured with the ring colour of the pen that drew it. Below the scene you choose the part — a shaft, a gear, a housing in section, a bracket or a bolt — and the line group: 0.35, 0.5, 0.7 or 1.0. The slider rewinds the plotting both ways.

left: control panel — group, weights on paper, sheet size, hatch spacingright: pen rack, series scale, lineweight table
Main action
Rewind0.0 s
Part
ISO 128 line group
Thick on paper
—
—
Thin on paper
—
—
Hatch spacing
—
—
Sheet
—
—

—

The √2 series and where the lines are now
weight, mm, logarithmic scale
The coloured rings are the nine pens of the series. The blue dot is the thick line on paper now, the green one the thin line; the pale dots show where they were before each reduction. To the left of the red mark at 0.13 there are no pens.
Weights by copy
thick and thin, mm
Four pairs of bars — A3 and three reductions. The dashed line is 0.13 mm. The pair now on the copier is highlighted.
Weights over time
mm, logarithmic scale
The steps are reductions on the copier. Each one lowers both lines by exactly one step of the series. Below the dashed line the thin line breaks up.
02 · Conversion
in millimetres
×10

A point is 1/72 inch, 0.3528 mm. A 1 pt line from graphics software is almost exactly 0.35 mm, the yellow-ring pen. A 0.25 pt hairline is 0.09 mm, thinner than the lower limit of the series.

The AutoCAD lineweight list is longer than the ISO series: it has 0.30, 0.53, 1.06 and 2.11 mm for old pens and inch sets. For an ESKD drawing the nine values of the series are enough.

LWEIGHT, mmISO peninchespt
03 · Orders of magnitude
LINE WIDTH FROM 0.01 TO 10 mm, LOGARITHMIC SCALE

04 · Measuring instruments
0.5 ISO
technical pen with colour ring
A tubular pen for ink. The line width is set by the inner diameter of the tube, so there are as many pens as there are weights. Ring colour under ISO 9175: brown — 0.5 mm.
pen plotter carousel
The plotter takes a pen from the slot whose number is assigned to the layer or colour. The line weight on paper is the width of the pen; in the software it is only assigned.
01 mm×10
measuring magnifier ×10
A glass scale with 0.1 mm divisions is laid straight on the sheet. The weight is read at the edges of the stroke; 0.5 and 0.25 mm are told apart at first glance, 0.13 only with the scale.
71 %A3 → A4
reducing copier
The 71 % button turns A3 into A4, 50 % turns A3 into A5. Lengths and weights shrink equally, and the √2 series keeps the lines on standard values.
05 · Writing rules
Correct
one group for the whole sheet: thick 0.5, thin 0.25
take weights from the series: 0.13 · 0.18 · 0.25 · 0.35 · 0.5 · 0.7 · 1 · 1.4 · 2
for a drawing that will be reduced — group 0.7 or 1.0
spacing between parallel lines at least 0.7 mm
assign weights to layers, not objects; plot with lineweights
Incorrect
thin 0.18 on an A3 that will be reduced to A4 — it comes out at 0.13 and less
a «default weight» of 0.25 on every line — a drawing without hierarchy
thick 0.3 or 0.6 — there are no such pens in the series
1 mm hatch spacing on a sheet to be reduced — it will merge into grey
changing weights with the view scale — weight does not depend on scale
Series · Drafting and CAD
desk tips for every sheet
AutoCAD · lineweights and plotting
Command:
Lineweight√2 series · ISO 128-20 · GOST 2.303
Lit.
s
Scale
У
0.5
1:1
SIMETRIUM · «Drafting and CAD» seriessheet border — continuous thick line s
06 · Neighbouring units
07 · Historical section
A3A4A5
sheet size and line together
Metrological note

Line weight is measured on paper, with a magnifier with a measuring scale or under a microscope, at the edges of the stroke. The edge is never perfect: ink spreads along the fibres, toner lies in grains. That is why the series is not finely divided: neighbouring values differ by a factor of 1.4, and by eye 0.35 cannot be confused with either 0.25 or 0.5.

The lower limit of 0.13 mm is set for reproduction: copying, microfilming and scanning lose finer strokes. Hence the rule for choosing a group — look not at the original sheet but at the smallest size the drawing will be reduced to. The weight on a CAD screen has nothing to do with it: the monitor draws it in pixels and usually not to scale.

0.18 mm0.13 — the limit0.09 — breaks up
toner and a thin line
Catalogue of quantities
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The seven SI base units

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