ISOMETRIC PROJECTION
When a solid is resting in its simple position, the front or top view, taken separately, gives an incomplete
idea of the form of the object. When the solid is tilted from its simple position such that its axis is inclined to both
H.P and V.P, the front view or the top view or sometimes both, give an „air idea of the pictorial form of the
object, i.e., all the surfaces are visualized in a single orthographic view.
“Iso” means „equal‟ and “metric projection” means „a projection to a reduced measure‟. An isometric
projection is one type of pictorial projection in which the three dimensions of a solid are not only shown in one
view, but also their dimension can be scaled from this drawing.
R
C
D
30o
45o
B
G
120o
A
H
120
o
120o
F
E
It is seen that all the edges and faces of the rectangular prism are equally inclined to the plane of all the edges
and faces of the cube are equally inclined to the plane of projection. Hence the rectangular faces are seen as
similar and equal rhombuses.
The three lines AB, AD and AE are meeting at A. These edges are mutually perpendicular to each other in the
solid. Since all these edges are equally inclined to H.P, they are making and angle of 120 o with each other in the
plane of projection; also they are equally foreshortened. This leads us to the problem of selecting an isometric
scale.
Isometric Axes:
The lines AB, AD and AE meeting at a point A and making an angle of 120 o with each other are termed
„isometric axes‟
1
Isometric Lines:
The lines parallel to the isometric axes are termed isometric lines. The lines CD, CB etc are examples of isometric
lines.
Non-isometric Lines:
The lines which are not parallel to isometric axes are termed non-isometric lines. The BD is an example.
Isometric Planes:
The planes representing the faces of the rectangular prism as well as other planes parallel to these planes are
termed isometric planes.
Isometric scale:
Isometric projection is drawn using isometric scale, which converts true lengths into isometric lengths
(foreshortened)
Construction of isometric scale:

Draw a horizontal line AB.

From A draw a line AC at 45o to represent actual or true length and another line AD at 30o to AB to
measure isometric length.

On AC mark the point 0, 1, 2 etc to represent actual lengths.

From these points draw verticals to meet AD at 0 , 1 , 2 etc. The length A1 represents the isometric scale
length of A1 and so on.
C
Isometric Length
3
AB
= cos 45o = 1
AC
2
AB
3
= cos 30o =
2
AD
2
Actual Length
D
3
1
2
AB
AC
AB
×
AC
AB
3
= 1
2
AD
2
AD
= 1 × 2
AB
2
3
AD
2
=
= 0.81
3
AC
0
0
1
30
o
A
45
Isometric Length
o
90
o
B
AD = 0.81× AC
Isometric Length = 0.81 × Actual Length
2
Difference between isometric view and isometric projection
Isometric View
Drawn to actual scale
Isometric Projection
Drawn to isometric scale
When lines are drawn parallel to isometric
axes, the true lengths are laid off.
When lines are drawn parallel to isometric axes, the
lengths are foreshortened to 0.81 time the actual lengths.
ORTHOGRAPHIC
PROJECTION
ISOMETRIC
PROJECTION
ISOMETRIC
VIEW
Isometric Plane and Non-isometric Plane:
Isometric Planes are marked as 1 and Non-isometric Planes are marked as 2
2
1
1
1
30o
30o
C
D
G
B
A
H
F
E
3
Problem
Draw the isometric projection of a rectangular prism of base 50 mm × 10 mm and height 75 mm, when it rests
with its base on H.P and one its of rectangular faces is parallel to V.P
DA
CB
R
3
75 mm
Z
75 mm
2
50 mm
1
40 mm
da
cb
FRONT VIEW
3
2
30o
1
45o
Y
X
Aa
Bb
Dd
Cc
40 mm
B
50 mm
TOP VIEW
C
A
D
b
c
a
30o
30o
30o
30o
d
4
BOX METHOD:
The isometric projection of solids like cube, square and rectangular prisms are drawn directly when their edges
are parallel to the three isometric axes. The isometric projection of all other types of prisms and cylinders are
drawn by enclosing them in a rectangular box. This method is called Box method.
EXAMPLE – 1
Draw an isometric of a Pentagonal prism of base 1.5 and length 2.5 resting on one of its rectangular faces
on H.P
D
E
C
A
D′
B
E′
1.5"
2.5"
D
C′
E
A′
C
B′
A
30o
30o
B
ISOMETRIC VIEW OF A REGULAR PENTAGONAL PRISM
(Resting on one of its rectangular faces on H.P)
5
EXAMPLE – 2
Draw an isometric of a Hexagonal Prism of base 1 and length 3 resting on one of its rectangular faces on
H.P
E
D
C
F
A
B
1"
E′
3"
D′
F′
E
D
C′
A′
F
B′
C
A
30o
B 30o
ISOMETRIC VIEW OF A REGULAR HEXAGONAL PRISM
(Resting on one of its rectangular faces on H.P)
6
EXAMPLE – 3
Draw an isometric of a Octagonal Prism of base 1.5 and length 2.5 resting on one of its rectangular faces on
H.P
G
H
E
F
C
D
A
B
1.5"
F′
2.5"
E′
G′
F
H′
D′
E
G
C′
A′
H
D
B′
C
A
B
30
30
o
o
ISOMETRIC VIEW OF AN OCTAGONAL PRISM
(Resting on one of its rectangular faces on H.P)
7
EXAMPLE – 4
Draw an isometric of a regular Hexagonal Pyramid of base 1 and height 3 resting on one of its hexagonal
faces on H.P
E
D
C
F
A
B
1"
E′
F′
D′
A′
C′
B′
3"
E
F
D
A
C
B
30
30o
o
ISOMETRIC VIEW OF A REGULAR HEXAGONAL PRISM
(Resting on one of its hexagonal faces on H.P)
8
FOUR CENTERED METHOD:
EXAMPLE – 5
Draw an isometric of a cylinder of base 1 diameter and height 3 lying on H.P
Drawing Procedure
 Join P with B and C which are the mid-points of the opposite sides of the rhombus. Similarly join R with
A and D.
 With P as centre and PC as radius draw an arc CB. Similarly with R as centre and RA as radius draw an
arc AD.
 The lines PC and RD intersect at O1. With O1 as centre and O1D as radius draw an arc DC.
 Similarly with O2 (intersection of RA and PB) as centre and O2B as radius draw an arc BA. Thus
complete the ellipse.
 Refer step 1-3 in the Offset method and complete the isometric view of the cylinder.
1"
S
C
R
O1
B
D
O2
P
A
30o
30o
Q
ISOMETRIC VIEW OF A CYLINDER
(Lying on H.P)
9
EXAMPLE – 6
Draw an isometric of a cylinder of base 1 diameter and height 3 lying on V.P
Drawing Procedure
 Join P with B and C which are the mid-points of the opposite sides of the rhombus. Similarly join R with
A and D.
 With P as centre and PC as radius draw an arc CB. Similarly with R as centre and RA as radius draw an
arc AD.
 The lines PC and RD intersect at O1. With O1 as centre and O1D as radius draw an arc DC.
 Similarly with O2 (intersection of RA and PB) as centre and O2B as radius draw an arc BA. Thus
complete the ellipse.
 Refer step 1-3 in the Offset method and complete the isometric view of the cylinder.
1"
R
S
C
B
O1
O2
A
D
30
o
30
o
P
ISOMETRIC VIEW OF A CYLINDER
(Lying on V.P)
10
Q
CO-ORDINATE OR OFFSET METHOD:
EXAMPLE – 1
The isometric view of a hexagonal pyramid of side of base 30 mm and height 75 mm, when it is resting on H.P such that an edge of the base is parallel to V.P
Drawing Procedure
 Draw the top and front views of the hexagonal pyramid.
 Enclose the hexagon in a rectangle PQRS in the top view.
 Draw the isometric vies of the base of the pyramid in the parallogram PQRS.
 Note that FC is an isometric line on which O1 lies. Hence mark O1 on the isometric line FC such that FO1 = y.
 From O1 erect a vertical line and mark the apex O such that O1O = length of the axis = 75 mm
 Join O with all the corners of the base of the pyramid and complete the isometric as shown.
O
75 mm
O
F
AE
S
E
BD
C
D
R
O
R
D
D
C
E
OO1
F
E
C
S
OO1
Q
O1
A
B
B
F
A
Q
P
y
O1
B
F
P
C
30 mm
11
A
EXAMPLE – 2
Draw the isometric projection of a cone of base 40 mm diameter and height 58 mm when it rest with its base on H.P
Drawing Procedure
 Draw the orthographic projections of the cone.
 Enclose the circle in top view in a square PQRS.
 Draw the isometric vies of the base of the pyramid in the parallogram PQRS.
 Draw the base of the cone as an ellipse by Four-centre method.
 From B and C draw line parallel to isometric axes and obtain O1 (Offset method).
 From O1 draw a line parallel to the third axis. On this line mark O such that O1O = height of the cone = 58 mm
 From O draw two tangents to the ellipse and complete the isometric projection of the cone.
O
58 mm
O
A
BD
O
C
R
D
R
C
C
D
OO1
40 mm
Q
S
O1
S
x
A
B
x
P
12
Q
O1
B
A
P
Draw the Top view, Front view, Right view, Left view and Back view for the following isometric view
1.
1′ – 6"
3′ – 0"
10"
6"
3′ – 0"
10"
6"
6"
6"
6"
6"
30o
30o
FRONT VIEW
3′ – 0"
6"
1′ – 6"
6"
10"
6"
10"
1′ - 6"
TOP VIEW
10"
LEFT VIEW
13
10"
½"
2.
3.
5½"
3½"
13"
½"
2¾"
1¼"
8
2¾"
½"
17
2¼"
"
8
3"
3 ¾"
3"
1¼"
½"
3¾"
5½"
15/8"
3½"
2¾"
11/8"
2¾"
½"
FRONT VIEW
LEFT VIEW
FRONT VIEW
LEFT VIEW
½"
2½"
TOP VIEW
TOP VIEW
14
½"
4.
½"
½"
½"
½"
½"
½"
1"
1"
2.5"
1"
1"
1"
½"
½"
½"
½"
1"
1"
½"
1"
½"
1"
1"
1"
RIGHT VIEW
LEFT VIEW
½"
1"
½"
1"
½"
1"
½"
½"
½"
½"
1"
½"
TOP VIEW
1.5"
FRONT VIEW
15
½"
5.
1"
1"
½"
½"
1"
1"
1"
½"
1"
½"
½"
1"
½"
1"
1"
1"
FRONT VIEW
TOP VIEW
½"
½"
½"
½"
½"
½"
½"
½"
1"
1"
1"
1"
LEFT VIEW
1"
RIGHT VIEW
16
6.
1"
1"
1"
½"
1"
½"
½"
½"
½"
1"
1"
1"
1
1
½
½
½
½
½
½
1
1
FRONT VIEW
1
LEFT VIEW
1
½
½
1
½
1
1
1
RIGHT VIEW
1
TOP VIEW
17
1
7.
14 -6
16 -8
3 -0
15 -0
10 -0
2 -6
3 -0
7 -0
1 -6
5 -0
12 -6
4 -8
5 -0
2 -6
18
1 -0
5 -0
1 -1
5 -0
1 -1
5 -0
1 -0
3 -6
1 -0
2 -0
7 -0
3@6 =1 -6
FRONT VIEW
4 -6
3 -0
3 -0
4 -0
3@6 =1 -6
1 -0
4 -9
3 -0
4 -9
LEFT VIEW
19
3@10 =2 -6
20