By the end of this chapter, you will be able to:
These skills will help you communicate design ideas clearly and professionally, which is essential in the technical drawing and interior design trades.
An isometric drawing is a pictorial drawing that shows an object in three dimensions on a flat sheet, with its width, depth and height all visible in one view. The object is drawn as if tilted so that its three main edges, called the isometric axes, are equally inclined to the picture plane, with the vertical edges drawn vertical and the horizontal edges drawn at 30° to the horizontal. Because measurements can be taken directly along the axes, isometric drawings combine a realistic three-dimensional look with true, measurable dimensions. Example: an interior designer presenting a built-in wardrobe for a hotel suite draws it in isometric so that the client can see the front, side and top at once, and the joiner can still read the sizes.
Isometric projection is a form of axonometric projection in which the object is turned and tilted so that its three principal axes make equal angles with the plane of projection, and the projectors are parallel to each other and perpendicular to that plane. The word isometric means "equal measure", because lengths along all three axes are shortened by the same amount. In true isometric projection every axis is foreshortened to about 0.816 of its real length, while in an isometric drawing, the form used in most practical work, full true lengths are used along the axes for convenience.
A cabinet edge is 600 mm long. Find its length in true isometric projection.
Isometric length = true length × 0.816
Isometric length = 600 × 0.816
Answer: 489.6 mm (in an isometric drawing it would be drawn at the full 600 mm)
In an isometric view the three axes meet at a point with equal angles of 120° between each pair, because the object is turned so that its three faces are equally visible. On paper this is achieved by drawing one axis vertical and the other two at 30° above the horizontal to the left and right. The equal angles give each visible face of a cube the same shape, a rhombus, which makes the drawing balanced and easy to read. Example: when drawing a cubic storage unit for a children's library, the three faces appear as identical rhombuses because of the 120° spacing of the axes.
The vertical axis is at 90° to the horizontal and the right-hand axis is at 30° to the horizontal. Find the angle between them.
Angle between vertical and right axis = 90° − 30° = 60° above the right axis, measured on the other side 30° + 90° = 120°
The two receding axes are each 30° below their side of the horizontal line through the corner, so the angle between them = 180° − 30° − 30° = 120°
Answer: each pair of axes is 120° apart, and 120° × 3 = 360°
Uniform scaling means the same scale is applied along all three isometric axes, so a given length measures the same whether it is drawn along the width, depth or height axis. This is what keeps the proportions of the object correct and allows dimensions to be scaled straight off the drawing. If different scales were used on different axes, the object would look stretched or squashed and could not be measured reliably. Example: a 900 mm wide by 600 mm deep by 750 mm high desk for a bank's front office, drawn at 1:10, is drawn 90 mm, 60 mm and 75 mm along the three axes.
Draw a reception counter 2,400 mm long, 700 mm deep and 1,100 mm high at a scale of 1:20.
Length on drawing = 2,400 ÷ 20 = 120 mm
Depth on drawing = 700 ÷ 20 = 35 mm
Height on drawing = 1,100 ÷ 20 = 55 mm
Answer: 120 mm, 35 mm and 55 mm, each set off along its isometric axis at the same scale
In isometric drawing, edges that are parallel on the real object stay parallel on the drawing, and lines parallel to the isometric axes, called isometric lines, are drawn true to scale. Lines that are not parallel to any axis, such as sloping or diagonal edges, are called non-isometric lines and are not shown at their true length, so they are drawn by locating their end points along isometric lines first. This rule lets designers measure directly along isometric lines but warns them not to measure sloping edges. Example: the sloping top of a lectern for a church is drawn by marking the high and low points on vertical isometric lines and joining them, rather than measuring the slope itself.
The front face of a box is 400 mm wide and 300 mm high. Find the true length of its diagonal, which is a non-isometric line.
True diagonal = √(400² + 300²) = √(160,000 + 90,000) = √250,000
Answer: 500 mm, which will not measure 500 mm on the isometric drawing because the diagonal is not parallel to an axis
Isometric drawings have no perspective, meaning objects do not get smaller as they go back into the drawing and there are no vanishing points. Every edge of the same real length is drawn the same length wherever it appears, so dimensions can be taken directly from the drawing. This makes isometric drawings ideal for technical communication, although they look less natural than perspective drawings, which show how the eye actually sees space. Example: a kitchen layout for a restaurant drawn in isometric shows all cabinets of the same width at the same size, front or back, so the fabricator can check sizes, while the client might be shown a perspective for realism.
An isometric drawing shows all three dimensions of an object, its width, height and depth, in a single view, unlike orthographic views, which show only two dimensions at a time. Width and depth are set out along the two 30° axes and height along the vertical axis, so the top, front and side of the object are all visible together. This helps people who cannot read plans and elevations to understand the form of a design quickly. Example: a sales office for a furniture showroom uses isometric drawings of modular shelving so that customers can see how deep, wide and tall each unit is from one picture.
| Dimension | Isometric axis | Direction on paper |
|---|---|---|
| Width | Right receding axis | 30° above horizontal to the right |
| Depth | Left receding axis | 30° above horizontal to the left |
| Height | Vertical axis | Straight up |
In isometric drawing the receding edges that show depth and width are drawn at 30° to the horizontal, using a 30°/60° set square against a T-square or a drawing board edge. This fixed angle gives the drawing its characteristic look and ensures that every isometric line is drawn consistently. Points along a 30° line can also be located using horizontal and vertical offsets when drawing on squared or digital grids.
Horizontal offset = length × cos 30°
Vertical offset = length × sin 30°
Find the horizontal and vertical offsets for a 400 mm depth line drawn at 30°.
Horizontal offset = 400 × cos 30° = 400 × 0.866 = 346.4 mm
Vertical offset = 400 × sin 30° = 400 × 0.5
Answer: 346.4 mm across and 200 mm up
Complex objects are easier to draw in isometric when they are first broken down into simple geometric shapes such as boxes, prisms and cylinders. The designer usually draws a light enclosing box, sometimes called a crate, using the overall width, depth and height, and then cuts away or adds parts to shape the object. Starting with basic forms keeps proportions correct and avoids errors in complex details. Example: an armchair for a hotel lobby is first drawn as one large box for the seat and back, then refined into cushions, armrests and legs.
An isometric drawing must communicate the form clearly at a glance, so only the details needed for its purpose should be shown. Too many lines, textures and small features make the drawing confusing and hide the main shape. Clarity is improved by using clear line weights, leaving out hidden lines unless necessary, and keeping annotations neat and minimal. Example: an isometric of a classroom layout for a primary school shows desks, shelves and the teacher's table as simple blocks rather than drawing every screw and grain pattern.
Consistent orientation means drawing objects from the same viewing direction and keeping their faces in a logical position, usually with the front face on one side and the most informative faces visible. When several isometric drawings in a set use the same orientation, viewers can compare them easily and relate them to the plans. Changing orientation without reason causes confusion about which face is the front. Example: in a set of joinery drawings for an office fit-out, every desk, cabinet and shelf is drawn with its front facing left and the top visible, so the fabricator can move from one drawing to the next without reorienting.
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