SME
Engineering Graphics & CAD · Problem type
Isometric projection length
Use this for “A 50 mm edge runs along an isometric axis. How long is it on a true isometric projection?”
Diagram
L′ = s × L = 0.8165 × 50 mm
L′ = 40.83 mm
The edge leans θ = cos⁻¹ s = 35.26° out of the plane, as every isometric axis does.
This is an example. Type your own values to start a new problem.
L′ (mm)
=
s
×
L (mm)
Formulas
L
′
=
s
×
L
40.825 = 0.8165 × 50
Assumptions
•
Each isometric axis tilts 35.26° out of the picture plane, so its edges shrink to cos 35.26° = √(2/3) ≈ 0.8165.
•
Only edges parallel to the three axes scale this way; plot a slanted edge from its two ends.
•
An isometric drawing skips the shrinking and draws full size (s = 1): larger, but easier to measure.
Step-by-step
WE KNOW
L = 50 mm, s = 0.8165
FIND
projected length (L′)
Step 1 · Find projected length (L′)
Use L′ = s × L
Every edge along an axis shrinks by the same scale.
L
′
=
0.8165
×
50
L
′
=
40.825
mm
Check
Put the numbers back in. Both sides should match.
40.825 = 0.8165 × 50 ✓
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