A scale is a ratio of drawn length to real length, written drawing : object. To convert, work out which side is larger and let the answer move the same way.
This lesson belongs to drawing conventions and scale. It builds on reading dimensions without measuring the screen.
How do you decide whether to multiply or divide?
Ask one question: is the drawing smaller or larger than the object?
| Scale | Type | Drawn compared with real | Drawn to real | Real to drawn |
|---|---|---|---|---|
| 1:2 | Reduction | Drawn is smaller | × 2 | ÷ 2 |
| 1:5 | Reduction | Drawn is smaller | × 5 | ÷ 5 |
| 2:1 | Enlargement | Drawn is larger | ÷ 2 | × 2 |
| 5:1 | Enlargement | Drawn is larger | ÷ 5 | × 5 |
| 1:1 | Full size | Same | no change | no change |
On a reduction the real object is bigger, so going from drawn to real always makes the number larger. On an enlargement the opposite is true.
Worked example: a bracket drawn at 1:4
An original bracket is drawn at scale 1:4. A line measuring 35 mm on the printed drawing is the bracket’s length.
The drawing is smaller than the object, so the real length is larger:
real length = 35 × 4 = 140 mm
Now go the other way. The real height of the bracket is 96 mm. What length should be drawn at 1:4?
drawn length = 96 ÷ 4 = 24 mm
Check: 24 × 4 = 96, which matches the real height.
Worked example: a small part drawn at 5:1
A small pin has a real length of 14 mm and is drawn at 5:1 so the detail is visible. The drawing is larger, so the drawn line is longer:
drawn length = 14 × 5 = 70 mm
If a hole diameter is drawn as 15 mm on the same sheet, the real diameter is 15 ÷ 5 = 3 mm.
The mistake: multiplying on an enlargement
A student sees the scale 5:1, remembers that “you multiply by the second number” from the 1:4 example, and computes 15 × 1 = 15 mm for the real diameter. The working looks tidy but the answer is five times too large.
| Step | Wrong | Right |
|---|---|---|
| Identify type | Not checked | 5:1 is an enlargement |
| Real from drawn | Multiply by 1 | Divide by 5 |
| Real diameter | 15 mm | 3 mm |
| Sense check | A 15 mm hole on a 14 mm pin | A 3 mm hole on a 14 mm pin |
The sense check is what catches it. A 15 mm hole cannot sit in a pin that is only 14 mm long. Always compare the answer with the other sizes on the part.
Check yourself
A housing is drawn at scale 1:10. A wall thickness measures 4 mm on the drawing, and the real width of the housing is 650 mm. Find the real wall thickness and the width that should be drawn.
Answer
The scale 1:10 is a reduction, so real length is larger. Real wall thickness = 4 × 10 = 40 mm.
Drawn width = 650 ÷ 10 = 65 mm.
Sense check: a 65 mm drawn width is much larger than the 4 mm wall, and a 650 mm width is much larger than a 40 mm wall, so both results match the picture.
What to study next
Put all three skills in this cluster together with the drawing conventions and scale practice set. Scale slips also return in reviewing common scale, projection and labelling mistakes.
If you want a teacher to check which way you convert under time pressure, see online one-to-one Engineering Drawing tuition.