Tolerances

1. Tolerances
Slide 1
Tolerance is the measurement variation allowed so that the item is acceptable.
𝑡𝑜𝑙𝑒𝑟𝑎𝑛𝑐𝑒 = 𝑚𝑎𝑥𝑖𝑚𝑢𝑚 − 𝑚𝑖𝑛𝑖𝑚𝑢𝑚
Nominal value is the target value for a measurement.
𝑛𝑜𝑚𝑖𝑛𝑎𝑙 𝑣𝑎𝑙𝑢𝑒 =
𝑚𝑎𝑥𝑖𝑚𝑢𝑚 + 𝑚𝑖𝑛𝑖𝑚𝑢𝑚
2
The manufacturing tolerance is the difference between the maximum acceptable
dimension and the minimum acceptable dimension.
It can be expressed in several ways:
• 𝑚𝑎𝑥𝑖𝑚𝑢𝑚 𝑣𝑎𝑙𝑢𝑒
𝑚𝑖𝑛𝑖𝑚𝑢𝑚 𝑣𝑎𝑙𝑢𝑒
• 𝑛𝑜𝑚𝑖𝑛𝑎𝑙 𝑣𝑎𝑙𝑢𝑒 ±
1
2
𝑡𝑜𝑙𝑒𝑟𝑎𝑛𝑐𝑒
• 𝑚𝑖𝑛𝑖𝑚𝑢𝑚 𝑣𝑎𝑙𝑢𝑒 −0
+𝑡𝑜𝑙𝑒𝑟𝑎𝑛𝑐𝑒
• 𝑚𝑎𝑥𝑖𝑚𝑢𝑚 𝑣𝑎𝑙𝑢𝑒 −𝑡𝑜𝑙𝑒𝑟𝑎𝑛𝑐𝑒
+0

2. Slide 2
Activity 2.3 – Tolerances in Carpentry (textbook page 98)
• You are making a wooden stool that will look like the one shown
below.
• Your measurements will have a tolerance of
1
16
of an inch
Calculate the maximum and minimum values of the dimensions for the
legs, top and bottom crosspieces and seat.

3. Slide 3
𝑡𝑜𝑙𝑒𝑟𝑎𝑛𝑐𝑒 =
1
16

1
2
𝑡𝑜𝑙𝑒𝑟𝑎𝑛𝑐𝑒 =
1
2
1
16
=
1
32
Points to consider:
• The seat diameter and seat thickness doesn’t need to be as accurate
as the other measurements, since these dimensions don’t affect any
of the other measurements. To show that the dimensions can be
anywhere within the  range, the measurements should be written as
nominal value 
1
2
(tolerance)
• The leg length, leg width, top cross-piece length, bottom cross-piece
length, and the cross-piece diameter are dimensions that need to fit
with other pieces of the wooden stool. Therefore, it would be safest
to make them slightly larger, and then sand them down to size if they
are too big. To show this, the measurements could be written as
𝑚𝑎𝑥𝑖𝑚𝑢𝑚 𝑣𝑎𝑙𝑢𝑒 −𝑡𝑜𝑙𝑒𝑟𝑎𝑛𝑐𝑒
+0

4. Slide 4
Maximum
Value
Minimum
Value
Measurement
with tolerance
Seat diameter
= 14
1
8
+
1
32
= 14
4
32
+
1
32
= 14
5
32
= 14
1
8
−
1
32
= 14
4
32
−
1
32
= 14
3
32
= 14
1
8
" ±
1
32
"
Seat thickness
= 1
1
2
+
1
32
= 1
16
32
+
1
32
= 1
17
32
= 1
1
2
−
1
32
= 1
16
32
−
1
32
= 1
15
32
= 1
1
2
" ±
1
32
"

5. Slide 5
Maximum
Value
Minimum
Value
Measurement
with tolerance
Leg length
= 26 +
1
32
= 𝟐𝟔
𝟏
𝟑𝟐
= 26 −
1
32
= 25
32
32
−
1
32
= 25
31
32
= 𝟐𝟔
𝟏
𝟑𝟐
"
−
𝟏
𝟏𝟔"
+ 𝟎
Leg width
= 1
3
4
+
1
32
= 1
24
32
+
1
32
= 𝟏
𝟐𝟓
𝟑𝟐
= 1
3
4
−
1
32
= 1
24
32
−
1
32
= 1
23
32
= 𝟏
𝟐𝟓
𝟑𝟐
"
−
𝟏
𝟏𝟔
"
+ 𝟎
Reminder: 𝑡𝑜𝑙𝑒𝑟𝑎𝑛𝑐𝑒 =
1
16

6. Slide 6
Max Value Min Value Measurement with tolerance
Top cross-
piece length
= 7
1
2
+
1
32
= 7
16
32
+
1
32
= 𝟕
𝟏𝟕
𝟑𝟐
= 7
1
2
−
1
32
= 7
16
32
−
1
32
= 7
15
32
= 𝟕
𝟏𝟕
𝟑𝟐
"
−
𝟏
𝟏𝟔"
+ 𝟎
Bottom cross-
piece length
= 9 +
1
32
= 𝟗
𝟏
𝟑𝟐
= 9 −
1
32
= 8
32
32
−
1
32
= 8
31
32
= 𝟗
𝟏
𝟑𝟐
"
−
𝟏
𝟏𝟔"
+ 𝟎
Cross piece
diameter
= 1
1
4
+
1
32
= 1
8
32
+
1
32
= 𝟏
𝟗
𝟑𝟐
= 1
1
4
−
1
32
= 1
8
32
−
1
32
= 1
7
32
= 𝟏
𝟗
𝟑𝟐
"
−
𝟏
𝟏𝟔"
+ 𝟎