Brian H. Lumley



CARPENTRY Construction Math



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Construction math and advanced problems


Đ2020 Brian H. Lumley

Imperial measurement



1 yd. = 3’, 1’ = 12”, inches are divided into fractions

For construction math the fractions are usually divided into 1/16”, 1/8”, ž”, ―”

You will need to know how to change Imperial yards, feet, inches and fractions into decimals, and back again to fractions

1) Divide inches by 12 to find feet

2) Multiply decimal remainder of feet by 12 to find inches.

3) Multiply decimal remainder of inches by 16 to get fractions of an inch

Example; Convert 162¾” to feet & inches

162¾” = 162.75” ÷ 12” = 13.562’

0.562’ X 12” = 6.744”

0.744” X 16 = 11.90/16” = 12/16” = ¾”

13’- 6¾”



Example; building span 13’-9”, roof slope 5/12

Find rafter length. Run = 1/2 building span = 13’-9” ÷ 2 = 6’-10½”

6’-10½” = 6+(10.5 ÷ 12) = 6.875’

Or 13’-9” = 13.75’ ÷ 2 = 6.875’

convert to inches = 6.875 X 12= 82.5”

Total rise= 6.875 X 5” = 34.375”

Hypotenuse or rafter length = aē+bē= cē

34.375ē” + 82. 5ē” = 1181.641” + 6806.25” = 7987.891”

√ 7987.891” = 89.375” ÷ 12 = 7.447’ = 7’-5 3/8”

Rafter length = 7.447’

.447 X 12 = 5.364”

.364 X 16 = 5.824/16" = 3/8”


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