Derivation of D2/162 in Steel Weight Calculation

Probably D²/162 is the first formula we ever learn in the construction industry. We know it is used to calculate the weight of steel bars.

Also, know the importance of estimation in the Bar Bending Schedule. Here we are going to discuss the derivation of this formula.

Derivation of D²/162 

We know, Weight = Area X Density

To find out the weight of steel,

Weight of steel per metre = Area of Steel X Density of Steel X Length of Steel

We know that 

• The unit weight of steel is 7850 Kg/m3. Refer Unit weight of construction materials topic.
• Area of steel (circular shape) = πr2 or πD2/4

So,

Weight of Steel per metre =  Area of Steel X Density of Steel X Length of Steel

= πD2/4 x 7850 x 1m

= 3.14 x (D2 / 4) x 7850 x 1m

When multiplying all values should have the same unit. Here diameter is in mm and unit weight is in m3.

1 mm = 1/1000 m ; 1 mm2 = 1/(1000)2 mm2

= 3.14 x (D² / 4) x 1/(1000)2 x 7850

= D² x 6162.5 x 1/(1000)2

= D² X (0.006162)

= D² X 1/(0.006162)-1

= D²/162.28

Weight of Steel per metre = D²/162.28

If you want to know the steel weight per foot. 1 metre = 3.281 ft. Just multiply the same.

Weight of steel per foot = D2/162.28 x 3.281 = D² / 533

Happy Learning 🙂