Probably D^{2}/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 D**^{2}**/162Â **

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 thatÂ

- The unit weight of steel is 7850 Kg/m3. Refer Unit weight of construction materials topic.
- Area of steel (circular shape) = Ï€r2 or Ï€D2/4

So,

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

= Ï€D2/4 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 (D^{2}Â / 4) x 1/(1000)2 x 7850

= D^{2}Â x 6162.5 x 1/(1000)2

= D^{2}Â X (0.006162)

= D^{2}Â X 1/(0.006162)-1

= D^{2}/162.28

Weight of Steel per metre = D^{2}/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 = D

^{2}/ 533

Happy Learning ðŸ™‚