Why d2/162.2 is used to calculate weight of Rebar?

The most common question which people ask in interview is about, why we take d²/162.2 for calculating weight of rebars and how it is derived. 

The formula is used to find out the weight of steel rebar. It is the Mild Steel used as structural steel which tends to show low carbon content with a carbon parentage of ( 0.2- 0.35%)

To find the derivation of d²/162.2 , Firstly we should know the physical properties of the Steel.

S.No	Properties	Value
1.	Unit mass of steel	7850 kg/m3
2.	Modulus Of Elasticity	2 x 105 N/mm2
3.	Modulus Of Rigidity	0.769 x 105 N/mm2
4.	Coeff Of Thermal Expansion	12 x 10-6 /degree C

 

We know the formula of Calculating Mass, which is

Mass= Density x Volume

To find Out the formula we will need the density and the volume of steel member.

Density = 7850 kg/m³

Volume Of steel = Volume of Cylinder =  π x R² x Height

Derivation

We calculate the formula for Bar Length = 1 meter.

Therefore,

Mass = Density x Volume

= π x R² x Height x 7850 kg/m³ 

= 3.14 x D²/4 x 1000 mm x 7850/1000x1000x1000

= (D² x 6162.25) / 100000

= d² x 0.00616225

= d² x (1/0.00616225)^-1

= d² / 162.278

= d² / 162.28

This this how the Formula has been derived and if we want to take out the weight in ft , than the formula is used as d²/533.