**Diameter and length of steel bars are structural requirements of a building, and they are decided based on design procedures given by IS(Indian Standard) codes. Steel bars are sold in the market in price per weight. So we need to calculate the weight of steel required to estimate cost of construction.**

**The formula**

*D²L/162*is very common and used frequently to calculate the weight of steel bars. In this post, the simple derivation behind this formula is discussed. I hope you will enjoy it.

###
__The formula to calculate the weight of steel is:__

__The formula to calculate the weight of steel is:__

**W=D²L/162**
Where,

**W**= Weight of steel in Kg

**D =**Diameter of steel bars in millimeters (mm)

**L=**Length of steel bars in meter (m)

###
__Derivation of the Formula:__

We know that,

*Volume= Cross-sectional area x Length*

*Weight = Volume × Unit weight*
Mathematically,

**W = A x L x ρ**

A

π (pi)

D

L

*=*Area*=*πD²/4π (pi)

*=*3.14D

*=*Diameter of steel barL

*=*Length of steel bar

*ρ (Rho) = Density of steel bar = 7850 kg/m³*
Therefore,

**W = 3.14 x D²/4 x L x 7850 kg**

Where D and L are in m

We generally express diameter in millimeter (mm) and length in meter (m) unit. So to make the formula more handy let's take diameter as D mm.

**D mm = D/1000 m**

Putting D mm value in the expansion of W,

**W = 3.141 x (D/1000)²/4 x L x 7850 kg**

Or,

**W = D²L/162 kg***D in mm*

*& L in m*

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