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 The 162 Formula: Simplifying Steel Reinforcement Calculations in Construction

📌 Introduction

Steel reinforcement is the backbone of reinforced concrete structures. To ensure strength, durability, and safety, civil engineers must calculate the weight of reinforcement bars (rebars) accurately. However, instead of using complex mathematical steps each time, engineers use a shortcut known as the 162 formula.

This blog explains why we use 162 in reinforcement calculations and provides a clear step-by-step guide with examples.

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🧮 Step 1: Understanding the Need for Weight Calculation

Steel bars are supplied in different diameters (6mm, 8mm, 10mm, 12mm, etc.) and measured by length at the site.
But billing, design, and estimation require steel weight (in kg).

So, we need a formula to convert length → weight.

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🧮 Step 2: General Formula for Weight of Steel Bar

The weight of a bar is calculated using density:

Weight = Volume × Density

• Density of steel = 7850 kg/m³
• Volume of bar = Cross-sectional area × Length

Cross-sectional area of a circular bar:

A = (π/4) × d²

where d = diameter in millimetres (mm).

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🧮 Step 3: Deriving the Shortcut (162)

1. Convert diameter from mm to metres:
   d (mm) = d ÷ 1000 (m)

2. Cross-sectional area:
   A = (π/4) × (d ÷ 1000)²

3. Volume of 1m length:
   V = A × 1 = (π/4) × (d ÷ 1000)²

4. Multiply by density of steel (7850):
   Weight = V × 7850

   Weight = (π/4) × (d² ÷ 1,000,000) × 7850

5. Simplify constants:
   (π/4) × (7850 ÷ 1,000,000) = (3.1416 ÷ 4) × 0.00785 = 0.006165

   Weight = 0.006165 × d²

6. To make it easy, engineers use:

   Weight (kg/m) = d² ÷ 162

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✅ Final Formula

Weight of Steel Bar (kg/m) = d² ÷ 162

where d = diameter of bar in mm.

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🧾 Step 4: Examples

1. 12mm bar
   Weight = 12² ÷ 162 = 144 ÷ 162 = 0.89 kg/m

2. 16mm bar
   Weight = 16² ÷ 162 = 256 ÷ 162 = 1.58 kg/m

3. 20mm bar
   Weight = 20² ÷ 162 = 400 ÷ 162 = 2.47 kg/m

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🌍 Importance of the 162 Formula

• Saves Time: Quick calculation without complex maths.
• Universal Use: Adopted by engineers, site supervisors, and quantity surveyors.
• Accuracy: Gives results within ±2% tolerance.
• Billing & Estimation: Helps in preparing BOQ and cutting lists.

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🔑 Conclusion

The 162 formula is a simple yet powerful tool in construction. It transforms a complex derivation into a quick calculation, enabling engineers to estimate reinforcement weight accurately and efficiently.

By understanding why 162 is used, you can ensure precise calculations, reduce wastage, and improve cost efficiency in every project.

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