How to find the weight of steel/reinforcement (rebar) and derive the steel weight formula.
How to find reinforcement weight using a formula?
Quick Answer: Steel Weight Formula
Steel weight (kg) = (D² / 162) × L
Where:
- D = nominal diameter of bar in mm
- L = length of bar in metres
- Result = theoretical steel mass in kg
Weight per metre = D² / 162 kg/m
Why Is the Steel Weight Formula D²/162?
The weight of a steel bar depends on two things:
- Volume of the steel bar
- Density of steel
Since reinforcement bars are approximately circular, we first calculate the cross-sectional area of the bar. Then we multiply the area by the bar length and the density of steel.
This gives the relationship:
Weight ∝ D² × Length
After substituting the standard steel density and converting the units, the relationship simplifies to:
Weight = D²/162 × Length
The next section then shows exactly how 162 is derived step by step.
Derivation of D²/162
Circular bar area
A = πd^2 / 4
Then consider a 1-metre length, convert the units properly, use steel density of approximately 7850 kg/m³, and simplify.
weight = volume x density
volume = (area x height)
= (( πd^2 / 4) x 1000mm) x 7850 kg/m3
= ((3.14/4)xd^2 x 1000) x (7850/10^8)kg/mm3
= 785xd2x7.85e-6
= d2 x 0.00616
= (d2/1) x (0.00616/1)
= (d2/162.29) ~ (d2/162)
= (d2/162) is per m
= ((d2/162) x L) is for the required meter; L is the required meter or length
How to Calculate Steel Weight
A simple procedure:
Step 1: Identify bar diameter
Step 2: Measure/obtain bar length
Step 3: Apply D²/162
Step 4: Multiply by total length
Step 5: Convert kg → tonnes when required
Worked Examples
Example 1
8 mm × 12 m bar
= {(8^2)/162} x 12
=4.74 kg or 0.395 kg/m
Example 2
16 mm × 12 m bar
= {(16^2)/162} x 12
=18.96 kg or 1.580 kg/m
Example 3
20 mm × 6 m bar
= {(20^2)/162} x 6
=14.81 kg or 2.469 kg/m
Steel Bar Weight Chart
| Bar Dia. | Approx. kg/m | 6 m | 12 m |
|---|---|---|---|
| 6 mm | 0.222 | 1.33 | 2.66 |
| 8 mm | 0.395 | 2.37 | 4.74 |
| 10 mm | 0.617 | 3.70 | 7.40 |
| 12 mm | 0.888 | 5.33 | 10.66 |
| 16 mm | 1.58 | 9.48 | 18.96 |
| 20 mm | 2.47 | 14.82 | 29.64 |
| 25 mm | 3.85 | 23.10 | 46.20 |
| 32 mm | 6.31 | 37.86 | 75.72 |
| 40 mm | 9.86 | 59.16 | 118.32 |
Note – As per IS Codebook 1786:2000, Kg/m upto 12 mm is three decimals, and above 12 mm, two decimals only.
Steel Weight Calculation from Total Bar Length
A very useful site shortcut:
If you already know the total length of 16 mm reinforcement:
=(16^2)/162 = 1.58 kg/m
Therefore:
Total steel weight = Total length × 1.58
This is especially useful when checking a BBS.
Theoretical Weight vs Actual Weight vs Rolling Margin
When calculating reinforcement steel quantities, it is important to understand the difference between theoretical weight, actual weight, and rolling margin.
These terms are often used interchangeably at construction sites, but they do not mean the same thing.
Theoretical Weight
Theoretical weight is the weight calculated from the nominal diameter and length of the reinforcement bar, using the standard theoretical relationship:
Theoretical Weight (kg) = (D² / 162) × L
Actual Weight
Actual weight is the physical weight of the reinforcement steel measured using a suitable weighing system, such as a calibrated weighing scale or weighbridge.
For example:
Theoretical weight = 10,000 kg
The supplied steel is physically weighed as:
Actual weight = 10,150 kg
The actual weight is therefore 150 kg higher than the theoretical weight.
The difference does not automatically mean that the material is incorrect. The actual mass of manufactured reinforcement can differ from the theoretical mass calculated from the nominal diameter, subject to the applicable product standard and its permitted tolerances.
What Is Rolling Margin?
In construction and steel-trade practice, the term rolling margin is commonly used to describe the difference between the actual measured weight of reinforcement steel and its theoretical or nominal weight.
It can be expressed as:
Rolling Margin (%) = [(Actual Weight − Theoretical Weight) / Theoretical Weight] × 100
Example
Suppose:
- Theoretical weight = 10,000 kg
- Actual measured weight = 10,150 kg
Then:
Rolling Margin = [(10,150 − 10,000) / 10,000] × 100
Rolling Margin = +1.5%
Therefore, the actual supplied steel is 1.5% heavier than the theoretical weight.
If the actual measured weight were 9,900 kg:
Rolling Margin = [(9,900 − 10,000) / 10,000] × 100
Rolling Margin = −1.0%
In that case, the actual weight is 1% lower than the theoretical weight.
The key provision: IS 1786:2008, Clause 7.2
Clause 7.2 covers Nominal Mass. It specifies that, for checking nominal mass, the density of steel is taken as 0.00785 kg/mm² of cross-sectional area per metre, and provides tolerances on nominal mass.
Table 2 Tolerances on Nominal Mass
(Clauses 6.2 and 7.2.2)
| Nominal bar size | Batch tolerance | Individual sample* | Coil individual sample |
|---|---|---|---|
| Up to and including 10 mm | ±7% | −8% | ±8% |
| >10 mm to 16 mm | ±5% | −6% | ±6% |
| >16 mm | ±3% | −4% | ±4% |
These are the nominal-mass tolerances specified in IS 1786:2008.
*The standard has specific wording concerning the individual-sample tolerance; therefore, we should reproduce the table carefully rather than simplifying it to a generic “±X%” statement.
Note – In current construction and steel procurement practice, a rolling margin of around 2% is often considered a practical benchmark for quantity and commercial calculations. However, 2% should not be interpreted as a permissible limit specified by IS 1786. The acceptable variation should be determined based on the applicable Indian Standard, purchase specification, contract conditions, and project requirements.
Common Mistakes
- Using diameter in metres instead of mm
- Using length in mm instead of metres
- Forgetting to multiply by total number of bars
- Confusing kg/m with total kg
- Using the formula for non-circular steel sections
- Treating theoretical weight as actual measured weight
- Mixing up bar diameter and bar spacing
Steel Weight Calculator
Need a quick calculation? Use the civil practical knowledge Steel Weight Calculator to calculate reinforcement weight from diameter and length.
Frequently Asked Questions
Q1. What is the formula for steel weight?
The theoretical steel weight formula is: Weight (kg) = (D² / 162) × L, where D is the bar diameter in mm, and L is the length in metres.
Q2. Why is 162 used in the steel weight formula?
The constant 162 comes from the circular cross-sectional area of the bar, the density of steel, and the necessary unit conversions.
Q3. How much does a 12 m 16 mm bar weigh?
A 16 mm bar weighs approximately 1.58 kg/m. Therefore, a 12 m bar weighs approximately 18.96 kg.
Q4. How do I calculate steel weight per metre?
Use: Weight per metre = D² / 162 kg/m.
Q5. Is D²/162 the actual weight of reinforcement?
No. It gives the theoretical/nominal weight. The actual weight can vary within the applicable product-standard tolerances.
Q6. Can I use D²/162 for all steel sections?
No. It is intended for circular reinforcement bars. It should not be directly applied to angles, channels, plates, or other non-circular steel sections.
Q7. How many kilograms are in one tonne of reinforcement steel?
1 tonne = 1,000 kg.