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Calculating Theoretical Metal Weight: Formulas for Professionals

Last updated:
June 7, 2024
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I. Theoretical Weight Calculation Formulas for Common Metal Materials

The theoretical weight calculation formulas for common metal materials are shown in Table 1 below.

Table 1 Theoretical Weight Calculation Formulas for Common Metal Materials

No.CategoryTheoretical Weight m/(kg/m)
1Round Steel, Steel Wire Rods, Steel Wirem=0.00617×Diameter2
2Square Steelm=0.00785×Side Length2
3Hexagonal Steelm=0.0068×Distance Across Flats2
4Octagonal Steelm=0.0065×Distance Across Flats2
5Equal Angle Steelm=0.00785×Thickness×(2×Width-Thickness)
6Unequal Angle Steelm=0.00785×Thickness×(Long Side Width+Short Side Width-Thickness)
7I-beamm=0.00785×Web Thickness×[Height+f×(Flange Width-Web Thickness)]
8Channel Steelm=0.00785×Web Thickness×[Height+e×(Flange Width-Web Thickness)]
9Flat Steel, Steel Plate, Steel Strip m=0.00785×Width×Thickness
10Steel Pipem=0.02466×Wall Thickness×(Outer Diameter-Wall Thickness)
11Pure Copper Rodm=0.00698×diameter2
12Hexagonal pure copper rodm=0.0077×opposite side distance2
13Pure copper plate m=8.89×thickness
14Pure copper tubem=0.02794×wall thickness×(outer diameter-wall thickness)
15Brass rodm=0.00668×diameter2
16Hexagonal brass rodm=0.00736×opposite side distance2
17Brass plate m=8.5×thickness
18Brass tubem=0.0267×wall thickness×(outer diameter-wall thickness)
19Aluminum rodm=0.0022×diameter2
20Aluminum plate m=2.71×thickness
21Aluminum tubem=0.008478×wall thickness×(outer diameter-wall thickness)
22Lead plate m=11.37×thickness
23Lead tubem=0.0355×wall thickness×(outer diameter-wall thickness)

Note:

1. For I-beams with the same waist height, if there are several different leg widths and waist thicknesses, add a, b, c to the right of the model to distinguish, such as 32a, 32b, 32c, etc. For channel steel with the same waist height, if there are several different leg widths and waist thicknesses, also add a, b, c to the right of the model to distinguish.

2. f value: The general model and those with an a are 3.34, those with a b are 2.65, and those with a c are 2.26.

3. e value: The general model and those with an a are 3.26, those with a b are 2.44, and those with a c are 2.24.

4. All length units are in mm.

① The unit of theoretical weight m is kg/m².

II. Calculation Formula for Theoretical Weight of Steel

See Table 2 below

Table 2 Calculation Formula for Theoretical Weight of Steel

NameUnitCalculation FormulaCalculation Example
Round Steel Barkg/mW=0.006165d2
In the formula, d is the diameter (mm)
For a round steel with a diameter of 80mm, calculate the weight per meter

Mass per meter = 0.006165×80²kg = 39.46kg
Rebarkg/mW=0.00617d2
In the formula, d is the cross-sectional diameter (mm)
For rebar with a cross-sectional diameter of 12mm, calculate the weight per meter

Mass per meter=0.00617×12²kg=0.89kg
Square Steelkg/mW=0.00785d2
In the formula, d is the width of the side (mm)
For square steel with a side width of 30mm, calculate the weight per meter

Mass per meter=0.00785×30²kg=7.07kg
Flat Steelkg/mW=0.00785db
In the formula, d is the width of the side (mm); b is the thickness (mm)
For flat steel with a side width of 40mm and thickness of 5mm, calculate the weight per meter

Mass per meter=0.00785×40×5kg=1.57kg
Hexagonal Steelkg/mW=0.006798d2
In the formula, d is the distance between opposite sides (mm)
For hexagonal steel with an opposite side distance of 50mm, calculate the weight per meter

Mass per meter=0.006798×50²kg=17kg
Octagonal Steelkg/mW=0.0065d2
In the formula, d is the distance between opposite sides (mm)
For octagonal steel with an opposite side distance of 80mm, calculate the weight per meter

Mass per meter=0.0065×80²kg=41.60kg
Equal Angle Steelkg/mW=0.00785×[d(2b-d)+0.215(R2-2r2)]
In the formula, b is the width of the side (mm); d is the thickness of the side (mm); R is the inner arc radius (mm); r is the end arc radius (mm)
To calculate the weight per meter of 4mm×20mm equal angle steel, find from GB/T 706—2008 that the R of 4mm×20mm equal angle steel is 3.5mm, and r is 1.2mm

Mass per meter=0.00785×[4(2×20-4)+0.215(3.5²-2×1.2²)]kg=1.15kg
Unequal Angle Steel kg/mW=0.00785×[d(B+b-d)+0.215(R2-2r2)]
In the formula, B is the width of the long side (mm); b is the width of the short side (mm); d is the thickness of the side (mm); R is the inner arc radius (mm); r is the end arc radius (mm)
Request the mass per meter for unequal angle steel of 30mm×20mm×4mm. From GB/T 706—2008, the R of 30mm×20mm×4mm unequal angle steel is found to be 3.5mm, and r is 1.2mm

Mass per meter=0.00785×[4(30+20-4)+0.215(3.5²-2×1.2²)]kg=1.46kg
Channel steel kg/mW=0.00785×[hd+2t(b-d)+0.349(R2-r2)]
In the formula, h is height (mm); b is leg length (mm); d is waist thickness (mm); t is average leg thickness (mm); R is inner arc radius (mm); r is end arc radius (mm)
Request the mass per meter for 80mm×43mm×5mm channel steel. From GB/T 706—2008, it is found that the t of this channel steel is 8mm, R is 8mm, and r is 4mm

Mass per meter=0.00785×[80×5+2×8(43-5)+0.349(8²-4²)]kg=8.04kg
I-beam kg/mW=0.00785×[hd+2t(b-d)+0.8584(R2-r2)]
In the formula, h is height (mm); b is leg length (mm); d is waist thickness (mm); t is average leg thickness (mm); R is inner arc radius (mm); r is end arc radius (mm)
For 250mm×118mm×10mm

The mass per meter for I-beam. From GB/T706—2008, it is found that the t of this I-beam is 13mm, R is 10mm, and r is 5mm

Mass per meter=0.00785×[250×10+2×13×(118-10)+0.8584(10²-5²)]kg=42.2kg
Steel platekg/m2W=7.85b
In the formula, b is thickness (mm)
For a steel plate with a thickness of 6mm, request the mass per square meter

Mass per square meter = 7.85×6kg =47.1kg
Steel pipe (including seamless and welded steel pipes) kg/mW=0.02466S(D-S)
In the formula, D is outer diameter (mm); S is wall thickness (mm)
For a seamless steel pipe with an outer diameter of 60mm and a wall thickness of 4mm, request the mass per meter

Mass per meter=0.02466×4×(60-4)kg=5.52kg

Note: The theoretical mass calculated using the formula may differ from the actual mass, with a general error margin of about 0.2% to 0.7%, and can only be used as a reference for estimation.

III. Calculation formulas for the theoretical mass of non-ferrous metal materials

See Table 3 below

Table 3 Calculation formulas for the theoretical mass of non-ferrous metal materials

NameUnit of massCalculation formulaCalculation example
Pure copper rodkg/mW=0.00698×d2
In the formula, d is diameter (mm)
For a pure copper rod with a diameter of 100mm, the mass per meter =
0.00698×100²kg=69.8kg
Hexagonal pure copper rodW=0.0077×d2
In the formula, d is distance between opposite sides (mm)
For a hexagonal pure copper rod with a distance between opposite sides of 10mm, the mass per meter

Mass=0.0077×10²kg=0.77kg
Pure copper plateW=8.89×b
In the formula, b is thickness (mm)
5mm thick pure copper plate, mass per square meter =
8.89×5kg=44.45kg
Pure copper tubeW=0.02794×S(D-S)
In the formula, D is the outer diameter (mm); S is the wall thickness (mm)
Pure copper tube with an outer diameter of 60mm, thickness of 4mm, per

Mass per meter=0.02794×4(60-4)kg=6.26kg
Brass rodW=0.00668×d2
In the formula, d is the diameter (mm)
Brass rod with a diameter of 100mm, mass per meter =
0.00668×100²kg=66.8kg
Hexagonal brass rodW=0.00736×d2
In the formula, d is the distance between opposite sides (mm)
Hexagonal brass rod with a distance between opposite sides of 10mm, per

Mass per meter=0.00736×10²kg=0.736kg
Brass plateW=8.5×b
In the formula, b is the thickness (mm)
Brass plate with a thickness of 5mm, mass per square meter

Mass=8.5×5kg=42.5kg
Brass tubeW=0.0267×S(D-S)
In the formula, D is the outer diameter (mm); S is the wall thickness (mm)
Brass tube with an outer diameter of 60mm, thickness of 4mm, per meter

Mass=0.0267×4(60-4)kg=5.98kg
Aluminum rodW=0.0022×d2
In the formula, d is the diameter (mm)
Aluminum rod with a diameter of 10mm, mass per meter =
0.0022×10²kg=0.22kg
Aluminum plateW=2.71×b
In the formula, b is the thickness (mm)
Aluminum plate with a thickness of 10mm, mass per square meter

Mass=2.71×10kg=27.1kg
Aluminum tubeW=0.008796×S(D-S)
In the formula, D is the outer diameter (mm); S is the wall thickness (mm)
Aluminum tube with an outer diameter of 30mm, wall thickness of 5mm,

Mass per meter=0.008796×5(30-5)kg=1.1kg
Aluminum plateW=11.37×b
In the formula, b is the thickness (mm)
5mm thick lead plate, mass per square meter =
11.37×5kg=56.85kg
Lead tubeW=0.355×S(D-S)
In the formula, D is the outer diameter (mm); S is the wall thickness (mm)
Lead pipe with an external diameter of 60mm and a thickness of 4mm, per meter quality

Mass=0.355×4(60-4)kg=7.95kg

If you prefer not to calculate the metal weight manually using the formulas provided above, you can use an online metal weight calculator instead.

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