Circular Hollow Section Area Calculator

This calculator works out the cross-sectional area of a circular hollow section (CHS) – commonly called a steel tube or pipe – from its outer diameter and wall thickness. Enter those two dimensions in millimetres or inches, and you get the metal area in square millimetres or square inches, which is the value used to estimate weight per metre and structural capacity.

Formula

The area of a circular hollow section is the difference between the area of the outer circle and the area of the inner circle. If the outer diameter is D and the wall thickness is t, the inner diameter is D − 2t. The formula is:

A = (π/4) × (D² − (D − 2t)²)

Where:

• A = cross-sectional area (mm² or in²)
• D = outer diameter (mm or in)
• t = wall thickness (mm or in)
• Ï€ ≈ 3.14159

This is the same as calculating the area of a ring: subtract the hole from the outer disc. The result is the area of the metal itself, not the area enclosed by the tube.

Worked Example

Using the default values from the calculator – outer diameter 60.3 mm and wall thickness 3.2 mm:

1. Inner diameter = 60.3 − 2 × 3.2 = 60.3 − 6.4 = 53.9 mm
2. Outer circle area = (π/4) × 60.3² = 0.7854 × 3636.09 ≈ 2856.0 mm²
3. Inner circle area = (π/4) × 53.9² = 0.7854 × 2905.21 ≈ 2281.8 mm²
4. Metal area = 2856.0 − 2281.8 = 574.2 mm²

The calculator shows 574.2 mm², matching the manual calculation. The second output, area per metre, is the same value expressed per metre of tube length: 574.2 mm² per metre (0.000574 m² per metre).

Why the Cross-Sectional Area Matters

The area you get from this calculator is not just a geometry exercise – it is the starting point for two common engineering tasks:

• Weight estimation: Multiply the area by the density of the material. For steel, density is about 7850 kg/m³. A 574.2 mm² section is 0.000574 m², so each metre weighs 0.000574 × 7850 ≈ 4.5 kg/m. Most steel suppliers list CHS weights per metre this way.
• Axial load capacity: For a column or tension member, the cross-sectional area times the material’s yield strength gives the theoretical axial capacity. A larger area means a stronger member, but the shape (diameter and wall thickness) also affects buckling resistance.

For bending and torsion, you also need the second moment of area (I) and the section modulus (W), which depend on the same two dimensions but are different calculations. This calculator gives only the area, which is the first step for weight and axial checks.

How to Read the Result

The result is the area of the metal ring in the cross-section. It is not the surface area of the tube (which would be the circumference times the length) and it is not the internal volume. If you need the surface area for painting or galvanising, you would calculate the outer circumference (π × D) times the length, plus the inner circumference if both sides are exposed.

When you have the area in mm², you can convert to m² by dividing by 1,000,000. For weight per metre in kilograms, use the formula:

Weight per metre (kg/m) = Area (mm²) × Density (kg/m³) / 1,000,000

For example, with 574.2 mm² and steel density 7850 kg/m³: 574.2 × 7850 / 1,000,000 = 4.51 kg/m. This matches typical published weights for a 60.3 mm OD, 3.2 mm wall CHS.

Common Mistakes and Unit Mix-Ups

The most frequent error is mixing units. If you enter the diameter in millimetres but the wall thickness in inches, the formula will produce a nonsense number. Always check that both dimensions use the same unit.

Another common mistake is using the inner diameter directly instead of subtracting twice the wall thickness. Remember that the wall thickness applies to both sides of the tube, so the inner diameter is D − 2t, not D − t.

A third issue is confusing cross-sectional area with surface area. If you are ordering paint or wrapping material, you need surface area, not this value. For a 1-metre length of 60.3 mm OD tube, the outer surface area is π × 0.0603 × 1 ≈ 0.189 m², while the cross-sectional area is only 0.000574 m² – a factor of about 330 difference.

Choosing the Right Dimensions

When selecting a CHS for a project, the outer diameter and wall thickness are usually chosen based on the load and the available sizes from suppliers. Standard metric CHS sizes often follow a series – for example, 21.3, 26.9, 33.7, 42.4, 48.3, 60.3, 76.1, 88.9, 101.6, 114.3 mm – with wall thicknesses like 2.0, 2.6, 3.2, 4.0, 5.0, 6.3 mm. The exact range depends on regional standards and what your local steel stockholder carries.

For a given outer diameter, a thicker wall increases the area and the weight, but also increases the cost. For a given wall thickness, a larger diameter increases the area and the bending stiffness dramatically (the second moment of area scales roughly with the cube of the diameter). So for a beam, you often want a larger diameter with a thinner wall; for a heavily loaded column, you may need both large diameter and thick wall.

Always confirm the actual dimensions with your supplier before ordering – the nominal size may differ slightly from the actual measured dimensions.

Limitations of This Calculator

This calculator assumes a perfectly circular, uniform wall thickness. Real tubes have manufacturing tolerances – the wall may vary slightly around the circumference, and the tube may be slightly oval. For most design work, those tolerances are small enough to ignore, but for precision engineering you should use the actual measured dimensions.

The calculator also does not account for any coating, galvanising, or internal liners. If the tube is galvanised, the zinc layer adds a small amount of area and weight, but it is usually negligible for structural calculations.

Finally, the area alone is not enough for structural design. You need the material grade (e.g., S235, S355 for steel), the yield strength, and the appropriate design standard. Always have a qualified engineer verify any load-bearing design.

Frequently Asked Questions

What is the difference between a circular hollow section and a pipe?
A circular hollow section (CHS) is a structural steel tube with a defined outer diameter and wall thickness, used for construction and mechanical purposes. A pipe is typically specified by its nominal bore and schedule, and is used for conveying fluids. The same geometry applies to both, but the sizing conventions differ.

How do I convert the area to weight per metre?
Multiply the area in mm² by the material density in kg/m³ and divide by 1,000,000. For steel, use 7850 kg/m³. For example, 574.2 mm² × 7850 / 1,000,000 = 4.51 kg/m.

Can I use this calculator for aluminium or stainless steel?
Yes, the area calculation is the same for any material. Only the density changes when you convert area to weight. Aluminium is about 2700 kg/m³, stainless steel about 7900 kg/m³.

Why do I need to subtract twice the wall thickness?
The wall thickness is measured radially – from the outer surface to the inner surface. That thickness exists on both sides of the cross-section, so the inner diameter is reduced by two wall thicknesses. If you subtract only once, you are calculating the area of a solid bar with a hole that is too large.

Is the cross-sectional area the same as the surface area?
No. The cross-sectional area is the area of the metal ring when you cut the tube perpendicular to its length. The surface area is the total external (and internal) area of the tube, which depends on the length. For a 1-metre length of 60.3 mm OD tube, the outer surface area is about 0.189 m², while the cross-sectional area is 0.000574 m².

What if I only know the inner diameter and wall thickness?
You can still use this calculator by entering the outer diameter as the inner diameter plus twice the wall thickness. For example, if the inner diameter is 50 mm and the wall is 3 mm, the outer diameter is 56 mm. Then use the same formula.

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in od | Outer diameter | mm | 60.3 | 0 | 1000
in wt | Wall thickness | mm | 3.2 | 0 | 100
out a | Cross-section area | mm² | (pi/4) * (od^2 - (od - 2*wt)^2) | 1
out am | Area per metre | m²/m | (pi/4) * (od^2 - (od - 2*wt)^2) / 1000000 * 1000 | 3