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Circular tube — Geometric properties

Calculate area, centroid, second moments of area, section moduli and radii of gyration with clearly defined dimensions.

Created v1.0

By Thibaut Grzelak, Mechanical Analysis Engineer

8 profiles available
01

Choose a shape

02

Calculation inputs

Circular tube
mm
mm

Uniform thickness. Concentric tube. D > 2t.

Results are up to date.

03

Diagram

Dt
04

Results

Area A
1,492.26mm²
Centroid x̄
50mm
Centroid ȳ
50mm
Second moment Iₓ
1.68812E6mm⁴
Second moment Iᵧ
1.68812E6mm⁴
05Show additional results
Section modulus Wₓ (Sₓ)33,762.3 mm³
Section modulus Wᵧ (Sᵧ)33,762.3 mm³
Radius of gyration rₓ33.6341 mm
Radius of gyration rᵧ33.6341 mm
Product of inertia Iₓᵧ0 mm⁴
Principal moment I₁ (max.)1.68812E6 mm⁴
Principal moment I₂ (min.)1.68812E6 mm⁴
Principal-axis angle θₚ0 °
Torsion constant J3.37623E6 mm⁴
Plastic modulus Wpl,x45,166.7 mm³
Plastic modulus Wpl,y45,166.7 mm³
Shear area Av,xNot available
Shear area Av,yNot available

Wpl is integrated exactly over the geometry. J is shown only where an exact implemented solution applies; code-dependent shear areas remain unavailable.

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Calculation note

Full calculation details

Show additional results

Wpl,x
∫A |y − yp| dA
Wpl,y
∫A |x − xp| dA
J
J = π(D⁴ − d⁴)/32
Av,x / Av,y
Not available

Wpl is integrated exactly over the geometry. J is shown only where an exact implemented solution applies; code-dependent shear areas remain unavailable.

01Equations and symbols

Formulas used

dD − 2t
Aπ(D² − d²) / 4
Iₓ = Iᵧπ(D⁴ − d⁴) / 64
Wₓ = WᵧI / (D / 2)
rₓ = rᵧ√(I / A)
SymbolMeaningDimension
DOuter diameter DL
tThickness tL
dInner diameterL
AMaterial areaL²
Iₓ = IᵧSecond momentsL⁴
Wₓ = WᵧSection moduliL³
rₓ = rᵧRadii of gyrationL
02Assumptions and limits

Assumptions and limits

  • Uniform thickness.
  • Concentric tube.
  • D > 2t.

This calculation does not check strength, stability or code compliance.

03Calculator validation

Calculator validation

The hollow case, symmetry and inner diameter are checked.

  • D = 100 mm and t = 5 mm give d = 90 mm.
  • A = 1,492.2565 mm² and Iₓ = Iᵧ.
  • D ≤ 2t is rejected.
  • The result is unit invariant.
04References

References

  1. Roark’s Formulas for Stress and Strain, 9th edition, section-property tables.
  2. Young, Budynas & Sadegh, Roark’s Formulas for Stress and Strain, McGraw-Hill.
  3. BIPM, The International System of Units (SI), 9th edition.

Calculation path and sources

Section properties can be reused for linear mass, bending and buckling checks.

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Continue with a mechanical calculation

Geometric properties become inputs for mass, stress, deformation and stability checks.

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External technical sources

Geometric properties

Second moment of area and section modulus: which value to use?

I describes material distribution and W connects geometry to bending stress. Values change with the x or y axis.

Second moment of area I

Also called area moment of inertia, I is used in deflection and buckling.

I [mm⁴, cm⁴, m⁴, in⁴]

Elastic section modulus W

W uses distance c to the extreme fibre. For an unsymmetrical section, check both sides.

W = I / c

Choose the correct shape

Rectangle, circle, tube, I, channel, T and angle sections require different geometries.

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