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Solid circle — 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

Solid circle
mm

Solid homogeneous circle. Out-of-roundness ignored.

Results are up to date.

03

Diagram

D
04

Results

Area A
7,853.98mm²
Centroid x̄
50mm
Centroid ȳ
50mm
Second moment Iₓ
4.90874E6mm⁴
Second moment Iᵧ
4.90874E6mm⁴
05Show additional results
Section modulus Wₓ (Sₓ)98,174.8 mm³
Section modulus Wᵧ (Sᵧ)98,174.8 mm³
Radius of gyration rₓ25 mm
Radius of gyration rᵧ25 mm
Product of inertia Iₓᵧ0 mm⁴
Principal moment I₁ (max.)4.90874E6 mm⁴
Principal moment I₂ (min.)4.90874E6 mm⁴
Principal-axis angle θₚ0 °
Torsion constant J9.81748E6 mm⁴
Plastic modulus Wpl,x166,667 mm³
Plastic modulus Wpl,y166,667 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 = πd⁴/32
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

Aπ · d² / 4
x̄ = ȳd / 2
Iₓ = Iᵧπ · d⁴ / 64
Wₓ = Wᵧπ · d³ / 32
rₓ = rᵧd / 4
SymbolMeaningDimension
dDiameter dL
AAreaL²
x̄ = ȳCentre from OL
Iₓ = IᵧSecond momentsL⁴
Wₓ = WᵧSection moduliL³
rₓ = rᵧRadii of gyrationL
02Assumptions and limits

Assumptions and limits

  • Solid homogeneous circle.
  • Out-of-roundness ignored.

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

03Calculator validation

Calculator validation

Symmetry and diameter power laws provide direct checks.

  • For d = 100 mm, A = 7,853.9816 mm².
  • Iₓ = Iᵧ and Wₓ = Wᵧ.
  • Doubling d gives A × 4 and I × 16.
  • Unit conversions preserve geometry.
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.

Reuse the results

Continue with a mechanical calculation

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

Continue on Formulaxis

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.

The result W is an elastic modulus. Plastic modulus Zp is a different quantity.
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