Circle section properties
Solid circle about a diameter.
Method
A = πd²/4, I = πd⁴/64, Z = πd³/32. Worked case: 100 mm gives A 7,854 mm², I 4.91×10⁶ mm⁴, Z 98,175 mm³.
Logic: how this figure is built.
How to read a circle
This page answers one question: for a solid circular bar, what are the area, the second moment about a diameter, and the elastic section modulus. It is the section property you need before a stress or a deflection check, not the check itself.
Area is πd²/4. Second moment about a diameter is πd⁴/64. Elastic modulus is πd³/32, which is I divided by the radius. A 100 mm diameter bar is 7,854 mm², 4.91×10⁶ mm⁴ and 98,175 mm³. Those three numbers are consistent with each other. If a model reports a different I for a 100 mm solid circle, the section is not this idealisation.
The diameter is the outside diameter of a solid bar. A hollow tube, a rebar with a rib, or a circle drawn as a plate in plan is a different shape. Second moment grows with the fourth power of diameter, so a 10% error in diameter is about a 46% error in I. Measure the diameter the section was modelled at, not the nominal bar size from a note if the two differ.
Use the result beside a model when you are checking that a circular member has the stiffness or the elastic modulus you think it has. Do not use it to size a strut, to claim a utilisation, or to replace a steel-table section. A hollow circular hollow section needs the outside and inside diameters. This page does not subtract a hole.
- Related: rectangle section
- structural logic
Last checked 3 October 2026. See the disclaimer.