Circular Plastic Modulus Calculator
Plastic modulus and shape factor of a solid circle. The elastic modulus comes from the circular-section engine. Runs locally.
Trust summary Engine tested · Source checked · 4/4 tests · Production surface contract 6/6 · v1.0.0
- Input interpretation
- Enter values to calculate.
- Result
- —
- Model
- Plastic modulus and shape factor of one solid circle about a centroidal diameter.
- Scope
- Calculation runs locally in the browser; values are not uploaded.
- Verification
- Engine tested · 4/4 tests · Production surface contract 6/6 · Source checked · v1.0.0
- Named expert review
- Optional · Not performed
- Sources
- Hibbeler, Mechanics of Materials
- Evidence
- 2 golden · 2 boundary · Production surface contract 6/6 · Artifact integrity PASS
- Production
- Embedded snapshot: unpublished · Build schema 1.0.0 ready · Semantic contract ✓ · Attestation report not published on origin · Live production status STALE (8 capabilities; 189 remain CURRENT) @ 2026-09-23T21:48:15.717Z
- Semantic contract
- PASS
Formulas
Core equations used by this calculator.
How to use
Enter the radius
r is positive. It sets the length unit.
Read Z and the shape factor
Z is about a centroidal diameter. f is 16/(3π) for every solid circle.
Example calculations
Common configurations with formula and result.
Radius 2
r = 2
Radius 1
r = 1
Circular Plastic Modulus calculator specification
Version 1.0.0 · Engine tested
- Engine tested 4/4 tests · Production surface contract 6/6
- Named expert review Not performed
- Calculation version 1.0.0
- Definition
- For a solid circle, the plastic modulus about a centroidal diameter is Z = 4 r³/3. The elastic modulus comes from the circular-section engine. The shape factor is 16/(3π).
- What it calculates
- Plastic modulus and shape factor of one solid circle about a centroidal diameter.
- Inputs
- r
- Outputs
- Z
- S
- f
- area
- Formula
Z = 4 r³/3, S = π r³/4, f = 16/(3π)- Assumptions
- Calculation runs locally in the browser; values are not uploaded.
- Keep units consistent with the labels on each field.
- S = π r³/4 is not recomputed here. A rectangle is the rectangular-plastic-modulus page. A hollow circle is its own page.
- Units
- r sets the length unit. Z and S are that unit cubed. The shape factor is dimensionless.
- Boundary conditions
- missing r → MISSING_REQUIRED_INPUT
- r ≤ 0 → VALUE_MUST_BE_POSITIVE
- Example
- r=2 → Z=32/3, S=2π, f=16/(3π)
- Validation cases
3 published on this page · 4/4 tests · Production surface contract 6/6 · View evidence
- r=2 → Z=32/3, S=2π, f=16/(3π)
- r=1 → Z=4/3, S=π/4, f=16/(3π)
- r=0 → VALUE_MUST_BE_POSITIVE
- Sources
- Hibbeler, Mechanics of Materials — Plastic deformation — circular sectionSupports: The plastic modulus of a solid circle about a diameter is 4 r³/3, and the shape factor is 16/(3π).
- Hibbeler, Mechanics of Materials — Plastic deformation — circular section
- Calculation version
- 1.0.0
Background
Interpretation and common distinctions.
Find the plastic modulus and shape factor of a solid circle.
Supported and not supported
Supported: one solid circle. Z = 4 r³/3 about a centroidal diameter. S comes from the circular-section engine. f = 16/(3π).
Not supported: a rectangle, a hollow circle, and the plastic moment. /calc/mechanical is not open.
Agent / API notes
Capability id: mechanical.statics.circular_plastic_modulus · tool id: circular-plastic-modulus · pin 1.0.0.
{ "r": 2 }
Share the link with r. The result is not written into the link.
Related tools
Other calculators in this family: Circular section, Rectangular plastic modulus, Bending stress .
Frequently asked questions
Key distinctions behind the calculation.
Is the shape factor 3/2?
No. A solid circle is 16/(3π), about 1.698. A rectangle is 3/2.
Does this include a hole?
No. A hollow circle is its own page.
Where does S come from?
From the circular-section engine. This page does not keep a second copy of π r³/4.