Rectangular Plastic Modulus Calculator
Plastic moduli and shape factor of a solid rectangle. Elastic Sx and Sy come from the rectangular-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 moduli and shape factors of one solid rectangle.
- 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- Embedded snapshot: unpublished · Build schema 1.0.0 ready · Semantic contract ✓ · Attestation report not published on origin · Live production status STALE (8 capabilities; 189 remain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 width and the height
b and h are positive. They set the length unit.
Read the plastic moduli
Zx and Zy are about the centroidal axes. fx and fy are both 3/2.
Example calculations
Common configurations with formula and result.
Width 2, height 6
b = 2, h = 6
Square of side 2
b = 2, h = 2
Rectangular 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 rectangle, Zx = b h²/4 and Zy = h b²/4. The elastic moduli come from the rectangular-section engine. The shape factor Z/S is 3/2.
- What it calculates
- Plastic moduli and shape factors of one solid rectangle.
- Inputs
- b
- h
- Outputs
- Zx
- Zy
- Sx
- Sy
- fx
- fy
- area
- Formula
Zx = b h²/4, Zy = h b²/4, fx = fy = 3/2- Assumptions
- Calculation runs locally in the browser; values are not uploaded.
- Keep units consistent with the labels on each field.
- b is parallel to x and h is parallel to y. Sx and Sy are not recomputed here. A circle is its own page.
- Units
- b and h set the length unit. Z and S are that unit cubed. The shape factor is dimensionless.
- Boundary conditions
- missing b or h → MISSING_REQUIRED_INPUT
- b ≤ 0 or h ≤ 0 → VALUE_MUST_BE_POSITIVE
- Example
- b=2 h=6 → Zx=18, Zy=6, Sx=12, Sy=4, fx=fy=3/2
- Validation cases
3 published on this page · 4/4 tests · Production surface contract 6/6 · View evidence
- b=2 h=6 → Zx=18, Zy=6, Sx=12, Sy=4, fx=1.5
- b=2 h=2 → Zx=Zy=2, fx=1.5
- b=0 → VALUE_MUST_BE_POSITIVE
- Sources
- Hibbeler, Mechanics of Materials — Plastic deformation — rectangular sectionSupports: The plastic modulus of a rectangle about the axis through mid-depth is b h²/4, and the shape factor is 3/2.
- Hibbeler, Mechanics of Materials — Plastic deformation — rectangular section
- Calculation version
- 1.0.0
Background
Interpretation and common distinctions.
Find the plastic moduli and shape factor of a solid rectangle.
Supported and not supported
Supported: one solid rectangle. Zx = b h²/4 and Zy = h b²/4. Sx and Sy come from the rectangular-section engine. fx and fy are 3/2.
Not supported: a circle, elastic bending stress, and the plastic moment. /calc/mechanical is not open.
Agent / API notes
Capability id: mechanical.statics.rectangular_plastic_modulus · tool id: rectangular-plastic-modulus · pin 1.0.0.
{ "b": 2, "h": 6 }
Share the link with b and h. The result is not written into the link.
Related tools
Other calculators in this family: Rectangular section, Bending stress, Section modulus .
Frequently asked questions
Key distinctions behind the calculation.
Is the shape factor always 3/2?
For a solid rectangle, Z/S is 3/2 about either centroidal axis. A circle is a different page.
Does this return the yield moment?
No. It returns Z and the shape factor. The plastic moment is its own page.
Where do Sx and Sy come from?
From the rectangular-section engine. This page does not keep a second copy of b h²/6.