Circular Section Elastic Modulus Calculator | Structural Strength in mm³/in³

This free engineering tool calculates both the section modulus (Z) and flexural rigidity (EI) of solid circular sections by simply inputting the diameter and material properties. Essential for structural engineers, mechanical designers, and fabricators working with round bars in bending applications.

What is the Elastic Section Modulus of a Circular Section?

The elastic section modulus is a key geometric property used in bending analysis of beams and structural profiles. For a solid circular section (such as a round bar), it helps determine the maximum bending stress a material can withstand under a given moment.

Formula:

S = (π · d3) / 32

Where:
S = Elastic Section Modulus (mm³ or in³)
d = Diameter of the round bar

Application:

This value is essential when calculating bending stress using:
σ = M / S
Where:
σ = Maximum bending stress
M = Bending moment

It is widely used in mechanical design, structural engineering, and profile bending applications to ensure safety and performance.

For Hollow Circular Sections:

A different formula applies when calculating the section modulus of hollow tubes:

S = [π · (D4 - d4)] / (32 · D)
Where:
D = Outer diameter
d = Inner diameter

Use our calculator to instantly compute the section modulus of round bars in both metric and imperial units.

1. 👉 Solid Rectangular Bar Section Modulus Calculator – Compare round and rectangular bar resistance.
2. 👉 Steel Bar Weight Calculator (Round, Square, Flat, Hex) – Need weight instead of strength? Try this.
3. 👉 Bar Bending Machines & Applications – Learn how section modulus affects real-world bending.

🔷 Key Features & Capabilities

• Calculates elastic section modulus (S) and plastic section modulus (Z)
• Computes flexural rigidity (EI) using material elastic modulus (E)
• Supports multiple materials (steel, aluminum, custom E values)
• Accepts diameter input in mm or inches
• Delivers results in consistent engineering units (cm³/in³, N·m²/lb·in²)
• Clean interface with instant calculations
• 100% browser-based – no installation required

🔷 How It Works

• Enter bar diameter
• Select material (or input custom elastic modulus)
• Choose units (metric/imperial)
• Get instant results for:
  • Section modulus (S, Z)
  • Moment of inertia (I)
  • Flexural stiffness (EI)

🔷 Engineering Applications

• Bending stress analysis of shafts and rods
• Structural deflection calculations
• Machine component design
• Educational demonstrations of beam theory

🔷 FAQ

• Q1: What is the section modulus used for?
  A: It helps engineers determine how much bending stress a solid round bar can safely handle.
• Q2: Can I calculate for hollow pipes?
  A: No. This tool is designed for solid round bars only. For pipes or tubes, use a pipe-specific calculator.
• Q3: Can I input the diameter in inches?
  A: Yes, simply choose “inches” as the input unit before calculating.
• Q4: Is this calculator useful for profile bending?
  A: Absolutely. Section modulus is essential for determining how easily or safely a bar can be bent.