Section Modulus Calculator

Section Modulus Calculator | Online Free Tool | Elysia Tools

Tool usage guide

Learn when to use this tool, what it supports, and how real users apply it.

Key facts

Category: Math & Numbers
Input types: select, number
Output type: json
Sample coverage: 4
API ready: Yes

Overview

The Section Modulus Calculator computes the elastic section modulus (W = I/y_max), moment of inertia (I), cross-sectional area (A), distance to the extreme fiber (c), and radius of gyration (r) for standard structural shapes. Supporting rectangles, solid circles, hollow tubes, and I-beams with dimensions in millimeters, this tool helps engineers and designers quickly evaluate beam strength and bending resistance.

When to use

When designing or analyzing structural beams to determine their bending stress resistance under load.
When calculating the moment of inertia and radius of gyration for standard shapes like rectangles, tubes, solid shafts, or I-beams.
When verifying cross-sectional properties during mechanical design or civil engineering calculations using millimeter dimensions.

How it works

1Select the cross-section shape from the options: Rectangle, Solid Circle, Hollow Circle (Tube), or I-Beam.
2Input the required dimensions in millimeters, such as width, height, diameters, or flange and web thicknesses.
3Set the desired decimal precision for the output calculations.
4Click calculate to instantly generate the area, moment of inertia, distance to the extreme fiber, elastic section modulus, and radius of gyration.

Use cases

Sizing a rectangular wooden beam to ensure it meets the minimum section modulus required for a specific bending moment.
Calculating the moment of inertia and radius of gyration of a hollow steel tube to evaluate its buckling resistance as a column.
Determining the elastic section modulus of an I-beam to calculate maximum bending stress under a concentrated load.

Examples

1. Calculating Properties for a Rectangular Timber Beam

Structural Designer

Background

A designer needs to verify if a 50 mm wide by 100 mm deep timber joist has sufficient bending capacity.

Problem

Quickly find the moment of inertia, area, and section modulus of the rectangular cross-section.

How to use

Select 'Rectangle' as the shape, enter 50 for Width b, and 100 for Height h, then run the calculation.

Shape: Rectangle, b: 50, h: 100, Decimal Places: 4

Outcome

The tool outputs a section modulus of 83,333.3333 mm³, a moment of inertia of 4,166,666.6667 mm⁴, and an area of 5,000 mm².

2. Analyzing a Hollow Steel Tube Column

Mechanical Engineer

Background

An engineer is selecting a hollow circular steel tube with an outer diameter of 100 mm and an inner diameter of 80 mm for a support frame.

Problem

Determine the radius of gyration and section modulus to check for buckling and bending limits.

How to use

Select 'Hollow Circle (Tube)' as the shape, enter 100 for Outer Diameter Do, and 80 for Inner Diameter Di.

FAQ

What shapes does this calculator support?

It supports four standard cross-sections: Rectangles, Solid Circles, Hollow Circles (Tubes), and I-Beams.

What units are used for the inputs and outputs?

All dimensional inputs are in millimeters (mm). The outputs are in mm² for area, mm⁴ for moment of inertia, mm³ for section modulus, and mm for radius of gyration and distance c.

How is the elastic section modulus (W) calculated?

It is calculated using the formula W = I / c, where I is the area moment of inertia and c is the distance from the neutral axis to the outermost fiber.

What is the radius of gyration (r) and how is it computed?

The radius of gyration describes the distribution of the cross-sectional area around its centroidal axis, calculated as the square root of the moment of inertia divided by the area (r = √(I/A)).

Can I calculate properties for custom asymmetric shapes?

No, this calculator is designed specifically for symmetric standard shapes: rectangles, solid circles, hollow tubes, and standard I-beams.

Shape: Hollow Circle, Do: 100, Di: 80, Decimal Places: 4

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Examples that match this tool

Continue with connected tools and hubs

Learn when to use this tool, what it supports, and how real users apply it.

Key facts

Overview

When to use

How it works

Use cases

Examples

1. Calculating Properties for a Rectangular Timber Beam

2. Analyzing a Hollow Steel Tube Column

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