Calculate the elastic section modulus W = I/y_max and associated geometric properties. Supports rectangle, solid circle, hollow tube, and I-beam; computes I, distance c, area A, and radius of gyration r. Units in mm.
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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.
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.