Engin Exam · Free practical tool

Section property calculator

Distinguish cross-sectional area from the second moment of area. See why changing the depth of a rectangular section affects bending stiffness much more than changing its width.

Free results and workingNo signupLocal calculations
Your inputsCalculated on your device

Example values loaded. Replace them with your own measurements.

Your result
↗

Make the numbers make sense.

Enter your values, choose the units, and calculate. You’ll see the result and the working here.

Free results. No account needed.

The method

Rectangle: A=bh, Ix=bh³/12. Circle: A=πD²/4, I=πD⁴/64. Hollow circle: subtract inner area and inertia. Z=I/c.

Before using the result

  • Centroidal bending axis parallel to rectangle width. Inner diameter is used only for a hollow circle; no code section tables or plastic section modulus.

Worked examples

These original training examples illustrate the method for Structural Engineering (SE) Examination. Use the matching “Load example” button above to explore a variation; example values are not equipment settings or prescribed criteria.

1. Worked example

Distinguish cross-sectional area from the second moment of area. See why changing the depth of a rectangular section affects bending stiffness much more than changing its width.

Cross-section
Rectangle
Rectangle width
0.1 m
Rectangle depth
0.2 m
  1. Section: Rectangle; area = 0.020000000000000004 m².
  2. I = 0.00006666666666666668 m⁴; Z = I/c = 0.0006666666666666668 m³.
  • Area: 0.02 m²
  • Centroidal I: 0.00006666667 m⁴
  • Elastic section modulus: 0.0006666667 m³

2. Comparison example

Compare a different supplied condition using the same method. For Engin Exam, the important check is that the input meaning, units and method assumptions still match the problem.

Cross-section
Rectangle
Rectangle width
0.1 m
Rectangle depth
0.3 m
  1. Section: Rectangle; area = 0.03 m².
  2. I = 0.00022499999999999997 m⁴; Z = I/c = 0.0014999999999999998 m³.
  • Area: 0.03 m²
  • Centroidal I: 0.000225 m⁴
  • Elastic section modulus: 0.0015 m³

Check your understanding

1. Which relationship is used?

Rectangle: A=bh, Ix=bh³/12. Circle: A=πD²/4, I=πD⁴/64. Hollow circle: subtract inner area and inertia. Z=I/c.

2. Which assumption should you check first?

Centroidal bending axis parallel to rectangle width. Inner diameter is used only for a hollow circle; no code section tables or plastic section modulus.

3. How should you verify a different unit system?

Convert every input to the displayed calculation units first. Equivalent physical inputs must give equivalent results; a unit label alone does not convert a number.

Continue with the matching exam topic

This tool connects to Structural Engineering (SE) Examination free practice. Work through a question independently, then use the calculation steps to identify where your method differs. The tool stays free whether or not you choose paid preparation.

Section property calculator — free with working | Engin Exam