Section Calculator
Calculate section properties for various shapes
Input Parameters (mm)
Results
Area
20000.0000 mm²
Centroid X
50.0000 mm
Centroid Y
100.0000 mm
Iₓ (Moment of Inertia)
66666666.6667 mm⁴
Iᵧ (Moment of Inertia)
16666666.6667 mm⁴
Sₓ (Section Modulus)
666666.6667 mm³
Sᵧ (Section Modulus)
333333.3333 mm³
rₓ (Radius of Gyration)
57.7350 mm
rᵧ (Radius of Gyration)
28.8675 mm
Formulas & Reference
Rectangle
Area: A = b × h
Moment of Inertia X: Iₓ = (b × h³) / 12
Moment of Inertia Y: Iᵧ = (h × b³) / 12
Section Modulus X: Sₓ = Iₓ / (h/2)
Radius of Gyration X: rₓ = √(Iₓ/A)
Circle
Area: A = π × (d/2)²
Moment of Inertia X: Iₓ = π × (d/2)⁴ / 4
Section Modulus X: Sₓ = Iₓ / (d/2)
Radius of Gyration X: rₓ = (d/2) / √2
I-Beam / Channel
Area: A = A_top + A_bottom + A_web
Moment of Inertia X: Iₓ = Σ(I_i + A_i × d_i²) (Parallel Axis Theorem)
Section Modulus X: Sₓ = Iₓ / c (c = distance from centroid to extreme fiber)
Angle
Area: A = A_leg1 + A_leg2
Centroid X: Cₓ = (A₁ × x₁ + A₂ × x₂) / A
Centroid Y: Cᵧ = (A₁ × y₁ + A₂ × y₂) / A
Moment of Inertia X: Iₓ = Σ(I_i + A_i × d_i²)
Section Properties Calculator - Civil Engineering Tool
Our Section Properties Calculator is an essential tool for civil engineers, structural designers, and engineering students. This powerful calculator allows you to quickly and accurately compute key section properties for various structural shapes including rectangles, circles, I-beams, channels, and angles.
**Why Use Our Section Calculator?**
Section properties are fundamental to structural analysis and design. The moment of inertia (I), section modulus (S), and radius of gyration (r) are critical parameters that determine a structure's resistance to bending, shear, and axial forces. Our calculator provides instant, precise results that you can trust.
**Key Features:**
1. **Multiple Section Types**: Calculate properties for rectangles, circles, I-beams, channels, and angle sections - the most commonly used shapes in civil engineering.
2. **Comprehensive Results**: Get all the essential section properties in one place: Area, Centroid coordinates, Moment of Inertia (Iₓ, Iᵧ), Section Modulus (Sₓ, Sᵧ), and Radius of Gyration (rₓ, rᵧ).
3. **Real-time Calculations**: See results instantly as you input parameters, making it easy to experiment with different dimensions and compare designs.
4. **Copy Results**: Quickly export your calculation results with a single click for documentation or further analysis.
**Understanding Section Properties:**
- **Area (A)**: The cross-sectional area of the section, which determines the amount of material used and affects the member's resistance to axial forces.
- **Centroid (Cₓ, Cᵧ)**: The geometric center of the section. This is crucial for determining the neutral axis in bending and for calculating moment of inertia about the correct axes.
- **Moment of Inertia (Iₓ, Iᵧ)**: A measure of the section's resistance to bending about the x or y axis. Higher moment of inertia means greater stiffness and resistance to deflection.
- **Section Modulus (Sₓ, Sᵧ)**: Calculated as I/c, where c is the distance from the centroid to the extreme fiber. This parameter is used to determine the bending stress in a member.
- **Radius of Gyration (rₓ, rᵧ)**: A measure of how far the area is distributed from the centroid. It's used in column design to determine slenderness ratio and buckling resistance.
**Engineering Applications:**
Our Section Calculator is used by engineers worldwide for:
- Beam design and analysis - Column design for axial and bending loads - Truss member sizing - Plate and slab design - Composite section analysis - Steel and reinforced concrete design
**Formulas Used:**
For a rectangle with width b and height h: - Area: A = b × h - Moment of Inertia about X-axis: Iₓ = (b × h³) / 12 - Moment of Inertia about Y-axis: Iᵧ = (h × b³) / 12 - Section Modulus: S = I / (h/2) - Radius of Gyration: r = √(I/A)
For a circle with diameter d: - Area: A = π × (d/2)² - Moment of Inertia: I = π × (d/2)⁴ / 4
For built-up sections like I-beams, channels, and angles, we use the parallel axis theorem to calculate the combined properties of each component.
**Built by Engineers, for Engineers:**
At UseCivilTools.com, we understand the importance of accurate, reliable calculations in civil engineering. Our team of experienced engineers has designed this tool to meet the highest standards of precision and usability. Whether you're working on a small residential project or a large-scale infrastructure development, our Section Calculator will help you make informed design decisions.
Start calculating section properties today and experience the power of professional-grade engineering tools at your fingertips.