Construction calculators » Geometric properties calculation: moment of inertia, section modulus, radius of gyration, area

Calculation of geometric properties: moment of inertia, section modulus, radius of gyration, area

Data input:

Diameter d mm

Name	Value	Units of Measurement
Circle diameter	{{D1*k1_1 \| fix2:x1}}
Circle area	{{A1*k1_2 \| fix2:x2}}
Section modulus Wx	{{Wx1*k1_3 \| fix2:x3}}
Section modulus Wy	{{Wy1*k1_4 \| fix2:x4}}
Moment of inertia Ix	{{Ix1*k1_5 \| fix2:x5}}
Moment of inertia Iy	{{Iy1*k1_6 \| fix2:x6}}
Radius of gyration ix	{{ix1*k1_7 \| fix2:x7}}
Radius of gyration iy	{{iy1*k1_8 \| fix2:x8}}

Data input:

Diameter d mm

Wall thickness t mm

Name	Value	Units of Measurement
Pipe diameter	{{D2*k2_1 \| fix2:x9}}
Pipe area	{{A2*k2_2 \| fix2:x10}}
Section modulus Wx	{{Wx2*k2_3 \| fix2:x11}}
Section modulus Wy	{{Wy2*k2_4 \| fix2:x12}}
Moment of inertia Ix	{{Ix2*k2_5 \| fix2:x13}}
Moment of inertia Iy	{{Iy2*k2_6 \| fix2:x14}}
Radius of gyration ix	{{ix2*k2_7 \| fix2:x15}}
Radius of gyration iy	{{iy2*k2_8 \| fix2:x16}}

Data input:

Height h mm

Width b mm

Wall thickness t mm

Flange height h1 mm

Name	Value	Units of Measurement
I-beam area	{{A3*k3_2 \| fix2:x17 }}
Section modulus Wx	{{ Wx3 *k3_3 \| fix2:x18 }}
Section modulus Wy	{{ Wy3*k3_4 \| fix2:x19 }}
Moment of inertia Ix	{{ Ix3 *k3_5 \| fix2:x20 }}
Moment of inertia Iy	{{ Iy3*k3_6 \| fix2:x21 }}
Radius of gyration ix	{{ ix3*k3_7 \| fix2:x22 }}
Radius of gyration iy	{{ iy3*k3_8 \| fix2:x23 }}

Name	Value	Units of Measurement
Channel area	{{ A4*k4_2 \| fix2:x24 }}
Section modulus Wx	{{ Wx4*k4_3 \| fix2:x25 }}
Section modulus Wy	{{ Wy4*k4_4 \| fix2:x26 }}
Moment of inertia Ix	{{ Ix4*k4_5 \| fix2:x27 }}
Moment of inertia Iy	{{ Iy4*k4_6 \| fix2:x28 }}
Radius of gyration ix	{{ ix4*k4_7 \| fix2:x29 }}
Radius of gyration iy	{{ iy4*k4_8 \| fix2:x30 }}

Name	Value	Units of Measurement
Angle area	{{ A5*k5_2 \| fix2:x31 }}
Section modulus Wx	{{ Wx5*k5_3 \| fix2:x32 }}
Section modulus Wy	{{ Wy5*k5_4 \| fix2:x33 }}
Section modulus Wuv	{{ Wuv5*k5_5 \| fix2:x34 }}
Moment of inertia Ix	{{ Ix5*k5_6 \| fix2:x35 }}
Moment of inertia Iy	{{ Iy5*k5_7 \| fix2:x36 }}
Moment of inertia Iuv (min)	{{ Iuv5*k5_8 \| fix2:x37 }}
Radius of gyration ix	{{ ix5*k5_9 \| fix2:x38 }}
Radius of gyration iy	{{ iy5*k5_10 \| fix2:x39 }}
Radius of gyration iuv (min)	{{ iuv5*k5_11 \| fix2:x40 }}

Data input:

Width b mm

Height h mm

Name	Value	Units of Measurement
Rectangle area	{{ A6*k6_2 \| fix2:x41 }}
Section modulus Wx	{{ Wx6*k6_3 \| fix2:x42 }}
Section modulus Wy	{{ Wy6*k6_4 \| fix2:x43 }}
Moment of inertia Ix	{{ Ix6*k6_5 \| fix2:x44 }}
Moment of inertia Iy	{{ Iy6*k6_6 \| fix2:x45 }}
Radius of gyration ix	{{ ix6*k6_7 \| fix2:x46 }}
Radius of gyration iy	{{ iy6*k6_8 \| fix2:x47 }}

Data input:

Height h mm

Width b mm

Thickness t mm

Name	Value	Units of Measurement
Pipe area	{{ A7*k7_2 \| fix2:x48 }}
Section modulus Wx	{{ Wx7*k7_3 \| fix2:x49 }}
Section modulus Wy	{{ Wy7*k7_4 \| fix2:x50 }}
Moment of inertia Ix	{{ Ix7*k7_5 \| fix2:x51 }}
Moment of inertia Iy	{{ Iy7*k7_6 \| fix2:x52 }}
Radius of gyration ix	{{ ix7*k7_7 \| fix2:x53 }}
Radius of gyration iy	{{ iy7*k7_8 \| fix2:x54 }}

Data input:

Height h mm

Width b mm

Thickness t mm

Thickness s mm

Name	Value	Units of Measurement
T-beam area	{{ A8*k8_2 \| fix2:x55 }}
Section modulus Wx (top)	{{ Wx8*k8_3 \| fix2:x56 }}
Section modulus Wx (bottom)	{{ Wx8_1*k8_9 \| fix2:x62 }}
Section modulus Wy	{{ Wy8*k8_4 \| fix2:x57 }}
Moment of inertia Ix	{{ Ix8*k8_5 \| fix2:x58 }}
Moment of inertia Iy	{{ Iy8*k8_6 \| fix2:x59 }}
Radius of gyration ix	{{ ix8*k8_7 \| fix2:x60 }}
Radius of gyration iy	{{ iy8*k8_8 \| fix2:x61 }}

This online calculator is designed for calculating the geometric properties of various cross-section types, which is particularly important when designing structures for strength, stability, or deflection. This tool helps quickly and accurately determine parameters such as cross-sectional area, moment of inertia, section modulus, and radius of gyration—critical steps in the analysis of structures with non-standard or complex shapes.

The calculator supports several types of cross-sections, including:

circle
circular tube
I-beam
channel
angle
rectangle
hollow section
T-section

Additionally, calculations for complex sections made up of combinations of angles and channels are available. To perform the calculation, select the type of cross-section, enter its dimensions, and click the "Calculate" button. The calculator will automatically provide the results in a table containing the following parameters:

cross-sectional area (A)
section modulus about the x-axis (Wx)
section modulus about the y-axis (Wy)
moment of inertia about the x-axis (Ix)
moment of inertia about the y-axis (Iy)
radius of gyration about the x-axis (ix)
radius of gyration about the y-axis (iy)
parameters of section modulus, moment of inertia, and radius of gyration for angled sections relative to the uv-axes (Wuv, Iuv, iuv)

Notes:

all calculated sections are assumed to have no rounding at the flanges and webs;
for complex sections composed of angles, the minimum moments relative to the principal uv-axes are calculated.

This calculation will be useful for engineers and designers working with various structures, as it speeds up the analysis of cross-sections and helps avoid errors associated with manual calculations.