Moment of Inertia Calculator

Circle Round pipe I-beam Channel Angle bar Rectangle Profiled pipe T-beam
Dimensions of the circle
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}}
Round pipe dimensions
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}}
I-beam dimensions
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 }}
Channels in a box Channels in an I-beam Channels in a box with a plate Single channel
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 }}
Cruciform angle Paired angle Single angle
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 }}
Rectangle dimensions
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 }}
Profiled pipe dimensions
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 }}
T-beam dimensions
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 }}

Information

The Moment of Inertia Calculator is an online tool for determining the geometric properties of various cross-sections. It plays an essential role in engineering tasks related to strength, stability, and deflection analysis. With this calculator, you can quickly and accurately compute parameters such as cross-sectional area, moment of inertia, section modulus, and radius of gyration—critical figures in the assessment of non-standard or complex section geometries.

This tool supports several types of cross-sections, including:

  • Circle
  • Circular Tube
  • I-Beam
  • Channel
  • Angle
  • Rectangle
  • Hollow Section
  • T-Section

Calculations for complex sections composed of combinations of angles and channels are also available. To perform a calculation, select the cross-section type, enter its dimensions, and click the "Calculate" button. The calculator will automatically display 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)
  • Section modulus, moment of inertia, and radius of gyration for inclined sections relative to the uv-axes (Wuv, Iuv, iuv)

Notes:

  • All calculations assume that the cross-sections have sharp flanges and webs, without any rounding.
  • For complex sections composed of angles, the minimum moments with respect to the principal uv-axes are calculated.

This Moment of Inertia Calculator is an invaluable resource for engineers and designers, streamlining the analysis of cross-sectional geometries and reducing potential errors associated with manual computations.

See also: