Radius of gyration calculator
Calculate the radius of gyration (rx, ry) of any beam or profile section from its dimensions. The radius of gyration r = √(I/A) sets the slenderness ratio that governs buckling, so it's the number you check for compression members and struts. Pick a shape or import a DXF, and Dimviz computes rx and ry exactly from the section polygon, alongside moments of inertia, section moduli and weight per metre.
DXF (LWPOLYLINE/CIRCLE) · CSV/XLSX with X,Y columns (blank row = new loop). DWG → export as DXF first.
EL 23,000 MPa · Pultruded FRP (E-glass / polyester)
| Area | A | 3800 | mm² |
| Mass / metre | m | 7.220(4.852 lb/ft) | kg/m |
| 2nd moment | Ix | 2.293e+7 | mm⁴ |
| 2nd moment | Iy | 1.682e+6 | mm⁴ |
| Section mod. | Sx | 229267 | mm³ |
| Section mod. | Sy | 33633 | mm³ |
| Gyration | rx | 77.67 | mm |
| Gyration | ry | 21.04 | mm |
| Torsion | J | 126667 | mm⁴ |
| Published catalogue weight: 5.80 kg/m · computed Δ 24% | |||
Derived exactly from the section polygon (Green’s theorem). Fillets excluded (<2% effect). Verify against certified data before release.
Why the radius of gyration matters
The radius of gyration describes how a section's area is distributed about an axis: r = √(I/A). A larger r means the material sits farther from the centroid, which resists buckling. Slenderness λ = L/r drives the buckling capacity of columns and struts, so rx (strong axis) and ry (weak axis) are what you feed a stability check. Buckling almost always governs about the axis with the smaller r.
Computed from your section, not a table
Instead of interpolating a nominal size, Dimviz integrates the section polygon (Green's theorem) to get Ix, Iy and A, then returns rx = √(Ix/A) and ry = √(Iy/A) for your actual geometry — including non-standard walls. Change a dimension and both values update live, so you can compare candidate sections against a slenderness limit in seconds.
FAQ
How do you calculate the radius of gyration?+
Radius of gyration r = √(I/A), where I is the second moment of area about an axis and A is the cross-sectional area. Dimviz computes I and A from the geometry and returns rx and ry about the centroidal axes.
What's the difference between rx and ry?+
rx is the radius of gyration about the horizontal (strong) axis and ry about the vertical (weak) axis. Column buckling is usually governed by the smaller of the two.
How does it relate to slenderness?+
Slenderness ratio λ = L/r, where L is the effective length. A smaller radius of gyration gives a higher slenderness and a lower buckling capacity, so ry often controls.