Calculator · Engineering Mechanics
Radius of Gyration Calculator
The distance at which the whole area or mass could be concentrated without changing the moment of inertia about the same axis. It is a length, not an inertia.
Quantity
Inputs
Results
| Radius of gyration k = √(I/A) | 0.02887 m |
|---|---|
| Check: I = A·k² | 1.667e-5 m⁴ |
Technical reference
k = √(I/A) (area mode)
k = √(I/m) (mass mode)
- I
- moment of inertia about the chosen axis, matching the selected mode[m⁴ or kg·m²]
- A, m
- area or mass in the selected mode[m² or kg]
- k
- radius of gyration about that same axis[m]
Physically, k is the distance from the axis at which the whole area or mass could be concentrated as a point without changing I about that axis.
Assumptions
- · I and the area or mass must refer to the SAME axis; mixing axes is meaningless.
- · k is a length in metres, even though it is derived from an inertia.
- · Area form uses I in m⁴ with A in m²; mass form uses I in kg·m² with m in kg. The two are never mixed.
- · A net area or mass of zero leaves k undefined rather than infinite.