About the Column Buckling Calculator
What is the Column Buckling Calculator?
Long, slender columns fail by bending sideways (buckling) well before the material yields. This column buckling calculator gives the Euler critical load for four end conditions, using IS 800 effective length factors.
It also reports the slenderness ratio, which tells you whether Euler's formula applies.
How to use the Column Buckling Calculator
- Elastic Modulus E (GPa) (sample: 200)
- Least Moment of Inertia (cm⁴) (sample: 150)
- Cross-Sectional Area (cm²) (sample: 32.3)
- Unsupported Length (m) (sample: 3)
- End Conditions (sample: Both ends pinned (K = 1.0))
- Press Calculate Buckling Load (results also refresh as you type). The result card shows the Euler Critical Load, along with Effective length (K × L), Radius of gyration, Slenderness ratio and Critical stress.
Formula used
P_cr = π² × E × I ÷ (K × L)²
- K = 1.0 both pinned, 0.65 both fixed, 0.8 fixed–pinned, 2.0 fixed–free
- Slenderness = K × L ÷ r, with r = √(I ÷ A)
For preliminary sizing only. Structural designs must be prepared and checked by a qualified structural engineer to IS 456, IS 800 and IS 875.
Worked example
These are the sample values already filled in the calculator above, and the result it returns for them:
| Input | Sample value |
|---|---|
| Elastic Modulus E (GPa) | 200 |
| Least Moment of Inertia (cm⁴) | 150 |
| Cross-Sectional Area (cm²) | 32.3 |
| Unsupported Length (m) | 3 |
| End Conditions | Both ends pinned (K = 1.0) |
| Result | Value |
|---|---|
| Euler Critical Load | 328.99 kN |
| Effective length (K × L) | 3 m |
| Radius of gyration | 21.55 mm |
| Slenderness ratio | 139.2 |
| Critical stress | 101.9 MPa |
| Applicability | Slender column – Euler formula applies |
Tips for using the Column Buckling Calculator
- Always use the smaller moment of inertia – columns buckle about their weakest axis.
- Bracing at mid-height halves the effective length and quadruples the Euler load.