Euler Buckling Load Calculator
Critical buckling load of a column, with the stress at that load and the slenderness ratio.
Results
What this tool does
A slender column fails by bending sideways long before the material is anywhere near its yield stress, and the load at which it does depends on the square of the length — double the length and the strength falls to a quarter. Euler's formula only applies while the column is slender enough to buckle elastically: if the critical stress comes out above roughly half the yield stress, the real failure is inelastic and the code's column curve is needed instead.
Formula
P critical = π² E I ÷ (K L)²
Variables
| Symbol | Meaning | Unit |
|---|---|---|
em | Young's modulus | GPa |
iy | Second moment of area | cm⁴ |
lb | Column length | m |
kf | Effective length factor | — |
ar | Cross-sectional area | cm² |
PC | Critical buckling load | kN |
SC | Critical stress | MPa |
SL | Slenderness ratio | — |
RG | Radius of gyration | mm |
Worked example
- Young's modulus210 GPa
- Second moment of area250 cm⁴
- Column length3 m
- Effective length factor1
- Cross-sectional area20 cm²
- Critical buckling load575.727 kN
- Critical stress287.863 MPa
- Slenderness ratio84.853
- Radius of gyration35.355 mm
Limitations
- The formula assumes ideal conditions: no friction losses, no air resistance and no efficiency losses unless you enter them.
- For work that must comply with a standard or be signed off, check the result against the applicable code and have it reviewed by a qualified engineer.
- The result is an estimate based only on the values you type. Real situations often include factors this calculator does not know about.
Frequently asked questions
What effective length factor should I use?
It depends entirely on how the ends are held. The theoretical values are 1.0 for pinned at both ends, 0.5 for built in at both ends, 0.7 for one end built in and the other pinned, and 2.0 for a cantilever built in at one end and free at the other. Design codes raise these to allow for joints that are never as rigid as drawn — 0.65 and 0.8 instead of 0.5 and 0.7 is common. Take the value from the code you are working to.