Euler column buckling calculator
Buckling is a column bowing sideways under compression before the material reaches its strength. Pick the end condition and enter the column data.
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How to use it
- Enter elastic modulus, least moment of inertia, column length and end conditions.
- The result appears straight away and updates as you edit.
- Copy the result, or copy a link that keeps the same values to share it.
How it is calculated
Pcr = π² E I ÷ (K L)². K = 1 pinned both ends, 2 fixed and free, 0.5 fixed both ends, 0.699 fixed and pinned (theoretical values).
Example
Inputs: Elastic modulus = 200 GPa, Least moment of inertia = 1,000 cm⁴, Column length = 3 m, End conditions = Pinned, pinned (K = 1). Result: Critical buckling load: 2,193.25 kN; Effective length: 3 m; Effective length factor K: 1.
Limits and caveats
- Euler applies to slender columns only; short columns fail by yielding first.
- Leaves out safety factors, eccentricity and initial crookedness that design codes include.
Questions about this tool
Which moment of inertia should I use?
The smaller of the two axes, because the column buckles about its weakest axis.
When does the Euler formula not apply?
When the stress Pcr ÷ A is above the proportional limit of the material, as in short or stocky columns.
Why do codes use different K values?
Full fixity is hard to achieve in practice, so some codes recommend slightly higher design values, such as 0.65 instead of 0.5.