Buckling Load (Euler) Calculator
Work out buckling load (euler) instantly with clear inputs, formula shown and shareable results.
About Buckling Load (Euler) Calculator
Euler's formula gives the load at which a slender column buckles: pi^2 EI/(KL)^2. End restraint enters through K, so fixing both ends halves the effective length and quadruples the capacity. A 2.5 m pinned steel column with I = 5e-7 m4 buckles at about 158 kN, regardless of the material's yield strength.
Formulas
Euler critical load
P(cr) = pi^2 E I / (K L)^2
Effective length
L(e) = K L
Worked example
With the default values below, Buckling Load (Euler) Calculator returns Euler Critical Buckling Load of 157.914. Change any input above and every figure here is recalculated in your browser.
Inputs used
- Young's modulusminimum 0 GPa
- 200 GPa
- Second moment of areaminimum 0 m4
- 0.000001 m4
- Column lengthminimum 0 m
- 2.5 m
- End conditionsone of Both ends pinned (K = 1.0), Both ends fixed (K = 0.5), One fixed, one pinned (K = 0.7), One fixed, one free (K = 2.0)
- Both ends pinned (K = 1.0)
Results
- Euler Critical Buckling Load
- 157.914 kN
- Same Load In Newtons
- 157,913.7
- Effective Length
- 2.500 m
- Effective Length Factor K
- 1.00
Step by step
- 1Values used
- 2Euler critical load
- 3Effective length
- 4Euler Critical Buckling Load= 157.914 kN
- 5Same Load In Newtons= 157,913.7
- 6Effective Length= 2.500 m
- 7Effective Length Factor K= 1.00
Assumptions and limits
- The result is derived only from the 4 inputs listed above. Anything not among them is not part of the calculation.
- In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
- Figures are rounded for display to 3 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.
Frequently Asked Questions
Does the material's strength matter?
Not for slender columns - only stiffness and geometry. Stocky columns fail by yielding instead, and codes blend the two through a slenderness limit.
Why does fixing the ends help so much?
Because capacity goes with the inverse square of effective length. Halving it multiplies the buckling load by four.