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Calcimator

Column Buckling Calculator

Calculate Euler critical buckling load, critical stress, and slenderness ratio for columns with various end conditions.

Inputs

MPa

AISC 360: steel E=200,000 MPa; EN 1993: aluminum 70,000 MPa; wood (DF-L) ≈ 11,000 MPa

mm⁴
ft

AISC 360 Table C-A-7.1: fixed-fixed K=0.65; fixed-pin K=0.80; pin-pin K=1.0; cantilever K=1.2

mm²

Results

Euler Critical Load (Pcr)

616,850.28 N

Critical Stress (σcr)

123.37 MPa

Slenderness Ratio (KL/r)126.5
Euler Stress123.37 MPa
Required Safety Factor1.67
How to Use This Calculator
  1. Enter the column unsupported length in feet and the effective length factor (K) for the end conditions.
  2. Input the modulus of elasticity and the moment of inertia for the chosen section.
  3. Set the applied axial load in kips.
  4. Review the Critical Buckling Load (Euler load) and the Slenderness Ratio.
  5. Check the Safety Factor - it should be 2.0 or greater per standard practice.

How the result changes with Column Length

Column LengthEuler Critical Load (Pcr)Critical Stress (σcr)
3.091,033,672.08 N206.73 MPa
1181,566.98 N16.31 MPa
2024,674.01 N4.93 MPa
2713,538.55 N2.71 MPa

What each input means

Elastic Modulus (E)
Modulus of elasticity of the column material per AISC 360 and EN 1993. Steel = 200,000 MPa; aluminum = 70,000 MPa; concrete (Ec=4700√f'c MPa); wood ≈ 11,000 MPa.
Moment of Inertia (I)
Minimum moment of inertia of the column cross-section about the buckling axis.
Column Length
Unbraced length of the column between supports.
Effective Length Factor (K)
Effective length factor per AISC 360 Commentary Table C-A-7.1. Theoretical values: 0.5 = fixed-fixed, 0.7 = fixed-pinned, 1.0 = pinned-pinned, 2.0 = fixed-free. AISC recommends using recommended values (0.65, 0.80, 1.0, 1.2) for practical design.
Cross-Section Area
Total cross-sectional area of the column section.

How this is calculated

Worked example, using the default values

  1. Identify Input Parameters
    4 parameters
    Elastic Modulus (E) = 200000, Moment of Inertia (I) = 5000000, Column Length = 4, Effective Length Factor (K) = 1 = 5 input(s) provided
  2. Calculate Euler Critical Load
    Euler Critical Load
    616850.28 = 616850.28
  3. Calculate Critical Stress
    Critical Stress
    123.37 = 123.37
  4. Calculate Slenderness Ratio
    Slenderness Ratio
    126.5 = 126.5
  5. Calculate Euler Stress
    Euler Stress
    123.37 = 123.37

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