Euler Buckling Load Calculator — Critical Load, Required Inertia & Allowable Column Load
Calculate critical buckling load using column length, Young’s modulus, effective length factor, and second moment of area.
Enter the known values and review the calculated result
Input parameters
Use consistent values and select the intended engineering units.
Calculation mode
Axial load
Column length
Material properties
Effective length factor
Safety factor
Cross-section
Results
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Method, application and limitations
Review the calculation method, intended application and engineering assumptions before using the result in a design decision.
Formula and calculation method
Critical buckling load formula:
Le = K · L
Pcr = π² · E · I / Le²
Buckling Safety Factor formula:
SFbuckling = Pcr / F
Required second moment of area formula:
Ireq = F · SF · Le² / (π² · E)
Maximum allowable load formula:
Fallow = Pcr / SF
Maximum column length formula:
Preq = F · SF
Le = √(π² · E · I / Preq)
Lmax = Le / K
where:
- Pcr — Critical buckling load (N)
- Ireq — Required second moment of area (m⁴)
- Fallow — Maximum allowable load (N)
- Lmax — Maximum column length (m)
- SFbuckling — Buckling Safety Factor (-)
- F — Axial load (N)
- L — Column length (m)
- Le — Effective length (m)
- E — Young’s modulus (Pa)
- I — Second moment of area (m⁴)
- K — Effective length factor (-)
- SF — Safety factor (-)
When to use this calculator
When to use this calculator:
- Calculate critical buckling load for a column with known length, Young’s modulus, end condition factor, and second moment of area.
- Determine the required second moment of area for a selected axial load, column length, material stiffness, and safety factor.
- Calculate the maximum allowable axial load from the Euler buckling load divided by the selected safety factor.
- Determine the maximum column length that satisfies the required critical load for the entered section stiffness and end condition factor.
- Check the buckling safety factor by comparing critical buckling load with the applied axial load.
How to interpret the result
Critical buckling load is defined as the axial load level calculated from Young’s modulus, second moment of area, and effective column length.
Buckling Safety Factor is defined as critical buckling load divided by axial load. Increasing critical buckling load increases Buckling Safety Factor, while increasing axial load decreases Buckling Safety Factor.
- Safe — In critical buckling load mode, the result is safe when Buckling Safety Factor is greater than or equal to 2.
- Warning — In critical buckling load mode, the result is warning when Buckling Safety Factor is greater than or equal to 1 and lower than 2.
- Unsafe — In critical buckling load mode, the result is unsafe when Buckling Safety Factor is lower than 1.
- Info — In required second moment of area, maximum allowable load, and maximum column length modes, the result is informational because the JS returns a calculated design value without safe, warning, or unsafe thresholds.
- Invalid — The result is invalid when required positive inputs are missing or invalid, including Young’s modulus, effective length factor, second moment of area, axial load in maximum length mode, or unsupported calculation mode.
The result is used to compare axial load with Euler buckling capacity, size the required section stiffness, calculate allowable load, or limit the column length for the selected safety factor.
Calculation example
Example:
A user checks a pinned-pinned column with a 2.0 m length, Young’s modulus of 210 GPa, second moment of area of 8.0 × 10⁻⁶ m⁴, and axial load of 300 kN.
- Mode: Critical buckling load
- F — Axial load = 300000 N
- L — Column length = 2.0 m
- E — Young’s modulus = 210000000000 Pa
- I — Second moment of area = 0.000008 m⁴
- K — Effective length factor = 1.0
Pcr = 4.145 × 10⁶ N and SFbuckling = 13.82.
Assumptions and limitations
- The calculation uses Euler buckling load based on Young’s modulus, second moment of area, and effective length.
- Effective length is calculated as end condition factor multiplied by column length.
- When no positive safety factor is entered in required second moment of area, maximum allowable load, or maximum column length mode, the calculation uses a safety factor of 1.
- For custom cross-sections, the entered second moment of area is used directly.
- For predefined cross-sections, section properties are taken from the section geometry model.
- Cross-sectional area is used only for secondary slenderness and stress outputs, not for the primary Euler buckling load calculation.