Check stability using end conditions, materials, and common section shapes in minutes. Get critical load, stress, and recommended safety margin for reports on site.
The calculator evaluates column stability using effective length and section stiffness. It reports elastic Euler buckling and, when yield strength is given, an inelastic Johnson adjustment.
| Case | Unit System | L | K | Section | E | Fy | FS | Typical Use |
|---|---|---|---|---|---|---|---|---|
| 1 | Metric | 3000 mm | 1.0 | Rectangle 200×300 mm (x-axis) | 200000 MPa | 345 MPa | 1.67 | Temporary bracing member check |
| 2 | Imperial | 120 in | 0.699 | I-beam (bf 8, tf 0.5, tw 0.375, d 12) | 29000 ksi | 50 ksi | 1.67 | Framing column preliminary sizing |
| 3 | Metric | 2500 mm | 2.0 | Circle d=250 mm | 200000 MPa | (blank) | 2.00 | Cantilever post stability screening |
Compression members can fail by instability before material crushing. For long, slender columns, stiffness (E·I) and end restraint dominate performance. This calculator reports effective length (K·L), slenderness (K·L/r), and a critical load estimate to support preliminary sizing and checking.
End conditions strongly affect stability. Common K values used in practice are approximately 0.5 for fixed–fixed, 0.699 for fixed–pinned, 1.0 for pinned–pinned, and 2.0 for fixed–free. In the field, partial fixity and connection slip can push K upward, lowering capacity.
The radius of gyration r = √(I/A) links geometry to stability. Increasing I is usually more effective than adding area alone, especially about the weak axis. For I-shaped sections, the minor-axis inertia can be an order of magnitude lower than the major-axis inertia, so weak-axis buckling often controls.
Euler load scales with E·I and inversely with (K·L)². Doubling the unbraced length reduces Euler capacity by roughly four times. Likewise, modest bracing that shortens the effective length can provide large stability gains without changing the section.
When yield strength is provided, the calculator applies a Johnson-type parabolic reduction for stockier columns below a transition slenderness. This supports cases where material yielding begins to influence stability and pure Euler behavior becomes less representative.
The allowable load is reported as (Fcr·A)/FS. Many workflows use FS between about 1.5 and 2.0 for screening, then shift to project-specific design checks. Exporting CSV and PDF helps document inputs, assumptions, and resulting capacities.
For steel, a common modulus is about 200,000 MPa (or 29,000 ksi). Typical yield strengths might range from 250–450 MPa (or 36–65 ksi), depending on grade. For reinforced concrete members, effective stiffness can be lower than the gross section, so engineering judgment is required.
If a service load is entered, utilization is shown as Service/Allowable. Values above 1.0 indicate insufficient capacity for the chosen assumptions. The calculator also estimates a conservative required inertia from an Euler-based rearrangement to guide section selection. Use these outputs to iterate on geometry, bracing, or end restraint efficiently.
Check both axes when possible. Many columns are much weaker about the minor axis, and weak-axis buckling often governs. Select the axis that matches the likely lateral deflection direction and bracing conditions.
K accounts for end restraint and how the column deforms between supports. Better fixity lowers K and increases stability. Connection flexibility, base plates, and frame drift can raise effective K.
Euler buckling varies with 1/(K·L)². Small increases in unbraced length can sharply reduce capacity. Adding bracing to shorten the effective length is often an efficient stability upgrade.
Enter Fy when you want an inelastic check for stocky columns where yielding may influence stability. If Fy is unknown, leave it blank and the calculator will report an elastic-only buckling estimate.
No. It is a conservative, Euler-based screening value for quick iteration. Final member design should follow your governing standard, including additional limit states, imperfections, and load combinations.
Use caution. The formulas assume a prismatic member with constant section. For tapered or stepped members, use an equivalent stiffness method or a dedicated analysis tool, then verify results with engineering judgment.
Design standards include additional factors: residual stresses, initial crookedness, effective stiffness reductions, and calibration to tests. This calculator is best for preliminary sizing and sensitivity checks, not code compliance alone.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.