K-Factor Calculator

K-factor has different meanings across engineering disciplines, so this calculator separates structural effective-length calculations from thermal conductivity calculations. In structural mode, K describes how column end restraints change the effective buckling length. The effective length is K times the unsupported column length. Ideal fixed-fixed ends use 0.5, fixed-pinned ends use 0.7, pinned-pinned ends use 1.0, and a fixed-free cantilever uses 2.0. Real connections rarely behave as perfectly ideal restraints, so these values are appropriate for conceptual checks rather than automatic final selection. The structural mode applies Euler's elastic buckling equation. Critical load equals pi squared times elastic modulus times the least second moment of area, divided by effective length squared. Rectangular inertia is width times depth cubed divided by twelve; circular inertia is pi times diameter to the fourth power divided by sixty-four. The calculator uses representative elastic moduli of 200,000 N/mm² for steel, 30,000 N/mm² for concrete, and 11,000 N/mm² for wood. It reports critical load in kilonewtons and compares the entered applied load as a percentage of that idealized capacity. Euler buckling is highly sensitive to length, restraint, and orientation because effective length is squared and section depth is cubed or diameter is raised to the fourth power. The formula describes a straight, slender, perfectly elastic member under concentric axial compression. It does not account for yielding, cracking, material variability, initial crookedness, residual stress, connection flexibility, eccentricity, local buckling, bracing imperfections, or code resistance factors. For rectangular sections, verify that the entered orientation corresponds to the buckling axis being investigated and repeat the check about the weaker axis. In thermal mode, lowercase k is thermal conductivity in W/m·K rather than a column restraint factor. Resistance equals material thickness in meters divided by conductivity. U-value is the reciprocal of that resistance for the single uniform layer. For example, 200 mm of material with conductivity 0.5 W/m·K has resistance 0.4 m²·K/W and U-value 2.5 W/m²·K. Complete building assemblies also include surface films, framing, finishes, cavities, and thermal bridges. These outputs are best used to understand formulas, compare alternatives, and catch unit errors during preliminary work. Structural design must follow the applicable material standard and load code under a qualified engineer. Thermal design should use certified conductivity data and account for all parallel and series heat-flow paths. Do not combine the structural and thermal meanings of K; they share a letter but represent distinct physical quantities and use different units.