Sources and scope for this page: Industry convention — no single governing standard (conventional usage, definitions vary between sources), covering the definition of effective length (k factor). No independent source check is recorded for this page: the content rests on the sources listed and on the working shown on the page. How sources, methods and updates are recorded.
Definition
K converts actual length into the equivalent pinned-pinned length: 1.0 for pinned ends, 0.7 for fixed-pinned, 0.5 for fixed-fixed and 2.0 for a free end.
Because K is squared in the Euler formula, the difference between 1.0 and 2.0 is a factor of four in capacity. Real connections are never perfectly pinned or fixed, which is why codes give K values based on the actual joint stiffness.
Common misuse
Using K = 1.0 for every column. A cantilever or a fixed-base column has very different capacity, and the error is a factor of four.