Tol

Tol is a short form used in several domains, most commonly as an abbreviation for tolerance. In mathematics and computing, tol denotes a numerical tolerance: a small positive value that defines when two quantities are effectively the same or when an algorithm has converged. For example, a solver may terminate when the difference between successive iterates is less than tol. In many libraries, tolerance parameters appear as atol (absolute tolerance) and rtol (relative tolerance), with tol serving as a conventional shorthand.

In engineering and manufacturing, tol is the designation for tolerance—the permissible deviation from a nominal dimension or specification. Tolerances appear on technical drawings and part data, expressed as a plus/minus value or a stated range, and they determine how parts will fit together and perform.

In other contexts tol may occur as a proper name or an acronym in project-specific language. As a stand-alone term, it does not have a single universal definition, so its meaning must be inferred from context. Some datasets or programming projects may assign tol to denote a particular threshold or parameter, but such usage is not standardized.