Definition
In law, "radius" denotes a measured distance extending outward from a fixed central point in all directions, forming a circular boundary. The term appears most commonly in two legal contexts:
1. Geographic restriction clauses. A radius defines the operative area of a restriction — typically in non-compete agreements, non-solicitation covenants, franchise territorial grants, or zoning and licensing conditions. A clause prohibiting a departing employee from competing "within a 25-mile radius" means within a circle of that diameter centered on a specified location.
2. Regulatory and municipal boundary provisions. Ordinances restricting the placement of businesses, structures, or activities (markets, liquor establishments, gaming venues, etc.) relative to schools, churches, or competing facilities commonly express that restriction as a radius from a designated point.
The legal meaning turns on how the radius is measured — straight-line ("as the crow flies") or along road or street distance — and from what center point it is calculated. Courts have resolved disputes on both questions.
Common Language
Modern common usage (Wiktionary): To give a rounded edge to something (verb form); also, the straight-line distance from the center of a circle to its circumference.
Historical common usage (Webster's 1913): "A right line drawn or extending from the center of a circle to the periphery; the semidiameter of a circle or sphere."
The common meaning is purely geometric — a straight-line measurement. The legal meaning inherits the geometry but immediately encounters practical ambiguity: in a built environment of streets, property lines, and landmarks, whether to apply straight-line or road-distance measurement is a genuine legal question that does not arise in pure mathematics. Drafters and researchers must not assume the geometric default controls.
Common Confusion
Straight-line versus road-distance measurement is the most persistent interpretive trap. The geometric definition implies straight-line measurement, but courts and regulators have not applied this uniformly. Bouvier's notes that a New Orleans ordinance prohibiting private markets "within a radius of six squares" of any public market was construed to mean six squares measured along city streets, not as a straight line. Anderson's similarly confirms that "within a radius of ten miles" from a village center means ten road miles where the context involves travel or road-based commerce. Researchers should not assume straight-line measurement governs without examining the regulatory or contractual context and any applicable judicial construction.
Why It Matters in Research
Radius provisions are live drafting and litigation targets in several active areas of law:
Non-compete and restrictive covenant law. The enforceability of post-employment restrictions frequently turns on whether the stated radius is "reasonable" given the employer's actual business footprint. Courts scrutinizing reasonableness require knowing what the radius actually covers — which means knowing the measurement method. Researchers working in this area must check whether the jurisdiction applies blue-penciling or reformation, as the radius figure itself may be redrawn by a court.
Franchise and territorial exclusivity. Franchise agreements routinely define protected territories by radius from a designated address. Disputes arise when the franchisor grants a competing location argued to fall outside (or inside) the restricted circle. Measurement method and center-point definition are both contested.
Municipal and zoning ordinances. Regulatory distance requirements (e.g., a bar must be 500 feet from a school) may specify radius, but the unit of measurement — whether along the nearest walkable path or straight line — is frequently litigated and varies by jurisdiction and drafting. Historical ordinance research, particularly in Louisiana sources, should note the street-measurement rule applied by Louisiana courts in the nineteenth century, which may not reflect modern or other jurisdictions' approaches.
Historical sources are thin on non-compete applications because the modern proliferation of restrictive covenant litigation postdates both Bouvier's and Anderson's. Researchers using historical dictionaries for guidance on radius in employment contracts should treat them as providing only the geometric baseline, not doctrine.
Historical Dictionary Support
Both Bouvier's and Anderson's treat radius primarily as a geometric term imported into legal usage, which is accurate as far as it goes. Bouvier's provides the more legally instructive entry: it notes the straight-line geometric definition, then immediately pivots to the street-measurement holding from Louisiana courts, signaling that the term's legal operation was already understood to diverge from the geometric default in regulatory contexts. Anderson's entry is narrower, addressing road-distance measurement in the context of a specific geographic restriction clause.
Neither source addresses radius in the context of private contractual restrictions (non-competes, franchise territories), reflecting that these forms were not yet subjects of systematic legal treatment when the dictionaries were compiled. The Louisiana street-measurement cases cited in Bouvier's (40 La. Ann. 174; 41 La. Ann. 46) are the most substantive historical authority on measurement method and remain illustrative of the interpretive issue even if their direct authority is limited outside Louisiana.
Jurisdictional Note
Measurement methodology for radius provisions — straight-line versus road distance — is not uniform and is often resolved by the specific regulatory or contractual language rather than a general rule. Louisiana courts historically applied street-distance measurement in municipal market ordinances. Modern non-compete jurisdictions vary. Researchers should examine the governing instrument and any applicable regulatory guidance before assuming geometric straight-line measurement controls.