Plural of “radius”

The plural of radius is radii (some dictionaries also accept radiuses).

Why

"Radius" is Latin for "a rod, ray, or spoke," and it follows the standard Latin second-declension -us/-i plural pattern, giving "radii," the same pattern behind "cactus/cacti," "nucleus/nuclei," and "alumnus/alumni."

"Radius" is also the name of one of the two forearm bones (paired with the ulna), and in anatomical writing its plural is consistently "radii" as well, showing no divergence between the geometric and anatomical senses of the word the way some Latin borrowings split their plural by meaning. In everyday, non-technical speech, "radius" has drifted into a looser meaning describing any rough circular zone around a point ("within walking distance, say a half-mile radius"), and in that casual, approximate sense, the word is rarely pluralized at all, since most such sentences describe only a single zone rather than multiple distinct radii being compared. Insurance policies and service contracts frequently use "radius" this way as well, defining a fixed service area in plain, everyday language rather than in the precise mathematical sense the word carries in geometry.

Usage note

"Radiuses" does appear in general and technical writing, particularly in engineering and design contexts describing curves and corner rounding ("a two-inch radius" or "radiuses" on a countertop edge), but "radii" remains dominant in mathematics, physics, and anatomy, where the word is used with high frequency by specialists trained in its classical plural.

Real-estate and delivery-service writing has popularized a looser, everyday use of "radius" as a rough distance zone ("within a five-mile radius"), and in that casual context "radiuses" occasionally slips in without much pushback, reflecting how far the word has traveled from its purely mathematical origin into ordinary spatial vocabulary. Broadcast meteorology occasionally uses "radii" when describing multiple distinct storm systems' respective wind fields ("the two storms' radii overlapped slightly”), a genuinely technical use of the plural that would otherwise be rare in everyday weather reporting, which usually just describes a single storm's reach. Writers unsure which to use in a borderline technical context can often sidestep the choice entirely by rephrasing around the plural, describing distances or measurements individually rather than needing to pluralize the noun at all.

Common real mistakes

Mistaking "radii" for a singular is a real, if fairly uncommon, error — the same family of mistake that trips people up with "criteria" or "data" — since a single measurement is always "a radius," never "a radii," no matter how often the plural crops up nearby in technical writing. There's a subtler slip worth noting too: writers sometimes reach for "radiuses" specifically for the anatomical forearm bone, assuming the classical plural belongs only to the geometric sense, when medical writing in fact uses "radii" consistently for both meanings, with no field-based split the way "appendix" or "medium" show.

The wider pattern

Grammatically, "radius/radii" sits alongside "cactus/cacti," "nucleus/nuclei," "alumnus/alumni," and "stimulus/stimuli" in the broader Latin second-declension -us/-i group — a set of words that came into English mainly through science, mathematics, and medicine, and that have held onto the classical plural most tightly precisely within those specialist fields.

Examples

• The circle's radius determines its entire area and circumference.
• Engineers specified different radii for each curved section.
• Both radii of the two circles were measured precisely.
• The X-ray showed a hairline fracture in the radius.
• Designers rounded the corners with a consistent radius throughout.
• The blast radius was calculated using standard engineering formulas.
• Several radii were tested before settling on the final design.
• A larger radius gives the wheel a smoother, gentler curve.
• The doctor examined both radii after the patient's fall.
• Search results were filtered within a ten-mile radius.
• The zoning law restricts new construction within a specific radius of the school.
• Both wheels had slightly different radii due to uneven wear over time.
• Delivery was only available within a fifteen-mile radius of the restaurant.
• The architect adjusted the radius of the archway to match the original design.