radius

radius — noun

1. in geometry, any line that runs from the centre point of a round shape such as a

1.nounB1
Definition

in geometry, any line that runs from the centre point of a round shape such as a circle out to its outer boundary is called a radius; the word also names the length of that same line.

Example

Joon drew a circle with a radius of five centimetres on the board.

radius of [measurement] for specifying size

The wheel has a radius of thirty centimetres from hub to rim.

Common collocations
  • radius of a circle
  • radius of a sphere
  • radius of [measurement]
  • calculate the radius
  • radius of curvature
Synonyms
  • diameter

    diameter is twice the radius, running from one edge through the centre to the opposite edge

  • half-diameter

    informal synonym for radius used in some technical contexts

Grammar Patterns

the radius of [circle/sphere]

radius of [number + unit]

Usage Note

In geometry, the plural form is radii (ˈreɪ.di.aɪ) rather than radiuses in formal contexts.

Common Mistakes

The radius of the circle is the distance across it.
The radius is half the distance across it
the full distance is the diameter.' — Radius runs from centre to edge, not from edge to edge.

2. the measurement that tells you how far a circular area extends outward from a gi

2.nounB1
Definition

the measurement that tells you how far a circular area extends outward from a given location; the whole region within that distance is also described using this word.

Example

The blast from the explosion was felt within a two-kilometre radius.

within a [number]-[unit] radius — common phrase for distance from a point

Padma agreed to drive anywhere within a thirty-minute radius of her home.

within a [time]-minute radius — extended use with travel time

Common collocations
  • within a radius of [place]
  • within a [number]-[unit] radius
  • ten-mile radius
  • search radius
Synonyms
  • range

    range is more general, not necessarily circular; often used for distance a vehicle can travel or a signal can reach

  • scope

    scope focuses on the limits of what something covers rather than a physical distance around a point

  • reach

    reach suggests the furthest point you can touch or access, not the whole circular area

Grammar Patterns

within a [number]-[unit] radius of [place]

within a radius of [number] [unit]

within [number] [unit] radius

Usage Note

When used with a prepositional phrase, the pattern 'within a [measurement] radius of [place]' is the most common. Native speakers also say 'within [measurement] of [place]' without the word radius, but adding radius makes the circular shape of the area explicit.

Common Mistakes

The hospital is at a ten-kilometre radius.
The hospital is within a ten-kilometre radius of the station.
Radius describes a circular area around a point, not a single straight-line distance to a specific location.

3. a forearm bone that runs from the elbow joint down to the wrist, sitting next to

3.nounB2
Definition

a forearm bone that runs from the elbow joint down to the wrist, sitting next to the thumb and letting you twist your palm around.

Example

Nikos broke his radius when he tried to catch his fall on the ice.

break one's radius — common injury collocation

The X-ray showed a clean fracture of the radius near the wrist.

fracture of the radius — medical phrasing

Common collocations
  • break one's radius
  • fracture of the radius
  • radius and ulna
  • distal radius
  • radial head
Synonyms
  • forearm bone

    a general term covering both the radius and the ulna; less precise

  • radial bone

    formal anatomical term for the radius

Antonyms
  • ulna

    the other bone in the forearm, located on the little-finger side

Grammar Patterns

the radius

fracture of the radius

break one's radius

Usage Note

This anatomical sense is often confused with the ulna, the other forearm bone. The radius is on the thumb side and is slightly shorter but wider; the ulna is on the little-finger side and extends to the elbow tip. In medical writing, the plural is radii or radiuses.

Common Mistakes

The radius is the bone on the little-finger side of the arm.
The radius is the bone on the thumb side; the ulna is on the little-finger side.
The two forearm bones are easy to swap.

Word family

Synonym discussion

Sense: noun/2

Radius, range, scope, reach, and area all describe how far something extends, but they differ in shape and usage. Radius is the most precise: it describes a circular zone measured outward from a single centre point ('within a 5-mile radius of the school'). Range is more general, covering any distance a vehicle, signal, or person can travel or cover regardless of shape ('the car's range is 400 km'). Scope focuses on the limits of what a plan, law, or discussion covers rather than physical distance ('the scope of the investigation'). Reach often suggests the practical limit of what you can access or control ('a product within reach of most families'). Area is the most neutral term for any region or surface and does not imply a circular shape. In everyday conversation, 'within a short driving distance of' is a good non-technical alternative for radius's circular-area meaning.

range ↗scope ↗reach ↗area ↗

Common collocations

Nouns

Phrases

  • within a radius of
  • radius of curvature
  • radius and ulna
  • radius of action

Prepositions

Etymology

LatinEnglish

Radius comes directly from Latin radius, meaning 'ray' or 'spoke of a wheel'. The ancient Romans noticed that spokes of a wheel radiate outward from the centre to the rim — the same shape as a geometric radius. By the late 1300s, English writers were using radius for the half-diameter of a circle. The anatomical sense appeared in the 1600s, named because the radius bone rotates around the ulna like a wheel spoke around an axle.