# Definition of radius in US English:

### noun

• 1A straight line from the center to the circumference of a circle or sphere.

• ‘David Gregory used p/r for the ratio of the circumference of a circle to its radius.’
• ‘Note that this curvature is the inverse of the radius of a circle tangent to the neutral line at this point.’
• ‘In the introduction he pointed out that a plane was a special case of a spherical surface, that is a sphere with infinite radius.’
• ‘The inverse of the radius of the circle equals the curvature in radians/m.’
• ‘Thus, the area of a circle is equal to half of the product of the radius and the circumference.’
• ‘He calculates the side of a regular pentagon in terms of the radius of the circumscribed circle.’
• ‘The particular tablet which interests us here investigates how to calculate the radius of a circle through the vertices of an isosceles triangle.’
• ‘The hexagon is a function between the radius and circumference of the circle, and is a naturally occurring form in nature.’
• ‘Recall that given a circle of radius r, the circumference is 2pr.’
• ‘Users can measure the distance of vertices/edges/faces, the angle of edges/faces, and the radii and diameters of circles.’
• ‘The point P is on the circumference of the circle of radius b.’
• ‘Because the slices are thin, the height of the rectangle is approximately the radius, r, of the circle.’
• ‘It states that the centre of gravity of a semicircle divides the radius in the ratio 3: 7.’
• ‘The radii of the given circles and n must stand in a certain relationship for the chain to close on itself.’
• ‘And, if anything, I'm quite nearly positive that Lancome is the guy who discovered the constant ratio of a circle's radius to its circumference.’
• ‘Given an angle CAB draw a circle with centre A so that AC and AB are radii of the circle.’
• ‘Company officials like to say that Rhino can go beyond high-school geometry, beyond straight lines and radiuses.’
• ‘So the radius of the sphere will be 1 and its surface area will be 4 Pi.’
• ‘A circle of radius 6 is circumscribed by a square of side-length 12.’
• ‘A circle and square have an equal area only if the ratio between a side of the square and a radius of the circle equals the square root of pi.’
1. 1.1 A radial line from the focus to any point of a curve.
• ‘Because of the very mountainous terrain and the need for very shallow radius curves, most of the route will be in tunnels, with consequent heavy civil engineering costs.’
• ‘The curve radii and crossfall of the road are measured and fed through algorithms from the Austroads Rural Road Design guide to generate a suggested advisory speed for all points along the road.’
• ‘The upper three curves are the pore radii for the three systems, whereas the lower three are the corresponding standard deviations of the upper curves.’
• ‘A minimum curve radius of 5 feet is suggested for 1/2-inch-diameter strand.’
• ‘The front rolled edge and curved radius of this striking two-tiered kitchen island can only be accomplished in solid surface material such as granite or Corian (tm).’
• ‘These apply to clear zones on the outside of horizontal curves with a radius of 900 m or less.’
• ‘Key factors to meet the new criteria include the length and width of runways, the width and curve radii of taxiways, and also the airport's pavement loading limits.’
• ‘Second, this lightweight insert extends the bullet nose and accommodates use of a longer ogive - the radius of the curve of the bullet tip.’
2. 1.2 The length of the radius of a circle or sphere.
• ‘Interestingly, though the analysis points to a ball with an average radius of 1.584 inches, the measured radius of a real baseball is 1.452 inches.’
• ‘As skaters pull their arms in, their radius decreases and they spin faster.’
• ‘Stephenson, who constructed both projects, believed that gradients should be less than 1 percent and that curves should have very wide radii of at least a kilometre.’
• ‘The cone shaped tip is just under one micrometer in length and has a radius of a few nanometers at its apex.’
3. 1.3 A specified distance from a center in all directions.
‘there are plenty of local pubs within a two-mile radius’
• ‘He concluded: ‘This year, I will enter half a dozen local races, all within a radius of 50 miles, and hope to do pretty well.’’
• ‘The IT professionals usually look out for areas surrounding a radius of 9 km from City Railway Station.’
• ‘It seems sensible to find somewhere with no population centres within a two-mile radius - like offshore.’
• ‘Police are investigating links between the arson attack on December 27 and another three within a half-mile radius over the last few days.’
• ‘To calculate a radius for each hospital's market area, we limited radii to a range between 10 and 35 miles.’
• ‘The explosions could reach a radius of 25 meters.’
• ‘Teams divided into four groups, combing through a two-mile radius searching for any clue of what might have happened.’
• ‘But one recommendation to come out of it was that masts should not be located within a radius of 500 metres of schools and homes.’
• ‘The Ride Safe program provides rides for students, staff and faculty members from the Student Life Centre to their homes within a certain radius around campus.’
• ‘B & Bs within a three-mile radius of the town were full.’
• ‘The department has acquired legal powers to close all footpaths within a two-mile radius of any free-range poultry farms.’
• ‘It should be known in this connection that according to the relevant law, no structure of any kind can be built within a radius of 100 metres of any registered national monument.’
• ‘Once Keaton laughed so hard he scared all the birds within a ten-foot radius out of their perches.’
• ‘A check of directories shows 37 hotels and motels within a three-mile radius of Florence and LaSalle.’
• ‘I spent half a century here, most of it within the confines of a small radius.’
• ‘At half-mile intervals, they stop and count the birds they see or hear within a radius of a quarter mile.’
• ‘Day said location is key when making an investment and believes investors should focus on the coastal strip within a 10-mile radius of the city.’
• ‘Tests results Tuesday showed that all 20 farms within a two mile radius of the original infected farm were negative for avian influenza.’
• ‘We do not allow students who live within a five-mile radius to use their cars to come to college.’
• ‘Those deemed more at risk of exposure are those who lived within a one-kilometer radius of the factory for more than 20 years between 1962 and 1987.’
• 2Anatomy
The thicker and shorter of the two bones in the human forearm.

Compare with ulna
• ‘Scaphoid fractures are rare children and the elderly because of the relative weakness of the distal radius compared with the scaphoid in these age groups.’
• ‘Common osteoporotic fracture sites include the vertebrae, the hip, the distal radius of the forearm, and the proximal humerus.’
• ‘He also had tenderness bilaterally over the distal radius and ulna, and anterior tibia.’
• ‘Bone mineral density was measured at the lumbar spine, radius, hip and femoral neck.’
• ‘Abduction is movement of the hand away from the body as the proximal carpal bones move medially on the radius.’
1. 2.1Zoology The corresponding bone in a vertebrate's foreleg or a bird's wing.
• ‘As is usual in chelonioids, the radius is notably longer than the ulna.’
• ‘For example, the radius, one of the lower bones of the foreleg, became much broader.’
• ‘In the equid foreleg, radius and ulna are united, and the ulna is greatly reduced so that all weight is born on the radius.’
• ‘To fit a horse radius into a human forearm would require a physique to rival Popeye.’
• ‘The humerus, radius, and ulna of Adriosaurus appear to be slightly wider than those of the current specimen, but this is probably a result of crushing.’
2. 2.2Entomology Any of the main veins in an insect's wing.
• 3Zoology
(in an echinoderm or coelenterate) any of the primary axes of radial symmetry.

### Origin

Late 16th century (in radius (sense 2 of the noun)): from Latin, literally ‘staff, spoke, ray’.