, a diameter of a circle
is any straight line segment
that passes through the centre of the circle and whose endpoints lie on the circle. It can also be defined as the longest chord
of the circle. Both definitions are also valid for the diameter of a sphere
In more modern usage, the length of a diameter is also called the diameter. In this sense one speaks of ''the'' diameter rather than ''a'' diameter (which refers to the line segment itself), because all diameters of a circle or sphere have the same length, this being twice the radius
For a convex shape
in the plane, the diameter is defined to be the largest distance that can be formed between two opposite parallel lines
tangent to its boundary, and the ''width'' is often defined to be the smallest such distance. Both quantities can be calculated efficiently using rotating calipers
. For a curve of constant width
such as the Reuleaux triangle
, the width and diameter are the same because all such pairs of parallel tangent lines have the same distance.
For an ellipse
, the standard terminology is different. A diameter of an ellipse is any chord
passing through the centre of the ellipse. For example, conjugate diameters
have the property that a tangent line to the ellipse at the endpoint of one diameter is parallel to the conjugate diameter. The longest diameter is called the major axis
The word "diameter" is derived from grc|διάμετρος (), "diameter of a circle", from (), "across, through" and (), "measure". It is often abbreviated ''DIA'', ''dia'', ''d'', or ''⌀''.
The definitions given above are only valid for circles, spheres and convex shapes. However, they are special cases of a more general definition that is valid for any kind of ''n''-dimensional convex or non-convex object, such as a hypercube
or a set of scattered points. The diameter of a subset
of a metric space
is the least upper bound
of the set of all distances between pairs of points in the subset. So, if is the subset, the diameter is
If the distance function
is viewed here as having codomain
R (the set of all real number
s), this implies that the diameter of the empty set
(the case ) equals −∞ (negative infinity
). Some authors prefer to treat the empty set as a special case, assigning it a diameter of 0, which corresponds to taking the codomain of to be the set of nonnegative reals.
For any solid object or set of scattered points in ''n''-dimensional Euclidean space
, the diameter of the object or set is the same as the diameter of its convex hull
. In medical parlance
concerning a lesion or in geology concerning a rock, the diameter of an object is the supremum of the set of all distances between pairs of points in the object.
In differential geometry
, the diameter is an important global Riemannian invariant
In plane geometry, a diameter of a conic section
is typically defined as any chord which passes through the conic's centre; such diameters are not necessarily of uniform length, except in the case of the circle, which has eccentricity
''e'' = 0.
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The [[symbol or [[variable (mathematics)|variable for diameter, , is sometimes used in technical drawings or specifications as a prefix or suffix for a number (e.g. "⌀ 55 mm", indicating that it represents diameter. For example, photographic filter thread
sizes are often denoted in this way.
, the diameter symbol (German ''Durchmesserzeichen
'') is also used as an average
It is similar in size and design
to , the Latin small letter o with stroke
. The diameter symbol ⌀ is distinct from the empty set
symbol , from an (italic
) uppercase phi
, and from the Nordic vowel (Latin capital letter O with stroke
). See also slashed zero
The symbol has a Unicode code point
at , in the Miscellaneous Technical
set. On an Apple Macintosh
, the diameter symbol can be entered via the character palette (this is opened by pressing in most applications), where it can be found in the Technical Symbols category. In Unix/Linux/ChromeOS systems, it is generated using It can be obtained in UNIX-like operating systems using a Compose key
by pressing, in sequence,
The character will sometimes not display correctly, however, since many font
s do not include it. In many situations the letter ø (the Latin small letter o with stroke) is an acceptable substitute
, which in Unicode is . and on a Macintosh by pressing (the letter o
, not the number 0
). In Unix/Linux/ChromeOS systems, it is generated using or . AutoCAD
uses available as a shortcut string .
In Microsoft Word
the diameter symbol can be acquired by typing 2300 and then pressing Alt+X.
the diameter symbol can be obtained with the command
from the wasysym package.
* Angular diameter
, tools for measuring diameters
* Conjugate diameters
* Diameter (group theory)
, a concept in group theory
, who calculated the diameter of the Earth
around 240 BC.
* Graph or network diameter
* Hydraulic diameter
* Inside diameter
* Jung's theorem
, an inequality relating the diameter to the radius of the smallest enclosing ball
* Sauter mean diameter
* Tangent lines to circles
* The diameters
of a screwthread
* Ø (disambiguation)