What is Diameter – Definition, Formula & Examples

The diameter of a circle is the longest chord — a straight line passing through the centre of the circle, connecting two points on its boundary.

Quick Reference:

Definition: The longest straight-line distance across a circle, passing through the centre.

Formula: $d = 2r$ (diameter = 2 × radius)

Radius from diameter: $r = \dfrac{d}{2}$

Circumference using diameter: $C = \pi d$

Area using diameter: $A = \pi\left(\dfrac{d}{2}\right)^2 = \dfrac{\pi d^2}{4}$

Symbol: $d$

Type: Line segment — circle geometry

Used in: Geometry, engineering, physics, pipe sizing, optics, astronomy

Definition

The diameter is a line segment that starts on the circle's boundary, passes through the exact centre, and ends on the opposite boundary. All diameters of a given circle are equal in length. A circle has infinitely many diameters — any line through the centre defines one.

The diameter is exactly twice the radius: $d = 2r$. Equivalently, the radius is half the diameter: $r = \frac{d}{2}$. The ratio of circumference to diameter is always $\pi$ — this is the geometric definition of $\pi$.

Origin

The term "diameter" comes from the Greek diametros (διάμετρος) — dia (across) + metron (measure). Euclid (c. 300 BCE, Greece) formally defined the diameter in Elements Book I, Definition 17: "A diameter of a circle is any straight line drawn through the centre and terminated in both directions by the circumference of the circle." The fundamental relationship $C = \pi d$ was approximated to six decimal places by Archimedes (c. 287–212 BCE, Sicily) and is the basis for all circle calculations.

Variable Key

Worked Examples

Example 1: Circumference from diameter

A circle has diameter $d = 14$ cm. Find the circumference. (Use $\pi = \frac{22}{7}$.)

$$C = \pi d = \frac{22}{7} \times 14 = 44 \text{ cm}$$

Final answer: $C = 44$ cm

Example 2: Diameter from circumference

A circle has circumference $C = 31.4$ cm. Find the diameter. (Use $\pi = 3.14$.)

$$d = \frac{C}{\pi} = \frac{31.4}{3.14} = 10 \text{ cm}$$

Final answer: $d = 10$ cm

Example 3: Area from diameter

A circular table has diameter 1.2 m. Find the area of the tabletop.

$$r = \frac{d}{2} = \frac{1.2}{2} = 0.6 \text{ m}$$

$$A = \pi r^2 = 3.14159 \times 0.6^2 = 3.14159 \times 0.36 \approx 1.13 \text{ m}^2$$

Final answer: $A \approx 1.13$ m²

Common Confusions: What is Diameter vs Radius vs Chord

Diameter vs radius: The radius goes from the centre to the boundary; the diameter goes all the way across through the centre. The diameter is always twice the radius — substituting radius for diameter in $C = \pi d$ gives double the correct circumference.

Diameter vs chord: Any straight line connecting two points on a circle is a chord. The diameter is the special chord that passes through the centre — and is always the longest possible chord. Not all chords are diameters.

Using diameter vs radius in area: The area formula is $A = \pi r^2$ (in terms of radius) or $A = \frac{\pi d^2}{4}$ (in terms of diameter). Substituting the diameter directly into $\pi r^2$ — using $d$ where $r$ belongs — gives four times the correct area.