Diameter
The diameter of a circle is a chord that passes through the centre, connecting two points on the circumference; it is the longest possible chord and equals twice the radius. The diameter determines the scale of a circle and is used directly in calculating circumference (C = πd) and indirectly in area calculations. In three dimensions, the diameter of a sphere is analogously the longest line segment passing through the centre between two surface points.
Key Formula
d = 2r
LaTeX: d = 2r
| Symbol | Meaning | Unit |
|---|---|---|
| d | Diameter | m (or any length unit) |
| r | Radius | m (or any length unit) |
Worked Example
Problem
A wheel has a circumference of 157.08 cm. Find its diameter and radius.
Solution
Step 1 — Use C = πd: d = C/π = 157.08 / 3.14159 ≈ 50.0 cm. Step 2 — Radius: r = d/2 = 50.0/2 = 25.0 cm. Step 3 — Verify: C = πd = 3.14159 × 50 ≈ 157.08 cm. ✓
Answer
Diameter = 50.0 cm, Radius = 25.0 cm
Diameter vs Radius vs Circumference for Common Circle Sizes
| Diameter (cm) | Radius (cm) | Circumference (cm) | Area (cm²) |
|---|---|---|---|
| 2 | 1 | 6.28 | 3.14 |
| 10 | 5 | 31.42 | 78.54 |
| 20 | 10 | 62.83 | 314.16 |
| 50 | 25 | 157.08 | 1963.50 |
| 100 | 50 | 314.16 | 7853.98 |
Interactive Tools
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Related Terms
Radius
The radius of a circle or sphere is the distance from the centre to any point on its boundary. It is one of the most fundamental measurements in circular geometry, directly determining the size of the circle. The radius relates to the diameter by the equation r = d/2 and appears in formulas for circumference, area, and arc length.
Area (geometry)
Area is the measure of the two-dimensional region enclosed within a closed geometric figure, expressed in square units. It quantifies how much flat surface a shape covers and is fundamental in fields ranging from architecture and land surveying to physics and engineering. Different shapes have distinct area formulas derived from their geometric properties, such as A = πr² for a circle or A = ½bh for a triangle.
Conic Section
A conic section is a curve obtained by intersecting a right circular cone with a plane at various angles, yielding four distinct types: circle, ellipse, parabola, and hyperbola. These curves were first studied systematically by the Greek mathematician Apollonius of Perga (c. 262–190 BCE) and later became fundamental in physics when Kepler showed that planetary orbits are ellipses. Conic sections are described by the general second-degree equation Ax² + Bxy + Cy² + Dx + Ey + F = 0, and the type is determined by the discriminant B² − 4AC.
From Greek "diametros" — "dia" (across) + "metron" (measure), meaning "measure across". The term was used by ancient Greek mathematicians including Euclid in his "Elements" (c. 300 BCE) to describe the full width of a circle.