Diameter in Math: Definition, Formula & Examples

Definitionnoun

What is the diameter of a circle?

The diameter of a circle is the distance straight across it through the center. It is twice the radius, d = 2r, and it is the longest chord any circle has. The word also names the line segment itself: a segment that passes through the center and touches both sides of the circle.

In Spanish: diámetro
Also called: across a circle, distance across a circle
How to say it: dye-AM-uh-ter
Grade level: 6-8

Grade 6Grade 7Grade 8CCSS 7.G.B.4GEDSATACT

Diameter in a picture

A diameter is two radii in a straight line through the center. Any other chord misses the center and is shorter.

Formal definition and notation

A diameter of a circle is a chord that passes through the center; its length is d = 2r, where r is the radius. Every circle has infinitely many diameters, all the same length, and each one splits the circle into two semicircles. The diameter also links to the circumference: d = Cπ. For a sphere, a diameter is a segment through the center with both ends on the surface.

Symbol	Read it as	Meaning
d	d	the length of the diameter
AB	segment A B	a diameter named by its endpoints, when A and B are opposite points of the circle
d = 2r	d equals two r	the diameter is twice the radius

Key facts

The diameter must pass through the center of the circle. A segment across the circle that misses the center is a shorter chord.
If radius = 4, diameter = 8. If diameter = 15, radius = 7.5.
The diameter cuts a circle in half: each half is a semicircle.
The circumference is about 3.14 diameters: C = π d.
On a coordinate grid, the midpoint of a diameter is the center of the circle.

Diameter formulas

d = 2r and d = Cπ

d: diameter
r: radius: center to edge, half the diameter
C: circumference: the distance around the circle

From the area: A = π r², so find r = √Aπ first, then double it.

Try it: drag the radius

Interactive

Drag the handle on the circle, or use the arrow keys, to change the radius. Watch the diameter stay exactly twice the radius while the circumference changes too.

This interactive needs JavaScript. The worked examples below show the same ideas step by step.

Diameter examples, step by step

Example 1: From radius to diameter

Warm-up

A clock face has a radius of 9 inches. What is its diameter?

The diameter is two radii laid end to end through the center.
d = 2r = 2 × 9.
2 × 9 = 18.

Answer: The diameter is 18 inches.

Example 2: From circumference to diameter

Core

A round tablecloth has a circumference of 50.24 inches. Find its diameter. Use 3.14 for pi.

Start from C = π d and divide both sides by π: d = Cπ.
d = 50.24 ÷ 3.14.
50.24 ÷ 3.14 = 16.

Answer: The diameter is 16 inches.

Example 3: A diameter on the coordinate plane

Test-style

The endpoints of a diameter of a circle are (−2, 1) and (6, 7). Find the diameter, the radius and the center.

Diameter length by the distance formula: √(6 − (−2))² + (7 − 1)².
8² + 6² = 64 + 36 = 100, and √100 = 10.
Radius = 10 ÷ 2 = 5.
The center is the midpoint: (−2 + 62, 1 + 72) = (2, 4).

Answer: The diameter is 10, the radius is 5, and the center is (2, 4).

Common mistakes

✗ MistakeMeasuring across the circle along a line that misses the center and calling it the diameter.

✓ InsteadDraw the segment through the center. Any other segment across the circle is a shorter chord.

The diameter must pass through the center of the circle. That is what makes it the longest distance across.

✗ MistakeHalving instead of doubling: radius 6, so diameter = 3.

✓ InsteadDiameter = 2 × 6 = 12. The radius is the half.

The radius goes from the center to the edge, so it is the shorter one. The diameter is two radii.

✗ MistakePutting the diameter into the area formula: d = 10, so A = π × 10² = 100π.

✓ InsteadUse the radius: r = 5, so A = π × 5² = 25π.

A = π r² needs the radius. Using the diameter makes the area 4 times too big.

Not to be confused with

Diametervs.Radius

The radius goes from the center to the edge; the diameter goes all the way across through the center. A radius of 4 means a diameter of 8.

Diametervs.Chord

A chord is any segment with both ends on the circle. The diameter is the one chord that passes through the center, so it is the longest.

Diametervs.Circumference

The circumference is the distance around the circle; the diameter is the distance across. C = π d, so C is about 3.14 times d.

Quick check: 3 questions

Question 1 of 3

If a circle has radius 7, what is its diameter?

Show answer and explanation

Answer: D. d = 2r = 2 × 7 = 14. Choice A halves the radius, choice B squares it, and choice C is π × 7, half of the circumference.

Question 2 of 3

Which segment is always a diameter of a circle?

Show answer and explanation

Answer: B. A diameter passes through the center and has both endpoints on the circle. Choice A describes any chord, choice C is a radius, and choice D is a tangent line.

Question 3 of 3

A circle has an area of 36π square cm. What is its diameter?

Show answer and explanation

Answer: A. π r² = 36π, so r² = 36 and r = 6. The diameter is 2 × 6 = 12 cm. Choice B stops at the radius, and choice D confuses r² with d.

Diameter: frequently asked questions

How do you find the diameter of a circle?

It depends on what you know. From the radius, double it: d = 2r. From the circumference, divide by pi: d = Cπ, so C = 31.4 gives d = 10. From the area, find the radius with r = √Aπ, then double it. On a real object, measure the widest distance straight across through the center.

Is the diameter twice the radius?

Yes, always. A diameter is made of two radii that point in opposite directions from the center, so d = 2r and r = d2. A coin with a 1 cm radius has a 2 cm diameter. This is true for every circle and for every sphere.

How many diameters does a circle have?

Infinitely many. You can draw a diameter through the center in any direction, and every one of them has the same length. That is why ‘the diameter’ of a circle can mean either one particular segment or the common length of all of them, such as ‘the diameter is 12 cm’.

Practice and tools

Effortless Math practicePractice on Effortless Math Circle CalculatorGet the diameter from the radius, circumference or area Distance and Midpoint CalculatorLength and center of a diameter on a grid

Sources

Updated November 2026·Reviewed by the Effortless Math team·Standards: CCSS 7.G.B.4

Cite this entry

Effortless Math Team. “Diameter.” Effortless Math Dictionary. Updated November 2026. https://www.effortlessmath.com/math-dictionary/diameter/

Flashcard

TermDiameterstraight across, through the center

DefinitionThe distance across a circle through its center; d = 2r. If the radius is 4, the diameter is 8.

Study the full deck

Browse all terms in the Math Dictionary · More geometry terms · Random term

CircleA circle is the set of all points in a flat plane that are the same distance from one fixed point, the center. That distance is the radius. A segment through the center from edge to edge is the diameter, twice the radius. The distance around is the circumference, 2π r, and the area inside is π r².Geometry · Kindergarten, Grade 1, Grade 7ChordA chord is a line segment whose two endpoints both lie on a circle. The diameter is the longest chord, because it passes through the center. A chord at distance d from the center of a circle with radius r has length 2√r² − d², so chords closer to the center are longer.Geometry · Grade 7, GeometryLengthLength is how long something is: the distance from one end of an object to the other. You measure it by counting equal units laid end to end with no gaps or overlaps, such as inches, feet, centimeters or meters. A new pencil is about 7 inches long.Measurement · Grade 1, Grade 2, Grade 3RadiusThe radius is a line segment from the center of a circle to any point on the circle, or the length of that segment. The radius is half the diameter: if the diameter is 10, the radius is 5. All radii in the same circle have equal length, and r is the radius in C = 2π r.Geometry · Grade 6, Grade 7, Grade 8CircumferenceCircumference is the distance around a circle, found by multiplying the diameter by pi, or the radius by 2 pi: C = π d = 2π r. It is the circle’s perimeter, measured in units of length. A circle with diameter 10 has a circumference of about 31.4, because π ≈ 3.14.Geometry · Grade 6, Grade 7, Grade 8SphereA sphere is a perfectly round solid shape, like a ball, in which every point on the surface is the same distance from the center. That distance is the radius. A sphere has no faces, edges or vertices. Its volume is V = 43π r³ and its surface area is 4π r².Geometry · Kindergarten, Grade 8, GeometryMidpointA midpoint is the point exactly halfway between the two endpoints of a line segment, so it splits the segment into two equal parts. On the coordinate plane, find it by averaging the coordinates: the midpoint of (x₁, y₁) and (x₂, y₂) is (x₁ + x₂2, y₁ + y₂2).Geometry · Grade 8, Algebra 1, GeometryInchAn inch is a US customary unit of length equal to one twelfth of a foot, about the width of an adult thumb. Its abbreviation is in. Rulers split each inch into halves, quarters, eighths and sixteenths. One inch is exactly 2.54 centimeters, and 12 inches make 1 foot.Measurement · Grade 2, Grade 3, Grade 4SideA side is one of the straight line segments that form the outline of a polygon. Two sides meet at each corner, or vertex. A triangle has 3 sides and a square has 4, and adding the lengths of all the sides gives the perimeter.Geometry · Kindergarten, Grade 1, Grade 2Distance FormulaThe distance formula finds the straight-line length between two points on the coordinate plane: d = √(x₂ − x₁)² + (y₂ − y₁)². It is the Pythagorean theorem in disguise: the horizontal and vertical differences are the legs of a right triangle, and the distance is the hypotenuse.Geometry · Grade 8, Algebra 1, GeometryAreaArea is the amount of surface a flat shape covers, measured in square units. It counts how many unit squares fit inside the shape, which is why the units are squared. A rectangle’s area is length times width, so a 5 by 3 rectangle has area 15 square units.Geometry · Grade 3, Grade 4, Grade 5Area of a CircleThe area of a circle is the amount of flat space inside the circle, measured in square units. It equals pi times the radius squared: A = π r². A circle with radius 5 cm has area 25π, about 78.5 square centimeters. If you know the diameter, halve it first to get the radius.Geometry · Grade 7, Grade 8, GeometryPiPi (π) is the number you get when you divide any circle’s circumference by its diameter. It is the same for every circle, about 3.14159. Pi is an irrational number: its decimal never ends or repeats, so we round it to 3.14 or use 227.Geometry · Grade 7, Grade 8, Geometry

Diameter

What is the diameter of a circle?

Diameter in a picture

Formal definition and notation

Key facts

Diameter formulas

Try it: drag the radius

Diameter examples, step by step

Example 1: From radius to diameter

Example 2: From circumference to diameter

Example 3: A diameter on the coordinate plane

Common mistakes

Not to be confused with

Quick check: 3 questions

Diameter: frequently asked questions

How do you find the diameter of a circle?

Is the diameter twice the radius?

How many diameters does a circle have?

Related terms

Practice and tools

Sources

Flashcard

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