Circumference 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.
Unroll any circle and its outline is π, about 3.14, times as long as its diameter. That ratio is why C = π d.
Formal definition and notation
For a circle with radiusr and diameterd = 2r, the circumference is the length of the circle itself, C = π d = 2π r. The numberπ is defined as the ratioCd, which is the same for every circle: π ≈ 3.14159. Because π is irrational, an exact circumference is written with π, as in 10π, and decimal answers are approximations.
Symbol
Read it as
Meaning
C
C
the circumference
π
pi
the ratio of circumference to diameter, about 3.14 or 227
10π
ten pi
an exact answer; 10π ≈ 31.4
Key facts
Every circle’s circumference is a little more than 3 times its diameter: Cd = π.
Circumference is a length, so its units are not squared: centimeters, not square centimeters.
Doubling the radius doubles the circumference: r = 3 gives 6π, and r = 6 gives 12π.
A wheel moves forward one circumference in each full turn.
An arc is part of the circumference: a semicircle’s curved edge is 12π d.
Circumference formula
Circumference formula
C = π d = 2π r
C
circumference, the distance around
d
diameter, the distance across through the center
r
radius, half the diameter: r = d2
π
pi, about 3.14 (use the π key for more accuracy)
To go backward, divide: d = Cπ. A circumference of 31.4 cm means a diameter of about 10 cm.
Try it: stretch the radius
Interactive
Drag the handle on the edge, or focus it and use the arrow keys, to change the radius. The readout shows the diameter, the circumference and the ratio of circumference to diameter.
This interactive needs JavaScript. The worked examples below show the same ideas step by step.
Circumference examples, step by step
Example 1: From the diameter
Warm-up
A plate has a diameter of 8 cm. Find its circumference. Use 3.14 for pi.
Use C = π d.
C = 3.14 × 8.
3.14 × 8 = 25.12. The exact answer is 8π cm.
Answer: The circumference is about 25.12 cm (exactly 8π cm).
Example 2: From the radius
Core
A circular garden has a radius of 7 feet. Find its circumference. Use 227 for pi.
Use C = 2π r, because the radius is given.
C = 2 × 227 × 7.
The 7s cancel: C = 2 × 22 = 44.
Answer: The circumference is 44 feet.
Example 3: Distance a wheel rolls
Test-style
A bicycle wheel has a diameter of 26 inches. How far does the bike travel when the wheel makes 100 full turns? Use 3.14 for pi.
One turn moves the bike one circumference: C = π d = 3.14 × 26 = 81.64 inches.
100 turns: 100 × 81.64 = 8164 inches.
To feet: 8164 ÷ 12 ≈ 680 feet.
Answer: The bike travels about 8,164 inches, or about 680 feet.
Common mistakes
✗ MistakeUsing the area formula: a circle with r = 5 has circumference π × 52 = 25π.
✓ InsteadC = 2π r = 2 × π × 5 = 10π ≈ 31.4.
Circumference is a distance around the circle, not the area inside it. π r2 is the area.
✗ MistakePutting the radius into C = π d: with r = 5, C = 5π.
✓ InsteadDouble the radius first: d = 10, so C = 10π.
π d needs the diameter. With a radius, use 2π r.
✗ MistakeWriting the answer in square units: 31.4 square cm.
✓ Instead31.4 cm. Circumference is a length.
Only area uses square units. Circumference measures how long the outline is.
Not to be confused with
Circumferencevs.Area of a circle
Area is the space inside, A = π r2, in square units. For r = 3: area 9π square units, circumference 6π units.
The diameter goes straight across through the center; the circumference goes all the way around. C is about 3.14 times d.
Quick check: 3 questions
Question 1 of 3
Which formula uses the diameter to find the circumference?
Show answer and explanation
Answer: C.C = π d. Choice A doubles the diameter twice, choice B is the area formula, and choice D uses the radius where the diameter belongs.
Question 2 of 3
A circle has radius 5. What is its exact circumference?
Show answer and explanation
Answer: B.C = 2π r = 2 × 5 × π = 10π. Choice A forgets to double the radius, and choice C is the area, π r2.
Question 3 of 3
A circle has a circumference of 18.84 cm. What is its diameter? Use 3.14 for pi.
Show answer and explanation
Answer: A.d = Cπ = 18.84 ÷ 3.14 = 6. Choice B is the radius, choice C halves the circumference, and choice D multiplies by pi instead of dividing.
Circumference: frequently asked questions
What is the formula for circumference?
Use C = π d when you know the diameter, or C = 2π r when you know the radius. Both say the same thing, because the diameter is twice the radius. For a circle with radius 4 cm: C = 2 × π × 4 = 8π ≈ 25.1 cm.
Should I use 3.14 or the pi button?
Follow the directions. Many problems say ‘use 3.14’ or ‘use 227‘; others ask for an exact answer such as 12π. If nothing is said, the π key gives a more accurate decimal. Answers with 3.14 and with the π key differ slightly, so round only at the end.
How do you find the diameter from the circumference?
Divide the circumference by pi: d = Cπ. For a circumference of 47.1 m, d = 47.1 ÷ 3.14 = 15 m. Halve that to get the radius, 7.5 m. This is how you find the width of a tree trunk from a tape measure wrapped around it.
Updated November 2026·Reviewed by the Effortless Math team·Standards: CCSS 7.G.B.4
Cite this entry
Effortless Math Team. “Circumference.” Effortless Math Dictionary. Updated November 2026. https://www.effortlessmath.com/math-dictionary/circumference/
Flashcard
TermCircumferencethe distance around a circle
DefinitionThe perimeter of a circle: C = π d = 2π r. A circle with diameter 10 has C ≈ 31.4.
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 7RadiusThe 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 8DiameterThe 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.Geometry · Grade 6, Grade 7, Grade 8LengthLength 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 3NumberA number is an amount or value used to count, measure, order and compare. We write numbers with digits (7), words (seven) or other symbols, but the number itself is the amount: 7 dots, the word seven and the numeral 7 all show the same number. Numbers include whole numbers, fractions, decimals and negatives.Number System · Kindergarten, Grade 1, Grade 2RatioA ratio compares two quantities by division. Ratios can be written with words, a colon, or a fraction: 3 boys to 5 girls is 3 to 5, 3 : 5, or 35. Order matters, and a ratio can compare part to part or part to whole. Multiplying both numbers by the same amount gives an equivalent ratio.Ratios and Proportions · Grade 6, Grade 7, Grade 8CentimeterA centimeter is a metric unit of length equal to one hundredth of a meter, about the width of a fingernail. Its symbol is cm. There are 100 centimeters in 1 meter and 10 millimeters in 1 centimeter, and 1 inch equals 2.54 centimeters.Measurement · Grade 3, Grade 4, Grade 5SquareA square is a quadrilateral with four equal sides and four right angles. It is a special rectangle and a special rhombus at the same time. For a square with side s, the perimeter is 4s, the area is s2, and each diagonal is s√2.Geometry · Kindergarten, Grade 2, Grade 3InchAn 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 4PerimeterPerimeter is the total distance around a two-dimensional shape. To find it, add the lengths of all the sides. A rectangle with sides 5 and 3 has perimeter 5 + 3 + 5 + 3 = 16. Perimeter is a length, so it uses length units such as inches or meters, never square units.Geometry · Grade 3, Grade 4, Grade 5Arc LengthArc length is the distance along a curved part of a circle, measured in units of length. An arc with central angle θ in a circle of radius r is θ360 of the circumference: s = θ360 × 2π r when θ is in degrees, or simply s = rθ when θ is in radians.Geometry · Geometry, PrecalculusPiPi (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, GeometryArea 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, 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 5ChordA 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, GeometryEquation of a CircleThe equation of a circle with center (h, k) and radius r is (x − h)2 + (y − k)2 = r2. It says that every point (x, y) on the circle is exactly r units from the center. A circle centered at the origin has the simpler equation x2 + y2 = r2.Geometry · Geometry, Algebra 2, Precalculus