From the radius
C = 2 × π × r
Multiply the radius by 2π.
Circumference of a Circle Calculator
Calculate the circumference of a circle, the distance around it, from the radius (C = 2πr) or the diameter (C = πd). Clear explanations, practical examples (bike wheel, garden edging, fencing) and the result in the length unit of your choice.
Circumference
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How does this tool work?
This calculator gives the circumference of a circle, the length of its outline, from the radius or the diameter. It covers the classic middle school exercises on the perimeter of a circle as well as everyday needs: edging around a round flower bed, the distance a wheel travels in one turn, fencing around a pond or ribbon around a cake.
The circumference of a circle is proportional to its diameter, and the constant of proportionality is π ≈ 3.14159: C = π × d. Since the diameter equals two radii, this is also written C = 2 × π × r. That is in fact the original definition of π: the ratio between the distance around a circle and its diameter, the same for every circle.
Choose the Radius or Diameter tab depending on the value given in the problem or measured on the object. The result is in the same length unit as the value you entered: centimeters give centimeters, feet give feet. Unlike area, circumference is never a square unit.
Because the relationship is proportional, doubling the diameter doubles the circumference. That makes quick mental checks easy: a circle 1 m across measures about 3.14 m around, a circle 10 m across about 31.4 m.
The calculation uses π with the browser's precision, about fifteen significant digits. Textbooks often round π to 3.14 or use 22/7; the difference from the precise value stays below 0.05%, but it can explain a mismatch in the last digit.
How to use this tool
Pick the measurement you know
Radius (distance from the center to the edge) or diameter (full width through the center).
Enter the value and its unit
All common length units are available, from millimeters to kilometers, plus inches, feet and yards.
Read the circumference
It appears instantly in the same unit and recalculates as you type.
Circumference formulas
The circumference is proportional to the diameter, with π as the constant.
From the diameter
C = π × d
Multiply the diameter by π.
Diameter from the circumference
d = C ÷ π
The inverse formula, useful for measuring a round object with a tape.
Arc length
L = 2πr × α ÷ 360
The part of the circumference cut off by a central angle α in degrees.
- C
- circumference (perimeter of the circle), in length units
- r
- radius
- d
- diameter, equal to 2r
- α
- central angle, in degrees
- π
- ratio of circumference to diameter, about 3.14159
Example: d = 50 cm, C = 50π ≈ 157.08 cm.
Use cases
Math homework
Check the circumference of a circle, the perimeter of a semicircle or a composite figure made of segments and arcs.
Garden, fencing and edging
Order the right length of edging, wire fencing, LED strip or hose to run around a round shape.
Mechanics and cycling
Work out the rollout of a wheel, a pulley or a drum, meaning the distance covered in one revolution.
Sewing and crafts
Find the length of fabric, piping or ribbon needed to trim a round cushion, a lampshade or a cake.
Examples
From the radius
C = 2 × π × 5 = 10π ≈ 31.42 cm.
Input
r = 5 cmResult
C ≈ 31.42 cmFrom the diameter
C = π × 8 = 8π ≈ 25.13 cm.
Input
d = 8 cmResult
C ≈ 25.13 cmDistance per wheel turn
Each turn moves the bike about 2.07 m forward; 1,000 turns cover about 2.07 km.
Input
bike wheel, d = 0.66 m (26 in)Result
C ≈ 2.073 mEdging for a round flower bed
You need just under 19 m of edging; allow a little extra for the joints.
Input
d = 6 mResult
C ≈ 18.85 mAround the Earth at the equator
Using the WGS 84 reference equatorial radius, 2πr gives about 40,075 km, or roughly 24,901 miles.
Input
r = 6,378.137 kmResult
C ≈ 40,075 kmTips and best practices
- Watch which value you have: the diameter is multiplied by π, the radius by 2π.
- For a closed semicircle, add the diameter to half the circumference: P = πr + 2r.
- Circumference is a length: its unit is cm, m or ft, never cm², m² or ft².
- To find the diameter of an object you measured around, divide that measurement by π; a tape measure is all you need.
- Round only the final result and keep the exact form when you can, such as 10π cm.
Sources and references
- Weisstein E.W., Circle (opens in a new tab), Wolfram MathWorldPage in English
- Weisstein E.W., Pi (opens in a new tab), Wolfram MathWorldPage in English
- Programme de mathématiques pour le cycle 3 (opens in a new tab), Ministère de l’Éducation nationalePage in French
Frequently asked questions
What is the formula for the circumference of a circle?
C = 2 × π × r with the radius, or C = π × d with the diameter. Both formulas are equivalent, since the diameter is twice the radius.
Circumference or perimeter: what is the difference?
None in substance: circumference is simply the special name for the perimeter of a circle. Both mean the length of its outline.
How do you find the diameter from the circumference?
Divide the circumference by π: d = C ÷ π. A tree trunk measuring 1.5 m around has a diameter of about 0.48 m. For the radius, divide by two again.
How do you find the perimeter of a semicircle?
The curved part measures π × r. If the shape is closed by the diameter, add 2r: P = πr + 2r. For r = 4 cm, that gives about 12.57 + 8 = 20.57 cm.
Why does π appear in the formula?
π is defined precisely as the constant ratio between a circle's circumference and its diameter. Whatever the circle, the distance around it is a little more than three times its width.
Should I use 3.14 or the exact value of π?
Follow the instructions of your assignment. The tool uses the precise value of π; with 3.14, a circle with a 10 cm radius measures 62.8 cm instead of 62.83 cm.
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