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cm
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Distance from center to edge
Key Circle Formulas:
C = 2πr | C = πd
A = πr² | d = 2r
r = C / (2π) | π = 3.14159
C = 2πr | C = πd
A = πr² | d = 2r
r = C / (2π) | π = 3.14159
Circumference
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📋 Full Circle Properties
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Sources & Methodology
Circumference formulas verified against NIST mathematical constants (pi = 3.14159265358979) and standard geometry curriculum per the Common Core State Standards for Mathematics.
Khan Academy — Circumference of a Circle
Definition of circumference, derivation of C = 2 x pi x r = pi x d, and worked examples covering all input forms
NIST — Mathematical Constants
Pi constant value 3.14159265358979323846 used for all circumference and area calculations throughout this tool
Methodology: Radius from input: r (direct), d/2 (from diameter), sqrt(A/pi) (from area). Then: Circumference = 2 x pi x r. Diameter = 2r. Area = pi x r^2. Semicircle perimeter = pi x r + 2r. Pi = 3.14159265358979.
⏱ Last reviewed: April 2026
How to Calculate Circumference of a Circle
Circumference is the distance around the outside of a circle — the circle's equivalent of perimeter. This circumference calculator is one of the most commonly needed geometry tools, used by students from middle school through college and by professionals in engineering, construction, and design. The formula C = 2πr connects three of the most fundamental circle properties.
All Circumference Formulas
C = 2 × π × r (from radius)
Example: r = 5 cm → C = 2 × π × 5 = 31.4159 cm
C = π × d (from diameter)
Example: d = 10 cm → C = π × 10 = 31.4159 cm
This is how pi was originally defined: pi = C / d
This is how pi was originally defined: pi = C / d
C = 2 × √(π × A) (from area)
Example: A = 78.54 cm² → r = sqrt(78.54 / pi) = 5, C = 2 x pi x 5 = 31.4159 cm
Circumference Reference Table
| Radius (r) | Diameter (d) | Circumference (C) | Area (A) |
|---|---|---|---|
| 1 | 2 | 6.2832 | 3.1416 |
| 2 | 4 | 12.5664 | 12.5664 |
| 5 | 10 | 31.4159 | 78.5398 |
| 7 | 14 | 43.9823 | 153.9380 |
| 10 | 20 | 62.8318 | 314.1593 |
| 15 | 30 | 94.2478 | 706.8583 |
| 20 | 40 | 125.6637 | 1,256.6371 |
Real-World Applications of Circumference
- Wheel and tire sizing — circumference = distance traveled per revolution
- Track and field — lane circumferences for staggered starts
- Pipe and cable — material needed to wrap around a cylindrical object
- Astronomy — planetary circumferences from known radii
- Construction — circular foundation perimeters and pipe sizing
💡 Pro Tip: Pi (π) is defined as the ratio of circumference to diameter: π = C / d. This means for any circle, dividing its circumference by its diameter always gives 3.14159... This is why knowing any one of {radius, diameter, circumference, area} lets you calculate all the others. The circumference formula C = πd is the direct expression of this definition.
Frequently Asked Questions
C = 2 x pi x r = pi x d, where r is radius, d is diameter, pi = 3.14159. From area A: C = 2 x sqrt(pi x A). Example: r = 5: C = 2 x pi x 5 = 31.4159 units.
C = pi x d. Example: d = 10: C = pi x 10 = 31.4159 units. This is the most direct form — pi was defined as C/d, meaning pi is just the circumference of any circle divided by its diameter.
C = 2 x pi x r. Example: r = 5: C = 2 x pi x 5 = 31.4159 units. Since diameter = 2r, this is the same as C = pi x d.
C = 2 x pi x 5 = 31.4159 units. Area = pi x 25 = 78.54 sq units. Diameter = 10 units.
C = pi x 10 = 31.4159 units. Radius = 5. Area = pi x 25 = 78.54 sq units.
Find radius: r = sqrt(A / pi). Then C = 2 x pi x r. Example: A = 78.54: r = sqrt(78.54/pi) = 5. C = 2 x pi x 5 = 31.416 units.
Circumference refers specifically to the perimeter of a circle. Perimeter applies to any closed shape. For a circle, they are the same measurement: the total distance around the outside of the circle.
Earth's equatorial circumference is approximately 40,075 km (24,901 miles). The polar circumference is about 40,008 km (24,860 miles). Earth is slightly flattened at the poles, making the equatorial circumference larger than the polar circumference.
C = 2 x pi x 10 = 62.832 units. Diameter = 20. Area = pi x 100 = 314.159 sq units.
d = C / pi. Example: C = 31.416: d = 31.416 / 3.14159 = 10 units. Radius = d/2 = 5 units. This follows directly from the definition pi = C / d.
Pi = 3.14159265... is the constant ratio of circumference to diameter for every circle: pi = C / d. Rearranging gives C = pi x d = 2 x pi x r. Pi is irrational with infinite non-repeating decimals.
r = C / (2 x pi). Example: C = 31.416: r = 31.416 / 6.2832 = 5 units. Diameter = 2r = 10 units.
Circumference uses the same linear unit as the radius or diameter input: cm, m, in, ft, etc. Unlike area, circumference is not squared. If radius is in cm, circumference is in cm.
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