Calculate the circumference of any circle using radius or diameter. Get instant results with step-by-step solutions, unit conversions, and educational explanations of circle geometry formulas.
Calculate the circumference of a circle using either radius or diameter
Circumference is the distance around the edge of a circle — the circular equivalent of perimeter. There are two standard formulas for calculating circumference, depending on whether you know the radius or the diameter. Both formulas rely on the mathematical constant π (pi), which is approximately 3.14159.
C = 2 × π × r
Multiply 2 times π times the radius. For example, a circle with radius 5 cm has a circumference of 2 × 3.14159 × 5 = 31.42 cm. The radius is the distance from the center to the edge of the circle.
C = π × d
Multiply π by the diameter. For example, a circle with diameter 10 cm has a circumference of 3.14159 × 10 = 31.42 cm. The diameter is the distance across the circle through its center, equal to 2r.
r = C / (2π)
You can also reverse the formula to find the radius or diameter when you know the circumference. Divide the circumference by 2π to get the radius, or divide by π to get the diameter.
Pi (π) is the mathematical constant that makes circumference calculations possible. It defines the fundamental relationship between a circle's diameter and its circumference — a ratio that remains constant for every circle regardless of size.
Pi (π) is the ratio of any circle's circumference to its diameter: π = C / d. Its value is approximately 3.14159265359 and it is an irrational number, meaning its decimal expansion never ends and never repeats.
Diameter = 2 × Radius. All points on a circle are equidistant from its center. The circumference is a one-dimensional measure (length), while the area (πr²) is a two-dimensional measure (surface).
Ancient civilizations approximated π thousands of years ago. The Babylonians used 3.125, the Egyptians used 3.1605, and Archimedes rigorously bounded it between 3.1408 and 3.1429. Today, computers have calculated trillions of digits.
The radius is the distance from the center to the edge. The diameter spans the full width through the center and equals exactly 2r. Either measurement is sufficient to calculate circumference since C = 2πr = πd.
The circumference is the arc length of the full 360° circle. A partial arc covering θ degrees has length L = (θ/360) × 2πr. In radians, the full circumference corresponds to an angle of 2π radians.
Circumference is always in the same unit as the radius or diameter. If the radius is in inches, the circumference is in inches. Convert between metric and imperial units as needed: 1 inch = 2.54 cm, 1 foot = 30.48 cm.
Circumference calculations appear in countless practical situations, from everyday tasks to advanced engineering. Knowing how to calculate the distance around a circle is essential in construction, manufacturing, transportation, and many other fields.
Circumference is the distance around the edge of a circle, essentially the perimeter of a circular shape. It is a linear measurement expressed in units of length such as centimeters, meters, inches, or feet. Every circle's circumference is directly proportional to its diameter, with the constant of proportionality being π (pi). For example, a circle with a diameter of 10 cm has a circumference of approximately 31.42 cm.
To calculate circumference from radius, use the formula C = 2πr, where C is the circumference, π is approximately 3.14159, and r is the radius. Multiply 2 times π times the radius. For example, if the radius is 7 cm: C = 2 × 3.14159 × 7 = 43.98 cm. The radius is the distance from the center of the circle to any point on its edge.
To calculate circumference from diameter, use the formula C = πd, where C is the circumference, π is approximately 3.14159, and d is the diameter. Simply multiply π by the diameter. For example, if the diameter is 14 cm: C = 3.14159 × 14 = 43.98 cm. The diameter is the distance across the circle through its center, which equals twice the radius.
Pi (π) is an irrational mathematical constant approximately equal to 3.14159265359. It represents the ratio of any circle's circumference to its diameter, meaning C/d = π for every circle regardless of size. Pi is fundamental to all circle calculations because it defines the exact relationship between a circle's linear dimensions and its perimeter. Without pi, it would be impossible to precisely calculate circumference, area, or any other circular measurement.
To find the radius from the circumference, rearrange the formula C = 2πr to get r = C / (2π). Divide the circumference by 2π (approximately 6.28318). For example, if the circumference is 50 cm: r = 50 / (2 × 3.14159) = 50 / 6.28318 = 7.96 cm. Similarly, to find the diameter from circumference, use d = C / π.
Circumference and area measure different properties of a circle. Circumference (C = 2πr) is a linear measurement of the distance around the circle's edge, expressed in units like cm or m. Area (A = πr²) is a surface measurement of the space enclosed within the circle, expressed in square units like cm² or m². For example, a circle with radius 5 cm has a circumference of 31.42 cm but an area of 78.54 cm². Circumference is used for perimeter-related tasks like fencing, while area is used for coverage tasks like flooring.