Calculate the circumference of a circle from radius, diameter, or area. Free online tool with step-by-step formulas and unit conversion.
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Circumference is the total distance around the boundary of a circle — think of it as the circle's perimeter. The two fundamental formulas are C = 2πr (using radius) and C = πd (using diameter), where π (pi) is approximately 3.14159. This circumference calculator goes beyond basic computation: enter any one of four values — radius, diameter, circumference, or area — and instantly get all circle properties with step-by-step mathematical solutions. Whether you're measuring fencing for a round garden, calculating pipe insulation length, determining wheel distance per rotation, or solving geometry homework, this tool handles metric and imperial units with full precision. The calculator also works in reverse: given a circumference, it finds the radius, diameter, and area, which is essential for engineering, construction, and scientific applications.
The circumference of a circle is the linear distance around its outer edge — the total length you would measure if you walked along the circle's boundary and returned to your starting point. It is the circle's equivalent of a polygon's perimeter. The circumference has a special mathematical relationship with the diameter: the ratio C ÷ d always equals π (pi), approximately 3.14159265. This constant ratio was discovered by ancient mathematicians and is one of the most fundamental constants in mathematics. The circumference formula C = 2πr connects three key measurements: C (circumference), r (radius, the distance from center to edge), and π. Alternatively, since the diameter d = 2r, the formula simplifies to C = πd. Understanding circumference is essential in fields ranging from engineering and architecture to astronomy and everyday problem-solving.
Formula
C = 2πr = πd, where r = radius, d = diameter, π ≈ 3.14159Enter any one value — radius, diameter, circumference, or area — and get all four circle properties instantly. No need to remember or manually apply different formulas for each conversion.
Manual calculations with π often introduce rounding errors. This calculator uses full-precision π (3.14159265...) for results accurate to 6+ decimal places, eliminating accumulated rounding mistakes.
Calculate in millimeters, centimeters, meters, kilometers, inches, feet, yards, or miles. Switch between metric and imperial units without performing separate conversion steps.
See the complete mathematical solution rendered in proper notation using LaTeX. Perfect for students checking homework, teachers demonstrating concepts, or engineers documenting calculations.
Know the circumference but need the radius or diameter? This calculator works both ways — enter circumference to find radius, diameter, and area. Most simpler tools only calculate in one direction.
Pre-built presets for common circular objects like pizza sizes, bicycle wheels, basketball hoops, pools, and pipes make it easy to get answers for practical projects instantly.
Computing C = 2π × 47.3 by hand is slow and error-prone. Get the exact answer in under a second with verified results, including a π verification check for confidence.
Students can verify circumference calculations, understand the step-by-step process, and practice converting between radius, diameter, circumference, and area. The LaTeX formula display helps visualize proper mathematical notation.
Calculate exactly how much fencing material you need for a circular garden, pool enclosure, round pen, or decorative border by entering the radius or diameter of the area.
Plumbers and engineers calculate the outer circumference of pipes to determine insulation wrap length, clamp sizes, heat tape requirements, or gasket dimensions for any pipe diameter.
Cyclists and automotive enthusiasts calculate wheel circumference for speedometer calibration, distance-per-rotation calculations, gear ratio planning, or tire fitment comparisons.
Calculate fabric needed for circular tablecloths, skirt hems, hat brims, wreaths, or any circular craft project based on the desired diameter or radius.
Determine material quantities for circular patios, round concrete pads, curved edging, circular driveways, or decorative garden borders with accurate circumference measurements.
Calculate orbital circumference, drum roller dimensions, circular tank sizing, rotating machinery specifications, or any application requiring precise circle measurements.
The circumference of a circle is calculated using C = 2πr (where r is the radius) or equivalently C = πd (where d is the diameter). Since the diameter is twice the radius (d = 2r), both formulas give the same result. π (pi) is approximately 3.14159265.
Multiply the diameter by π (pi). The formula is C = πd. For example, if the diameter is 10 cm, the circumference is π × 10 = 31.4159 cm. Simply enter the diameter in this calculator and select 'Diameter' as your input mode.
Multiply the radius by 2π. The formula is C = 2πr. For example, if the radius is 7 inches, the circumference is 2 × π × 7 = 43.9823 inches. Enter the radius value and select 'Radius' as the input mode.
For circles, circumference and perimeter mean the same thing — the total distance around the shape. The term 'circumference' is specifically used for circles and curved shapes, while 'perimeter' is the general term used for all shapes including polygons.
A circle with a 12-inch diameter has a circumference of π × 12 = 37.6991 inches (approximately 37.7 inches). If 12 inches is the radius instead, the circumference would be 2π × 12 = 75.3982 inches.
Divide the circumference by π. The formula is d = C ÷ π. For example, if the circumference is 50 cm, the diameter is 50 ÷ 3.14159 = 15.9155 cm. Use this calculator's 'Circumference' input mode to calculate this automatically.
Divide the circumference by 2π. The formula is r = C ÷ (2π). For example, if the circumference is 50 cm, the radius is 50 ÷ (2 × 3.14159) = 7.9577 cm. Select 'Circumference' as the input mode to perform this reverse calculation.
π (pi) is a mathematical constant approximately equal to 3.14159265. It represents the ratio of any circle's circumference to its diameter (C/d = π). This ratio is the same for every circle regardless of size, making it a fundamental constant in geometry. It's an irrational number, meaning its decimal digits never end or repeat.
Yes, circumference is the perimeter of a circle. Both terms describe the total distance around the circle's boundary. 'Circumference' is the preferred term when referring to circles specifically, while 'perimeter' is the broader mathematical term for the boundary length of any closed shape.
The perimeter of a semicircle includes half the circumference plus the diameter (straight edge). The formula is P = πr + 2r = r(π + 2), where r is the radius. For example, a semicircle with radius 5 cm has a perimeter of 5 × (3.14159 + 2) = 25.708 cm.
The Earth's circumference at the equator is approximately 40,075 km (24,901 miles). Using Earth's mean equatorial radius of 6,371 km: C = 2π × 6,371 = 40,030 km. The slight difference from the actual value is because Earth is not a perfect sphere but an oblate spheroid.
Both circumference and area depend on the radius. Circumference = 2πr and Area = πr². You can derive one from the other: if you know the circumference C, the area is A = C²/(4π). Conversely, if you know the area A, the circumference is C = 2√(πA).
Yes. First find the radius from area using r = √(A/π), then calculate circumference using C = 2πr. This calculator handles this automatically — select 'Area' as your input mode, enter the area value, and get the circumference instantly.
Circumference is a linear measurement, so it uses length units: millimeters (mm), centimeters (cm), meters (m), kilometers (km), inches (in), feet (ft), yards (yd), or miles (mi). This calculator supports all these units with instant conversion.
To convert circumference to diameter: d = C ÷ π. To convert diameter to circumference: C = π × d. For example, a circumference of 31.4159 cm equals a diameter of 10 cm, and a diameter of 10 cm equals a circumference of 31.4159 cm.