Circle Calculator
Solve for any circle property from any single measurement. Enter radius, diameter, circumference, or area and get all other values instantly.
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What should I know about Key Formulas?
Area of a circle = π × r², where r is the radius and π ≈ 3.14159265. Circumference = 2 × π × r = π × d (where d is the diameter). Diameter = 2 × r. Radius = diameter ÷ 2. For a circle with radius 5cm: Area = π × 25 = 78.54 cm². Circumference = 2π × 5 = 31.42 cm. For a circle with diameter 12cm: radius = 6cm, area = π × 36 = 113.1 cm², circumference = π × 12 = 37.70 cm. Arc length of a sector with angle θ degrees = (θ/360) × 2πr. Sector area = (θ/360) × πr².
What's the key thing to understand about Real-World Applications?
Circular calculations appear in construction (round slabs, pipes, ponds), cooking (pizza, cake tin sizing), engineering, and geometry. Knowing the circumference-to-diameter relationship is also the definition of π.
What should I know about Unit Consistency?
Enter all measurements in the same unit. If your radius is in metres, area will be in square metres and circumference in metres. For centimetres: area is cm², circumference is cm.
What should I know about Circles in Engineering and Design?
Circular geometry appears throughout engineering. Gear design: pitch circle diameter and circumference determine gear ratios and tooth spacing. Piping: flow rate through a circular pipe varies with the square of radius — doubling pipe radius quadruples flow rate. Architecture: a semicircular arch distributes loads along a curve, converting vertical loads to horizontal thrust — the structural basis of Roman arch construction and still used in modern bridge design. Understanding circumference, area, and the relationships between them is foundational to countless engineering applications, from gear design to pipe sizing.