Circle Calculator

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.

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.

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.

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, are