Circle Calculator

The area of a circle is calculated using the formula A = πr², where r is the radius. If you know the diameter (d), first divide by 2 to get the radius, then square it and multiply by π (approximately 3.14159). For example, a circle with radius 5 has area = π × 5² = π × 25 ≈ 78.54 square units.

The diameter is always twice the radius (d = 2r), and the circumference is π times the diameter (C = πd) or 2π times the radius (C = 2πr). If you know any one of these three values, you can calculate the other two. For instance, a circle with radius 7 has diameter 14 and circumference approximately 43.98.

Pi (π) is a mathematical constant representing the ratio of a circle's circumference to its diameter—approximately 3.14159265359. It's the same for every circle regardless of size, making it fundamental to all circle calculations. Common approximations include 22/7 (accurate to 2 decimal places) and 355/113 (accurate to 6 decimal places).

Arc length is the distance along a curved portion of the circle: Arc Length = (θ/360) × 2πr, where θ is the central angle in degrees. Sector area is the 'pie slice' region: Sector Area = (θ/360) × πr². For a 90° angle with radius 10, arc length = (90/360) × 2π × 10 ≈ 15.71, and sector area = (90/360) × π × 100 ≈ 78.54.

A chord is a straight line connecting two points on a circle. The chord length formula is: Chord = 2r × sin(θ/2), where r is the radius and θ is the central angle in radians. Alternatively, if you know the radius and the perpendicular distance from center to chord (d), use: Chord = 2 × √(r² - d²). The longest possible chord is the diameter.