Circle Calculator
Calculate circle area, circumference, and diameter from the radius, diameter, or area. Also computes arc length, sector area, chord length, and inscribed polygon properties.
Diameter (d)
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Circumference (C) —
Area (A) —
Extended More scenarios, charts & detailed breakdown ▾
Diameter
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Circumference —
Area —
Professional Full parameters & maximum detail ▾
Basic Properties
Diameter —
Circumference —
Area —
Arc & Sector (at given angle)
Arc Length (at given angle) —
Sector Area (at given angle) —
Segment Area —
Chord
Chord Length (at given d) —
Inscribed Polygon
Inscribed Polygon Perimeter —
Inscribed Polygon Area —
Circumscribed Polygon
Circumscribed Polygon Perimeter —
Circumscribed Polygon Area —
How to Use This Calculator
Enter the radius in the Simple tab to get diameter, circumference, and area instantly. Use the Extended tabs to start from diameter or area. The Professional mode adds arc length, sector area, chord length, and polygon properties.
Formula
d = 2r • C = 2πr • A = πr² • Arc = rθ • Sector = ½r²θ • Segment = ½r²(θ − sin θ)
Example
r = 5 → d = 10, C ≈ 31.416, A ≈ 78.540; at 90°: arc ≈ 7.854, sector ≈ 19.635
Frequently Asked Questions
- The area of a circle is A = πr², where r is the radius and π ≈ 3.14159. For a circle with radius 5 cm: A = π × 5² = 25π ≈ 78.54 square centimeters. To find the area from the diameter: first compute r = d/2, then apply A = π(d/2)² = πd²/4. For example, a circle with diameter 10 has area = π × 100/4 = 25π ≈ 78.54. The area grows as the square of the radius — doubling the radius quadruples the area.
- The circumference (perimeter of a circle) is C = 2πr = πd, where r is the radius and d = 2r is the diameter. For a circle with radius 5: C = 2 × π × 5 ≈ 31.416 units. For a circle with diameter 10: C = π × 10 ≈ 31.416 units (same result, as expected). The ratio of circumference to diameter is always π, by definition. To find radius from circumference: r = C / (2π). For C = 100: r = 100 / (2π) ≈ 15.915.
- Rearrange A = πr² to solve for r: r = √(A / π). For area = 78.54 square units: r = √(78.54 / π) = √(25) = 5 units. For area = 200: r = √(200/π) = √63.66 ≈ 7.98 units. Remember to take the positive square root — radius is always non-negative. If you know the circumference instead: r = C / (2π). These inverse formulas let you work backwards from any measurement.
- Arc length is the distance along the curved edge of a circular arc. Formula: s = rθ, where r is the radius and θ is the central angle in radians. For r = 5 and θ = 90°: first convert to radians: θ = 90 × π/180 = π/2 ≈ 1.5708, then s = 5 × 1.5708 ≈ 7.854 units. For a full circle (θ = 2π), arc length = 2πr, which equals the circumference. This calculator accepts degrees and converts automatically.
- A sector is the "pie slice" shaped region bounded by two radii and an arc — like a slice of pie. Its area = ½r²θ (θ in radians). A segment is the region between a chord (straight line connecting two points on the circle) and the arc it cuts off — like a crescent shape. Segment area = Sector area − Triangle area = ½r²(θ − sin θ). The sector always contains the center of the circle; the segment may or may not, depending on whether it is a minor or major segment.