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Circle Solver (Radius, Area, Circumference, Arc)

Calculate radius, diameter, circumference, area, and sector arc length with exact multiples of pi and decimal values.

Known Value

Known Parameter

Sector Arc Central Angle (Degrees ° optional)

Calculated Results

Circle Area (A = πr²)

78.54 Sq Units

Exact: 25π sq units

Circumference (C = 2πr)

31.42 Units

Exact: 10π units

Diameter (d = 2r)

10.00 Units

Across center

Radius (r)

5.00 Units

Center to perimeter

Sector Arc Length (60°)

5.24 Units

Sector area: 13.09 sq units

Frequently Asked Questions

What are the fundamental formulas for circle geometry?

Radius: r = d / 2. Diameter: d = 2r. Circumference: C = 2πr = πd. Area: A = πr² = (πd²) / 4.

What is the ratio π (Pi)?

Pi (approximately 3.14159265...) is the mathematical constant representing the ratio of any circle's circumference to its diameter (C / d). It is an irrational number that cannot be expressed as a simple fraction.

How do you calculate the area of a circle sector?

The area of a circle sector with central angle θ in degrees is: Area = (θ / 360°) × πr². The arc length is: Arc = (θ / 360°) × 2πr.

How do you find the radius from circle area?

To find radius from area: divide area by π and take the square root: r = √(Area / π).