Circle Calculator
Circle Calculator
Related Tools
About the Circle Calculator
A circle is one of the most fundamental shapes in geometry. This calculator helps you find all properties of a circle from any single known value - whether that's the radius, diameter, circumference, or area.
Beyond basic calculations, our tool also handles sectors and arcs, allowing you to calculate arc length, sector area, chord length, and segment area for any central angle. Perfect for students, engineers, architects, and anyone working with circular shapes.
All calculations use the mathematical constant π (Pi) ≈ 3.14159265359, providing accurate results for all your geometry needs.
Circle Formulas
Basic Circle Properties
d = 2r
Diameter equals twice the radius
C = 2πr = πd
Circumference (perimeter) of a circle
A = πr²
Area enclosed by the circle
Sector & Arc Properties
Arc = rθ
Arc length (θ in radians)
Sector Area = ½r²θ
Area of a sector (θ in radians)
Chord = 2r×sin(θ/2)
Chord length for central angle θ
Frequently Asked Questions
What is the difference between radius and diameter?
The radius is the distance from the center of a circle to any point on its edge. The diameter is the distance across the circle through its center, which is exactly twice the radius (d = 2r).
How do I find the area of a circle from its circumference?
First find the radius: r = C/(2π). Then calculate the area: A = πr². Our calculator does this automatically - just enter the circumference and it will calculate the area for you.
What is a sector of a circle?
A sector is a "pie slice" shaped portion of a circle, bounded by two radii and an arc. The area of a sector depends on the central angle - a 90° sector is 1/4 of the full circle, a 180° sector is 1/2, etc.
What is the value of Pi (π)?
Pi (π) is a mathematical constant representing the ratio of a circle's circumference to its diameter. It's approximately 3.14159265359... and is an irrational number, meaning its decimal representation goes on forever without repeating.
Examples
Circle with radius = 5
Diameter: 10 units
Circumference: 31.4159 units
Area: 78.5398 square units
Sector with r=10, θ=45°
Arc Length: 7.854 units
Sector Area: 39.27 square units
Chord Length: 7.654 units
Common Use Cases
- Construction: Calculate materials needed for circular structures, pools, or landscaping
- Engineering: Design circular components, calculate pipe dimensions, or determine wheel sizes
- Education: Learn and practice geometry formulas with instant feedback
- Cooking: Scale recipes for different pan sizes (area comparison)
- Crafts: Calculate fabric or material needed for circular projects
- Sports: Understand field markings, track distances, and equipment dimensions