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Circle Calculator

Calculate arc length, sector area, and chord length.

Circle Inputs

Enter the radius and central angle.

Area: — Circumference: — Diameter: —
Arc Length —
Chord Length —
Sector Area —

Enter a valid radius to compute the circle values.

About this topic

Radius, Diameter & Circumference The fundamental measurements of any circle.

Every circle is defined by its radius r — the distance from center to edge. From that single value you can derive the diameter, circumference, and area using π (≈ 3.14159).

Key formulas & rules

  • •Diameter: d = 2r
  • •Circumference: C = 2πr = πd
  • •Area: A = πr²
  • •π is irrational (≈ 3.14159265…)
  • •All circles are similar
  • •Ratio C/d is always exactly π

Examples

Input Output Note
r = 10 d = 20 Double the radius
r = 10 C ≈ 62.832 2πr
r = 10 A ≈ 314.159 πr²
r = 1 C = 2π ≈ 6.283 Unit circle

Real-world uses

Wheel sizing Pipe diameters Circular tracks
Arcs & Sectors Partial slices of a circle, measured by central angle.

A central angle θ cuts the circle into a sector (the 'pizza slice') and an arc (the curved edge). Both are simply fractions of the full circle: θ/360 of the whole.

Key formulas & rules

  • •Arc length: L = (θ/360) × 2πr
  • •Sector area: A = (θ/360) × πr²
  • •Full circle = 360° = 2π radians
  • •Sector area / circle area = θ / 360
  • •Arc length / circumference = θ / 360
  • •Radians: L = rθ (when θ is in radians)

Examples

Input Output Note
r=10, θ=90° Arc ≈ 15.708 Quarter circle
r=10, θ=90° Sector ≈ 78.540 Quarter area
r=10, θ=180° Arc ≈ 31.416 Semicircle
r=10, θ=360° Arc = 62.832 Full circle

Real-world uses

Pie charts Pizza slices Camera field of view
Chords & Inscribed Angles Straight lines cutting across the circle.

A chord is a straight line segment whose endpoints both lie on the circle. The longest possible chord is the diameter. Chords are closely tied to central angles and the perpendicular from the center.

Key formulas & rules

  • •Chord length: c = 2r·sin(θ/2)
  • •Longest chord = diameter (θ = 180°)
  • •Perpendicular from center bisects any chord
  • •Inscribed angle = ½ × central angle
  • •Equal chords are equidistant from the center
  • •Tangent ⊥ radius at point of contact

Examples

Input Output Note
r=10, θ=90° Chord ≈ 14.142 √2 × r
r=10, θ=60° Chord = 10 Equilateral
r=10, θ=180° Chord = 20 Diameter
r=5, θ=120° Chord ≈ 8.660 √3 × r

Real-world uses

Arch bridges Truss design Optics & lenses
Real-World Uses Circles are everywhere — from wheels to WiFi.

Circular geometry drives engineering, physics, and design. Arc length and sector area calculations are essential in everything from manufacturing to astronomy.

Key formulas & rules

  • •Angular velocity: v = rω
  • •Radians: 1 rad ≈ 57.2958°
  • •Circle equation: (x−h)² + (y−k)² = r²
  • •Area of annulus: π(R² − r²)
  • •Sphere volume: (4/3)πr³
  • •Cylinder volume: πr²h

Examples

Input Output Note
R=10, r=6 Annulus ≈ 201.062 Ring area
r = 3 Sphere Vol ≈ 113.097 3D ball
θ = 1 rad ≈ 57.2958° Radians → degrees
r = 2, h = 5 Cyl Vol ≈ 62.832 Cylinder

Real-world uses

Gears & pulleys Satellite orbits WiFi signal radius

Modes & formulas

1

Circle Properties

• Calculates dimensions based on radius and central angle. • Enter the radius and the angle (θ). • The calculator determines the arc length, chord length, and sector area.
Arc = (θ/360) × 2πr | Chord = 2r·sin(θ/2)

The central angle acts as a fraction of the full 360-degree circle. The tool visualizes the sector and chord dynamically.

How to use it

Enter the radius and a central angle. The tool will show the area, circumference, arc length, chord length, and a visual graph.

Frequently asked questions

What is a chord?
A straight line segment whose endpoints both lie on the circle.
What is a sector?
A region bounded by two radii and the arc between them — like a slice of pizza.
What is the difference between a chord and an arc?
A chord is a straight line segment whose endpoints lie on the circle. An arc is the curved portion of the circle’s edge between those two points.
What is the central angle?
An angle whose vertex is at the center of the circle. It determines the fraction of the circle you are measuring.
What is Pi (π)?
The ratio of a circle’s circumference to its diameter, approximately 3.14159.
How do I find the diameter?
The diameter is simply twice the radius (d = 2r).

Related calculators

Area & Perimeter Calculate area and perimeter for 2D geometric shapes. Pythagorean Theorem Solve for side A, B, or hypotenuse C. Triangle Solver Solve triangles using SSS, SAS, or ASA inputs. Distance & Midpoint Find the distance between two points (x₁,y₁) and (x₂,y₂).
Read the full Circle Calculator guide — examples & 18 FAQs