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Circle Calculator calculator →

Circle Calculator guide

The Circle Calculator computes area, circumference, diameter, arc length, chord length, and sector area. You only need the radius and (optionally) a central angle to unlock all properties of the circle and its slices.

Worked examples

Calculate the area and circumference of a circle

  1. Enter 10 as the Radius.
  2. Leave the Angle field at its default or ignore it.
  3. Click Calculate.
Result: Area = 314.1593 | Circumference = 62.8319

Area = πr² = π × 100 ≈ 314.159. Circumference = 2πr = 2 × π × 10 ≈ 62.832.

Find the arc length of a 90-degree sector

  1. Enter 10 as the Radius.
  2. Enter 90 as the Central Angle.
  3. Click Calculate.
Result: Arc Length = 15.7080

The arc length is a fraction of the total circumference: (90/360) × 62.832 = 15.708.

Find the chord length of a 60-degree arc

  1. Enter 10 as the Radius.
  2. Enter 60 as the Central Angle.
  3. Click Calculate.
Result: Chord Length = 10

The chord length formula is 2r·sin(θ/2). 2(10)·sin(30°) = 20 × 0.5 = 10. The chord equals the radius.

Tips

  • •The central angle must be between 0 and 360 degrees.
  • •A chord is the straight line connecting two points on the circle.
  • •The sector area is the area of the "pizza slice" bounded by the two radii and the arc.

Frequently asked questions

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 a sector?
A region of a circle bounded by two radii and an arc, shaped like a slice of pie or pizza.
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).
What is a tangent?
A line that touches the circle at exactly one point, creating a 90-degree angle with the radius at that point.
Can a chord be longer than the diameter?
No. The diameter is the longest possible chord in any circle.
What is a semicircle?
Half of a circle, formed by a central angle of 180 degrees. Its arc length is exactly half the circumference.
What is a quadrant?
A quarter of a circle, formed by a central angle of 90 degrees.
How does the calculator find the chord length?
Using the formula Chord = 2r × sin(θ/2), which is derived from splitting the isosceles triangle formed by the two radii and the chord.
Are the calculations done in degrees or radians?
The tool accepts degrees (0 to 360) for the central angle and handles the radian conversion internally.
What is the area of a circle with radius 0?
It is 0. A radius of zero is just a single point, not a circle.
What happens if I enter an angle of 360?
The arc length becomes the full circumference, and the sector area becomes the full area of the circle.
How do I find the radius if I only know the area?
Rearrange the formula: r = √(Area / π).
Can I calculate the volume of a sphere with this?
No, this is a 2D geometry tool. For a sphere, Volume = (4/3)πr³.
What is an inscribed angle?
An angle formed by two chords meeting on the circle’s edge. It is always half the measure of the central angle that subtends the same arc.
Why does the tool ask for the radius rather than the diameter?
Most mathematical formulas (Area = πr², Circumference = 2πr) are naturally based on the radius.
Are the results rounded?
Yes, results are rounded to 4 decimal places for display.
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