Enter circle radius and central angle to compute chord properties
Radius (R)
Central Angle (degrees)
Result
Chord Length
-
Arc Length
-
Segment Area
-
Sagitta (Height)
-
Detailed Derivation
Chord Length Formulas
Chord Length L = 2R x sin(theta/2)
Arc Length S = R x theta (theta in radians)
Segment Area Aseg = (R^2/2)(theta - sin(theta))
Sagitta h = R(1 - cos(theta/2))
A chord is a line segment connecting two points on a circle. The chord length, arc length, and sagitta are related through trigonometric functions of the central angle.
⚠Enter angle in degrees (0-360). At theta = 360, the chord length is 0 (full circle). At theta = 180, the chord equals the diameter (2R).
What Is a Chord?
A chord is a straight line connecting two points on a circle. The longest chord is the diameter, passing through the center. Chords have important geometric properties and are used extensively in trigonometry, engineering, and design.
Chord Formula
L = 2R x sin(theta/2). Derived from right triangle formed by radius and half-chord.
Diameter
The diameter is the longest chord (theta=180). D = 2R. All other chords are shorter and lie inside the circle.
Sagitta
The sagitta (height) measures how far the chord is from the circumference. A larger sagitta means a shorter chord.
Segment Area
The area between the chord and the arc is called a circular segment. It is the difference between the sector area and the triangle area.
Teaching Example: Circle radius R=10, central angle theta=60 deg. Half-angle = 30 deg. sin(30) = 0.5. Chord L = 2x10x0.5 = 10. Arc S = 10 x (60 x pi/180) = 10.472. Sagitta h = 10x(1-cos(30)) = 10x(1-0.866) = 1.34. Segment area = (100/2)(1.047-0.866) = 9.06.
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