Chord Calculator
Calculate chord length, sagitta (height), and apothem (distance from center) using radius and central angle.
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Frequently Asked Questions
What is a chord?
A chord is a straight line segment connecting two points on a circle. The diameter is the longest possible chord, passing through the center.
What is the formula for chord length?
c = 2r × sin(θ/2), where r is the radius and θ is the central angle in radians. This comes from dividing the isosceles triangle formed by the two radii and chord.
What is sagitta?
The sagitta (also called height or versine) is the perpendicular distance from the midpoint of the chord to the arc. It's calculated as h = r - r×cos(θ/2) = r(1 - cos(θ/2)).
What is apothem?
The apothem is the perpendicular distance from the center of the circle to the chord. It's calculated as a = r × cos(θ/2).
What is the relationship between sagitta and apothem?
They are complementary: sagitta + apothem = radius. The sagitta is the portion of the radius from the chord to the arc.
What is the chord length for 180 degrees?
For a 180° angle, the chord equals the diameter (2r), and it passes through the center. The sagitta equals the radius, and the apothem is zero.
Can a chord be longer than the diameter?
No, the diameter is always the longest chord in a circle. Any other chord will be shorter.
Where are chord calculations used?
Chord calculations are used in architecture (arched structures), engineering (bridge design), surveying, astronomy, and manufacturing of curved components.