Chord Length Calculator
Calculate the length of a chord in a circle using radius and central angle, chord height, or apothem
Calculate Chord Length
Distance from center to circumference
Chord Length Results
Formula used: c = 2r sin(α/2)
Method: Central angle method
Example Calculation
Central Angle Method
Given: Radius = 5 units, Central angle = 30°
Formula: c = 2r sin(α/2)
Calculation:
c = 2 × 5 × sin(30°/2)
c = 10 × sin(15°)
c = 10 × 0.2588
Result: c ≈ 2.588 units
Chord Height Method
Given: Radius = 10 units, Chord height = 2 units
Formula: c = 2√(2rh - h²)
Calculation:
c = 2√(2 × 10 × 2 - 2²)
c = 2√(40 - 4)
c = 2√36 = 2 × 6
Result: c = 12 units
Circle Chord Properties
Chord
Straight line connecting two points on circle
Chord Height
Distance from chord to arc (sagitta)
Apothem
Distance from center to chord
Chord Tips
Chord height is also called sagitta (from Latin "arrow")
Diameter is the longest possible chord
Arc length is always longer than chord length
Apothem + chord height = radius
Understanding Circle Chords
What is a Chord?
A chord is a straight line segment that connects any two points on a circle's circumference. Unlike the diameter, a chord doesn't have to pass through the center of the circle. The length of a chord depends on how far apart the two endpoints are on the circle.
Key Terms
- •Chord Height (Sagitta): Distance from chord midpoint to arc
- •Apothem: Perpendicular distance from center to chord
- •Central Angle: Angle subtended at circle center
- •Arc: Curved path between chord endpoints
Chord Length Formulas
Central Angle Method
c = 2r sin(α/2)
Where α is the central angle in radians
Chord Height Method
c = 2√(2rh - h²)
Where h is the chord height (sagitta)
Apothem Method
c = 2√(r² - d²)
Where d is the apothem distance