Chord Length Calculator

Compute circle segment and chord relationships. Provide radius/diameter and one segment parameter (angle, chord, height, or arc length) to calculate all values. Essential for keyways, circular features, and arc machining operations.

CIRCLE & SEGMENT

D = 38.000 mm
0° to 180° (minor segment)
Also called sagitta
Along the curved edge

DISPLAY OPTIONS

CIRCLE SEGMENT DIAGRAM

HR = 19.00c = 34.47θ = 130.2°

CALCULATED VALUES

RADIUS
19.0000mm
DIAMETER
38.0000mm
CENTRAL ANGLE
130.198°
CHORD LENGTH
34.4674mm
SEGMENT HEIGHT
11.0000mm
ARC LENGTH
43.1753mm

USAGE NOTES

Input Requirements: Provide radius or diameter, plus ONE of: central angle (θ), chord length (c), segment height (H), or arc length (s). The calculator computes all other values.

Formulas Used:

  • Chord: c = 2R sin(θ/2)
  • Arc: s = Rθ (θ in radians)
  • Height: H = R(1 - cos(θ/2))
  • From chord: θ = 2 arcsin(c/(2R))
  • From height: θ = 2 arccos((R-H)/R)

Constraints: Minor segment only (0° ≤ θ ≤ 180°). Chord cannot exceed diameter. Height cannot exceed radius.

Applications: Keyway dimensions, arc segments for machining, circular feature measurement, inspection calculations.

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