Chord Lengths
Chord Lengths - Related Videos
01:10
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FAQs
The central angle enters the calculation as half of θ, so the relationship is not based on the full angle directly. Substituting the radius and angle into c = 2r sin(θ/2) gives the straight-line span between the arc endpoints. This makes the formula useful when curved geometry must be represented by a direct linear dimension in engineering design.
For a fixed central angle, increasing the radius increases the chord length in direct proportion because r multiplies the sine term in c = 2r sin(θ/2). Thus, the same angular geometry produces different linear spans when applied to circles of different sizes. This scaling helps engineers transfer a geometric relationship across component sizes during design.
Chord length measures the direct span, whereas arc length follows the curve. The overview notes that these quantities become close for small angles, but they represent different geometric paths. Recognizing this distinction helps prevent curved distance from being substituted for a straight-line dimension when engineers convert circular or arc-based geometry into component measurements.
First identify the circle’s radius and the central angle subtended by the two endpoints. Then evaluate the half-angle sine and multiply it by twice the radius using c = 2r sin(θ/2). The resulting value supplies the linear span for checking a drawing, sizing a feature, or entering a geometric constraint in a CAD model.
Chord-length calculations are relevant to gears, blades, beams, pipes, and other curved components. In each case, they help translate an arc or circular layout into a straight-line dimension that can be analyzed or represented during design. This is especially valuable when the intended part must connect curved geometry with manufacturable dimensions or a precise CAD representation.
In CAD work, chord length provides a direct linear measure derived from a curved feature’s radius and subtended angle. Using that measure helps represent the intended geometry consistently and supports dimension checking. The same translation is useful in manufacturing-oriented design because it connects the mathematical description of an arc with dimensions that can be specified for a component.