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Radius Calculation Formula:
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The radius from segment calculation determines the radius of a circle when given the chord length (s) and the sagitta (h) - the height of the circular segment. This geometric relationship is fundamental in circular geometry and various engineering applications.
The calculator uses the geometric formula:
Where:
Explanation: This formula derives from the geometric properties of circles and the Pythagorean theorem, relating the chord length and segment height to the circle's radius.
Details: Calculating radius from chord and sagitta measurements is crucial in architecture, engineering, surveying, and manufacturing where circular shapes and arcs are involved. It allows determination of full circle dimensions from partial measurements.
Tips: Enter chord length (s) and sagitta (h) in meters. Both values must be positive numbers. The calculator will compute the corresponding radius of the circle.
Q1: What is sagitta in circular geometry?
A: Sagitta is the height of a circular segment - the perpendicular distance from the chord to the arc of the circle.
Q2: Can this formula be used for any circular segment?
A: Yes, this formula works for any circular segment where you know the chord length and the sagitta height.
Q3: What are practical applications of this calculation?
A: Used in bridge construction, arch design, pipe manufacturing, and any situation where you need to determine a circle's radius from partial measurements.
Q4: Are there limitations to this formula?
A: The formula assumes perfect circular geometry and may have precision limitations with very small sagitta values relative to chord length.
Q5: How accurate is this calculation?
A: The calculation is mathematically exact for perfect circles. Accuracy depends on the precision of your chord and sagitta measurements.