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Radius Calculation Formula:
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The formula \( r = \frac{Chord^2}{8h} + \frac{h}{2} \) calculates the radius of a circle when given the chord length and sagitta (the height from the chord to the arc). This is particularly useful in geometry, engineering, and construction applications.
The calculator uses the geometric formula:
Where:
Explanation: This formula derives from the geometric relationship between a chord, its sagitta, and the circle's radius, using the intersecting chords theorem.
Details: This calculation is essential in architecture for designing arches, in engineering for pipe and tank design, in surveying for circular land measurements, and in various manufacturing processes involving circular components.
Tips: Enter chord length and sagitta in consistent units (both meters or both feet). Both values must be positive numbers greater than zero for accurate calculation.
Q1: What is sagitta in geometry?
A: Sagitta is the height from the midpoint of a chord to the arc of the circle. It represents the maximum distance between the chord and the arc.
Q2: Can this formula be used for any chord position?
A: Yes, the formula works for any chord of a circle, as long as you have the chord length and the corresponding sagitta measurement.
Q3: What if my sagitta is larger than the radius?
A: This is geometrically impossible. The sagitta must always be less than or equal to the radius of the circle.
Q4: How accurate is this calculation?
A: The formula is mathematically exact for perfect circles. Accuracy depends on the precision of your chord and sagitta measurements.
Q5: Can I use different units for chord and sagitta?
A: No, both measurements must be in the same units (both meters or both feet) to get a valid radius result in those units.