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Diameter Formula:
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This calculation determines the diameter of a circle when you know the chord length and the sagitta (the height from the chord to the arc). This is particularly useful in geometry, engineering, and construction applications where circular measurements are needed.
The calculator uses the diameter formula:
Where:
Explanation: The formula is derived from the Pythagorean theorem applied to a right triangle formed by the radius, half the chord, and the radius minus the sagitta.
Details: This calculation is essential in various fields including architecture (designing arches), engineering (pipe and tank measurements), astronomy (calculating celestial object sizes), and manufacturing (circular component design).
Tips: Enter the chord length and sagitta in consistent units (both in meters or both in feet). Ensure all values are positive numbers greater than zero for accurate results.
Q1: What is the relationship between chord length and diameter?
A: The chord length is always less than or equal to the diameter, with the maximum chord length being equal to the diameter when it passes through the center.
Q2: Can I use this formula 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's the difference between chord length and arc length?
A: Chord length is the straight-line distance between two points on a circle, while arc length is the distance along the curved line between those two points.
Q4: How accurate is this calculation?
A: The calculation is mathematically precise for perfect circles. Accuracy in real-world applications depends on the precision of your chord and sagitta measurements.
Q5: Can I calculate radius instead of diameter?
A: Yes, the radius is simply half of the calculated diameter (\( R = \frac{D}{2} \)).