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The diameter of a quarter circle given its arc length is the length of the diameter of the full circle from which the quarter circle is derived. This calculation is fundamental in geometry for understanding circular segments and their properties.
The calculator uses the formula:
Where:
Explanation: The formula derives from the relationship between the circumference of a full circle and the arc length of its quarter segment.
Details: Calculating the diameter from arc length is crucial in various engineering, architectural, and mathematical applications where circular segments are involved, helping in design and analysis of curved structures.
Tips: Enter the arc length of the quarter circle in meters. The value must be positive and greater than zero for accurate calculation.
Q1: Why is π used in the formula?
A: π is the fundamental constant that relates the circumference of a circle to its diameter, making it essential in all circular calculations.
Q2: Can this calculator be used for other circular segments?
A: This specific formula is designed for quarter circles. Other segments would require different formulas based on their angular proportion.
Q3: What units should I use for input?
A: The calculator uses meters, but the formula works with any consistent unit system (cm, mm, inches, etc.) as long as input and output use the same units.
Q4: How accurate is the calculation?
A: The calculation uses PHP's built-in M_PI constant which provides high precision (approximately 3.1415926535898), ensuring accurate results.
Q5: What if I have the radius instead of arc length?
A: If you have the radius, the diameter is simply twice the radius. This calculator specifically converts arc length to diameter.