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Radius of a Curve Formula:
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The radius of a curve is a fundamental geometric measurement that describes the curvature of a circular arc. It represents the distance from the center of the circle to any point on the curve. This measurement is crucial in various fields including engineering, architecture, and surveying.
The calculator uses the formula:
Where:
Explanation: This formula calculates the radius of a circular curve when you know the chord length and the sagitta (the height of the arc).
Details: Calculating curve radius is essential in road design, railway construction, architectural planning, pipe bending, and any application involving circular arcs. Accurate radius calculation ensures proper fitting, structural integrity, and smooth transitions in curved elements.
Tips: Enter chord length and sagitta in meters. Both values must be positive numbers greater than zero. The calculator will compute the radius of the curve.
Q1: What is the difference between chord and sagitta?
A: The chord is the straight line distance between two points on a curve, while the sagitta is the perpendicular distance from the chord to the curve at its midpoint.
Q2: Can this formula be used for any circular arc?
A: Yes, this formula works for any circular arc segment where you can measure the chord length and sagitta.
Q3: What units should I use for measurements?
A: The calculator uses meters, but the formula works with any consistent unit system (e.g., centimeters, inches, feet) as long as all measurements use the same unit.
Q4: How accurate is this calculation?
A: The calculation is mathematically exact for perfect circular arcs. Accuracy depends on the precision of your chord and sagitta measurements.
Q5: What if my sagitta measurement is very small compared to the chord?
A: For very flat curves, ensure you have precise measurements as small errors in sagitta can significantly affect the calculated radius.