Chord to Radius Calculator

The Chord to Radius Calculator is a tool that computes the radius of a circle given the chord length and the sagitta (the perpendicular distance from the midpoint of the chord to the arc).

Formula

The formula to calculate the radius is:

\[ R = \frac{L^2}{8S} + \frac{S}{2} \]

Where:

• L is the chord length.
• S is the sagitta.

Example Calculation

For a chord length (L) of 10 units and a sagitta (S) of 2 units:

\[ R = \frac{10^2}{8 \times 2} + \frac{2}{2} = \frac{100}{16} + 1 = 6.25 + 1 = 7.25 \text{ units} \]

Application

This calculation is used in geometry, construction, and engineering to determine the radius of curved surfaces, arcs, and circular segments.