Calculate delta radius, arc length, or chord length from any two values, plus surveying curve length, radius, central angle, and derived curve data.

Delta Radius Calculator

Arc/Chord/Radius
Δ–R–L (Surveying)

Enter any 2 values to calculate the missing variable (when chord and radius are provided, the calculator returns the minor arc length).

Delta Radius Formula

The following relationships are used to calculate arc length, chord length, and radius for a circular arc:

\begin{aligned}
L &= R\theta \\
C &= 2R\sin(\theta/2) \\
R &= \frac{L}{\theta},\quad \text{where }\frac{C}{L}=\frac{2\sin(\theta/2)}{\theta}
\end{aligned}

Variables:

  • R is the delta radius (radius of the circle) (units)
  • L is the arc length (units)
  • C is the chord length (units)
  • θ is the central angle subtended by the arc (radians)

To calculate the delta radius from arc length (L) and chord length (C), you must first solve for the central angle θ from C/L = 2·sin(θ/2)/θ (θ in radians), then compute R = L/θ. This generally requires a numerical solve, which the calculator above performs automatically.

What is a Delta Radius?

The delta radius is the radius of the circle that would be formed if the arc and chord were part of a complete circle. It is a measure of the curvature of the arc and is used in various fields such as engineering, architecture, and mathematics to describe the properties of a circular segment.

How to Calculate Delta Radius?

The following steps outline how to calculate the Delta Radius.

  1. First, determine the arc length (L) in units.
  2. Next, determine the chord length (C) in units.
  3. Next, solve for the central angle θ (in radians) using C/L = 2·sin(θ/2)/θ, then compute R = L/θ.
  4. Finally, calculate the Delta Radius (R) in units.
  5. After inserting the variables and calculating the result, check your answer with the calculator above.

Example Problem:

Use the following variables as an example problem to test your knowledge.

arc length (L) = 10 units

chord length (C) = 5 units