Length of a Spiral

Determining the precise length of a spiral can be an interesting problem, particularly if the spiral has variable pitch or is non-planar.

For a planar spiral of constant pitch, however, there is an excellent solution based on just three variables: number of turns, pitch, and the distance from the center of the spiral to the beginning of the first turn. Although this is not an exact solution, it is extremely accurate, and in most cases the error will be only a small fraction of a percent.

The variables you will need to solve this problem are represented graphically in Figure 1, below:

Figure 1. Spiral Equation Variables.

To determine the length of the spiral, simply apply the following equation:

where G is the pitch, d is the distance from the center to the beginning of the first turn, and n is the number of turns of the spiral. The spiral shown above, for example, has n = 3 turns.