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# Length of a Spiral

## Calculate the length of a spiral or the length of material contained in a roll.

The length of a spiral can be calculated as

L = 3.14 n (D + d) / 2                  (1)

where

L = length of spiral (m, ft ...)

n = number of rings

D = spiral outside diameter (m, ft ...)

d = spiral inside diameter or opening (m, ft ...)

The equation can be used to calculate the length of a material of uniform thickness. Typical examples may be belts, garden hoses or ropes in a roll.

### Example - Water Solar Heater

A solar heater is made like a coil with 20 mm pipe inside a 1 m x 1 m window frame. The coil is done like a doughnut with an outer radius of 0.5 m and an inner radius of 0.1 m due to the bending limits of the pipe. If the coil is made with no space between the pipes the number of turns can be calculated as

n = ((0.5 m) - (0.1 m)) / (0.02 m)

= 20

The length of the water pipe in the solar heater can be calculated as

L = 3.14 (20) ((1 m) + (0.2 m)) / 2

= 37.7 m

## Related Topics

• ### Mathematics

Mathematical rules and laws - numbers, areas, volumes, exponents, trigonometric functions and more.

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## Citation

• The Engineering ToolBox (2021). Length of a Spiral. [online] Available at: https://www.engineeringtoolbox.com/spiral-length-d_2191.html [Accessed Day Month Year].

Modify the access date according your visit.

6.3.17

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