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.
Spiral Length Calculator
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.