Accurately calculate the total length of Archimedean spirals using our free online calculator. Whether for engineering, architecture, or educational purposes, get precise arc length measurements quickly. Understand the fascinating geometry of spirals and their practical applications.
Formula:
The length (L) of an Archimedean spiral r = aθ from θ = 0 to θ = Θ is given by the formula:
L = (a / 2) [Θ√(1 + Θ²) + ln(Θ + √(1 + Θ²))]
Where:
- L = Total length of the spiral
- a = Spiral constant (the rate at which the radius increases per radian)
- Θ (Theta) = Total angle traversed by the spiral in radians. In this calculator, it's derived from the number of turns:
Θ = 2πN - N = Number of turns