Spiral Length Calculator

Calculate the length of a spiral (helical) path formed by a point moving away from a central axis while rotating around it.

Input Parameters

Calculation Results

Calculation Formula

L = √(2π²rn² + h²)

Where:
L = Spiral Length
r = Horizontal Radius
h = Spiral Height
n = Number of Turns
π = Pi (approximately 3.14159)

Result

Spiral Length (L):

Spiral Length Calculator Usage Guide

Learn how to use the Spiral Length Calculator and understand its working principles

How to Use This Calculator

  1. Enter the Spiral Height (the vertical distance the spiral covers).
  2. Enter the Horizontal Radius (the distance from the central axis to the spiral's path).
  3. Enter the Number of Turns (how many complete rotations the spiral makes).
  4. Click the Calculate button to compute the spiral length.
  5. The result will be displayed in the same units as your inputs.

Understanding Spiral Length

A spiral (or helix) is a curve in three-dimensional space. The length of a spiral can be calculated using the formula:

L = √(2π²rn² + h²)

This formula accounts for both the vertical rise (h) and the horizontal distance traveled (rn) over multiple turns (n).

Example

Suppose you have a spiral with:

  • Height (h) = 10 meters
  • Radius (r) = 2 meters
  • Turns (n) = 5

Using the calculator, you would input these values and get a spiral length of approximately 63.62 meters.

Applications

Spiral calculations are useful in various fields including:

  • Architecture and design (staircases, springs)
  • Engineering (corkscrews, helical gears)
  • Physics (neutron spirals in particle accelerators)