Calculate helix

Online calculator and formulas for calculating a helix curve

Calculate helix


This calculator is used to calculate the slope, curvature, torsion and arc length of a helix. For the calculation, enter the radius, the height and the number of turns.


Helix calculator

 Input
Radius
Height of a turn
Number of turns
Decimal places
 Results
Slope
Curvature
Torsion
Arc length

Formula for calculating a helix curve (helix lines)

A helix is a curve that is created by a combination of rotation and translation along the axis of rotation. It can be seen as a curve which winds around the surface of a cylinder with a constant gradient.

A helix or helical lines play a role in the representation of spiral stairs, threads and twist drills, for example. The development of a helix is a straight line.

The helix becomes a straight line when the cylinder surfave with the helix is developed into a plane.

Slope

The slope is calculated by dividing the height of the turns by the circumference of the cylinder.

\(\displaystyle k=\frac{h}{2·π·r} \)

Curvature

\(\displaystyle κ= \frac{1}{r·(1+k^2)}\)

Torsion

The torsion kappa is the measure how much a wire is twisted when it is formed into a helix.

\(\displaystyle w= \frac{k}{r·(1+k^2)}\)

Arc length

\(\displaystyle s=2·π·r·\sqrt{1+k^2}*t\)
r Radius
h Height of a turn
t Number of turns
k Slope
κ Curvature (kappa)
w Torsion
s Arc length
Is this page helpful?            
Thank you for your feedback!

Sorry about that

How can we improve it?