Calculations at a helix. A helix is a cylindrical spiral. Here the one-dimensional borderline of the helix is calculated.
Enter the radius, height and number of turns. Choose the number of decimal places, then click Calculate.

Formulas:
k = h / ( 2 * π * r )
κ = 1 / [ r * ( 1 + k² ) ]
w = k / [ r * ( 1 + k² ) ] = k * κ
s = 2 * π * r * √ 1 + k² * t

pi:
π = 3.141592653589793...

Radius, height and arc length have the same one-dimensional unit (e.g. meter), curvature and torsion have that unit inverse (e.g. per meter, 1/m), number of turns and slope are dimensionless.

If there is more than one turn, the helix when projected onto a plane is simply a circle, and if there is less than one turn, it is a circular arc. If you take into account that when looking at the helix from above, the parts further away appear smaller, then from this perspective the image of a hyperbolic spiral emerges. A helix can be turned left or right, and the two shapes cannot be made to coincide. This property is called chiral.
One turn is a full rotation of 360 degrees. The slope of the helix is the ratio of the height and circumference of the projected circle. The curvature is the degree of bending in relation to the length. The torsion indicates the strength of the twist within itself. The helix appears, for example, in the thread of straight screws without point. A helix can be found in coiled cables and in coil springs such as those in ballpoint pens. Some climbing plants grow up trunks and posts as a helix. The genetic information of all living things on earth is arranged in a double helix of nucleic acids, in which two helices run around each other and are connected by bridges, the nucleic bases. One half of the nucleic bases on the helix forms the negative of the other, so that the information is always present twice.