Analyze radius, pitch, turns, coordinates, and motion values. Build accurate helix models for physics problems, engineering visuals, classroom demonstrations, and spatial data studies.
| Point | Theta (deg) | X | Y | Z | Path Fraction |
|---|---|---|---|---|---|
| 1 | 0.0000 | 5.000000 | 0.000000 | 0.000000 | 0.0000 |
| 2 | 90.0000 | 0.000000 | 5.000000 | 0.500000 | 0.2500 |
| 3 | 180.0000 | -5.000000 | 0.000000 | 1.000000 | 0.5000 |
| 4 | 270.0000 | 0.000000 | -5.000000 | 1.500000 | 0.7500 |
| 5 | 360.0000 | 5.000000 | 0.000000 | 2.000000 | 1.0000 |
For a standard helix, the parametric form is x = r cos(θ), y = r sin(θ), and z = (p / 2π)θ.
Here, r is radius and p is pitch per full turn.
Total height = pitch × turns.
Total angle = 2π × turns.
Arc length = √[(rθ)² + h²].
Curvature = r / [r² + (p / 2π)²].
Torsion = (p / 2π) / [r² + (p / 2π)²].
Slope angle = tan-1(pitch / 2πr).
Enter the spiral radius first.
Set the pitch for one complete turn.
Choose the total number of turns.
Add a start angle if rotation begins elsewhere.
Select handedness and the main axis direction.
Set angular speed for motion timing results.
Add optional linear speed to compare travel time.
Choose sample points for the generated coordinate table.
Press the calculate button to view results above the form.
A 3D spiral is often modeled as a helix. It appears in springs, coils, particle motion, orbital paths, and many geometric physics problems. This calculator helps you study that path with clear numeric outputs. It reports geometric properties and motion-based values together.
Radius controls the spiral width. Pitch controls vertical rise during one full turn. Turns define total revolutions. These inputs shape the full helix and directly affect height, arc length, slope, curvature, and torsion. Those measures are useful in mechanics, electromagnetism, modeling, and classroom demonstrations.
Helical motion appears when circular motion combines with steady axial motion. Charged particles in magnetic fields can follow this type of path. Springs and coils also resemble ideal helices. With the added speed inputs, this tool estimates travel time and derived linear motion along the spiral.
The generated coordinate table makes the calculator more practical. It gives sampled points along the path. You can export these values as CSV for spreadsheets or as PDF for reports. This is helpful for plotting, simulation, teaching, documentation, and design checking.
You can test different radii, pitches, axes, and handedness settings quickly. That makes this calculator useful for comparing compact spirals against stretched helices. It also helps explain how each variable changes shape and motion. The result layout stays simple, direct, and easy to review.
A 3D spiral is usually a helix. It wraps around an axis while rising or advancing along that axis. It appears in coil geometry and helical motion problems.
Pitch is the axial distance gained in one complete turn. A larger pitch stretches the spiral upward or forward. A smaller pitch makes the helix tighter.
Curvature describes how sharply the curve bends. Torsion describes how strongly the curve twists in space. Together, they define the local geometry of a helix.
Yes, for basic geometric estimation. It helps with coil spacing, total height, and path length. Final spring design still needs material, load, and stress analysis.
Angular speed measures rotational change per second. Linear speed measures distance traveled along the path per second. Both describe motion, but from different viewpoints.
Changing the axis rotates the coordinate interpretation. The same spiral can be aligned along x, y, or z. This helps match simulation or drawing needs.
Handedness changes the turning direction. A right-handed helix and a left-handed helix have mirrored rotation. This matters in geometry, modeling, and some physics contexts.
The coordinates are computed from the input formulas. They are accurate for the sampled points shown. More sample points give a smoother numerical representation.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.