Helix Length Calculator (Spiral Staircase, Coil, Handrail, Cable Wrap)
Length of material along a helix — a spiral stair handrail, a coiled wire, a cable wrapped round a drum or a pole — from its diameter, pitch and height or number of turns.
Results
The dashed line marks the value you entered.
What this tool does
Unroll one turn of a helix onto a flat sheet and it becomes the hypotenuse of a right triangle: one side is the circumference π D, the other is the pitch, the rise per full turn. So one turn is √((π D)² + p²) long, and the total is that times the number of turns. Use the diameter measured to the centre line of the material you are bending — the handrail's centre, not the outside of the stair — and you get a length you can cut. The slope angle is the same everywhere along a true helix, which is why a spiral staircase handrail keeps a constant gradient.
Formula
one turn = √((π D)² + p²) · length = turns × √((π D)² + p²) · turns = height ÷ p · slope = atan(p ÷ π D)
Variables
| Symbol | Meaning | Unit |
|---|---|---|
dm | Diameter of the helix (to the centre of the material) | — |
p | Pitch (rise per full turn) | — |
nt | Number of turns (if you know them) | — |
hh | Total height (if you know it) | — |
LH | Length along the helix for that height | — |
TU | Number of turns that height holds | — |
LN | Length along the helix for those turns | — |
HN | Height those turns reach | — |
LT | Length of one full turn | — |
AN | Slope of the helix above the horizontal | ° |
Worked example
- Diameter of the helix (to the centre of the material)1500
- Pitch (rise per full turn)1400
- Total height (if you know it)2800
- Length along the helix for that height9831.9
- Number of turns that height holds2.000
- Length of one full turn4916.0
- Slope of the helix above the horizontal16.55 °
Limitations
- Mixing units is the most common source of error. Convert every input to the units shown next to each field before calculating.
- The calculation runs at full precision and only the display is rounded. If you copy an intermediate value and retype it, small differences can appear.