Helix Length Calculator
Coil wire length from radius, turns, and height.
What it does
Springs, screws, and coils wind wire into helices whose true length hides inside the turns. Unwrapping one turn gives a right triangle: coil circumference one way, pitch rise the other, wire as hypotenuse.
The tool above takes coil radius, turn count, and total height. It returns wire length with coil run and rise beside it, in inches or centimeters.
The defaults (R 2, 5 turns, rise 10) unwind to 63.62 with a 62.83 coil run. The metric mirror (5.08 cm, 25.4 cm) gives 161.6 cm of wire.
The line matches OpenStax Calculus arc length with the helix derivation ending at root 4 pi squared N squared R squared plus h squared. LibreTexts prints the same derivation for the same curve.
How to use
- Pick imperial (in) or metric (cm).
- Enter coil radius to wire center.
- Enter turns, partials allowed.
- Enter total end to end height.
- Read wire length first.
- Add cut and bend waste after.
Formula
- R
- Coil radius to wire center.
- n
- Turn count, partials allowed.
- h
- Total end to end rise.
Zero radius returns the straight rise and zero height returns flat circle math, both handled inside. Wire thickness and end hooks sit outside; add shop waste after the line.
Worked example
Example: R 2, 5 turns, rise 10
Defaults: imperial, radius 2 in, 5 turns, height 10 in.
- Coil: 2 x pi x 2 x 5 = 62.83.
- Square: 62.83^2 + 10^2 = 4047.84.
- Length: root 4047.84 = 63.62.
- Tool shows 63.62 in, 62.83 coil run.
- Metric mirror gives 161.6 cm wire.
- Flat check R 1, 10 turns, 0 rise: 62.83.
Reference table
| Coil | Wire | Note |
|---|---|---|
| R 2, 5 turns, rise 10 | 63.62 in | Default |
| R 1, 10 turns, rise 0 | 62.83 in | Flat circle |
| R 0, 5 turns, rise 10 | 10 in | Straight |
Limits
- Centerline math, wire thickness out.
- End hooks and legs excluded.
- Variable pitch needs segments.
- Huge turns risk float fuzz.
Common mistakes
- Entering diameter as radius.
- Counting half turns as full.
- Measuring height with hooks on.
- Forgetting cut waste after.
- Mixing units mid inputs.
Try it yourself
Quick checks. Answers sit tucked under each question.
Flat R 1, 10 turns?
62.83 in of wire, circle math.
Straight R 0, rise 10?
10 in, no coil run.
Partial turns allowed?
Yes, enter decimals like 2.5.
Questions
What is helix length formula?
Root of coil run squared plus rise squared, coil as 2 pi R n.
Radius or diameter?
Radius to wire center; halve diameters first.
Spring wire estimate?
Run this page, then add hook and cut waste.
DNA helix too?
Same curve math at tiny scale with rise per turn.
Flat spiral?
Different curve; this page needs constant radius.
Screw threads?
One turn per pitch over the threaded length.