BIZOMAT MAKEOS · Geometry
Helix (Coil) Developed Length
How long is the wire, tube or strip wound into this helix?
Developed length, helix angle and lead of a helix such as a coil, spring, cooling coil or spiral guard, from its mean diameter, pitch and number of turns.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Mean coil diameter | mm | Diameter to the centre of the wire or tube. |
| Pitch (axial advance per turn) | mm | Axial distance between adjacent turns, centre to centre. |
| Number of turns | turns | Number of complete (or fractional) turns. |
| Straight end allowance (total) | mm | Extra straight length for tails and connections. |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Mean coil diameter
- What it is
- The diameter of the coil measured to the centre line of the wire, bar or tube, halfway between the inside and outside of the coil.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 1000000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 300 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Length per turn rises almost in proportion to diameter.
- Get it right
- Use the mean diameter: outside diameter minus one wire or tube diameter, or inside diameter plus one.
What this means: Pitch (axial advance per turn)
- What it is
- How far the coil advances along its axis in one full turn, measured centre to centre between neighbouring turns.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 mm to 1000000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 50 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A larger pitch raises the helix angle and coil height, and adds a little length per turn.
- Get it right
- For a multi-start helix use the lead, the advance of one strand per turn.
What this means: Number of turns
- What it is
- How many complete turns the coil makes, including any part turn as a decimal.
- Units and format
- Enter a number in turns: a number of turns. The form accepts 0.000001 turns to 1000000 turns. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 10 turns as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Developed length and coil height rise in direct proportion.
- Get it right
- Count turns of the helix only; straight tails go in the end allowance.
What this means: Straight end allowance (total)
- What it is
- The extra straight length added for tails, connections or lead-in sections at both ends together.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0 mm to 10000000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 0 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Adds directly to the developed length.
- Get it right
- Enter the total for both ends, not the length per end. Leave it at 0 for the helix alone.
Method and formulas
- Length per turn = √((π D)² + p²).
- Developed length = turns × length per turn + end allowance.
- Helix angle (from a plane normal to the axis) = atan(p ÷ π D); coil height = turns × p.
- Example: 10 turns at 300 mm diameter and 50 mm pitch need 9.438 m.
Limitations
- Uniform helix; transitions at the ends are covered only by the end allowance.
- Bending stretches the outside and compresses the inside; the centre-line length is used.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Estimate tube length for a cooling or heating coil
- Find wire length for a spring or guard
- Find the helix angle of a coil
Who it is for
- Design engineers
- Toolmakers
- Estimators
What you get
- Length per turn
- Developed length
- Helix angle
- Coil height
Interpreting the result
- Add cutting and bending allowances before ordering material.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 2060–2062, 304–320. Topic reference; no source tables or recommended settings are reproduced.
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