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Spiral Length Estimate & One-Turn Helix

Estimate a tightly wound planar spiral length, or calculate the length of one uniform helical turn around a cylinder.

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Calculator inputs

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

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Formula and method

A planar winding from 10 cm to 20 cm diameter with 0.1 cm radial spacing has 50 turns and estimated length 7.5π m, about 23.56 m.

Planar estimate = πN(D + d)/2, with N = (D − d)/(2t); one-turn helix = √(H² + (πD)²)

Worked example

Enter these known values and leave the other values blank.

Outer planar winding diameter
20 cm
Inner planar winding diameter
10 cm
Radial spacing per full turn
0.1 cm
Planar turn count
50
Approximate planar winding length
23.562 m

Assumptions and limitations

  • For the planar mode, outer diameter exceeds nonnegative inner diameter, and spacing and turn count are positive. Fractional turns are supported by the continuous model.
  • The planar formula uses mean circumference times turn count. It neglects the radial contribution to true Archimedean arc length and is most appropriate when spacing is small relative to radius.
  • The helix mode is a separate calculation for one full turn with positive diameter and positive axial rise. Its length must exceed both rise and circumference.
  • Use centerline dimensions consistently. The two sections do not automatically equate a planar winding to a cylindrical helix.

Common questions

Is the planar result an exact Archimedean arc length?

No. It is a tightly wound approximation based on mean circumference. Exact arc length includes radial travel and can differ appreciably for widely spaced turns.

How do I handle several equal helical turns?

Use the axial rise per turn to calculate one-turn length, then multiply by the number of equal turns. Entering total rise without changing the circumference models only one turn.

References

Bookify rejects helix lengths that cannot exceed both the positive axial rise and one-turn circumference.

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