Hong Life CalculatorsUnderstanding the helical coil calculator — concept and principle
This calculator finds the length of wire or tube needed to wind a helical coil, along with the length per turn, mean and inner diameters, coil height, helix angle, gap between turns and wire mass. It is useful for springs, heating elements, inductors and copper cooling or heat-exchanger coils.
How it is calculated
Mean diameter D_m = outer diameter − wire diameter d
Length per turn ℓ = √((π D_m)² + p²)
Total length = N × ℓ
Helix angle = atan(p ÷ (π D_m)); coil height ≈ N × p + d; gap = p − d
Inner diameter = outer diameter − 2d; mass = density × π d²/4 × length
- Dimensions in mm, length in m, density in g/cm³ and mass in g.
The principle
If you cut one turn of a helix and unroll it flat, it becomes the hypotenuse of a right triangle. One side is the circumference at the mean diameter, πD_m, and the other side is the pitch, the rise per turn. Pythagoras gives the length of one turn. The mean diameter is used because the centreline of the wire runs halfway through its thickness.
Worked example
Default inputs: outer diameter 30 mm, wire 2 mm, pitch 5 mm, 12 turns, density 8.96 g/cm³ (copper).
- D_m = 30 − 2 = 28 mm; inner diameter = 30 − 4 = 26 mm.
- ℓ = √((π × 28)² + 5²) = 88.11 mm per turn.
- Total = 12 × 88.11 = 1,057 mm = 1.057 m.
- Helix angle = atan(5 ÷ 87.96) = 3.25°; height = 12 × 5 + 2 = 62 mm; gap = 3 mm.
- Mass = 8.96 × π × 0.2²/4 × 105.7 = 29.8 g.
| Outer diameter of the coil (mm) | Wire length (m) |
|---|---|
| 7.5 | 0.216 |
| 15 | 0.494 |
| 22.5 | 0.775 |
| 30 | 1.057 |
| 37.5 | 1.34 |
| 45 | 1.622 |
| 60 | 2.187 |
How to read the result
With a small helix angle, as here, the length per turn is almost the circumference, so the pitch barely affects the total. Add the straight leads at each end before cutting wire or tube, and allow extra for trimming. For springs, remember that the coil height changes when compressed, but the wire length does not.
Common mistakes
- Using the outer diameter instead of the mean diameter.
- Forgetting the straight leads.
- Entering a pitch smaller than the wire diameter, which would make the turns overlap.
- Using the inner diameter of a tube instead of its outer diameter for d.
Frequently asked questions
How do I find the number of turns for a given length?
Divide the available wire length by the length per turn.
What is the helix angle?
The angle between a turn and a plane perpendicular to the coil axis.
Does the pitch matter much?
Only when it is large compared with the circumference.
Sources: Standard helix geometry (developed length as the hypotenuse of circumference and pitch)