Quick answer
How the tube length is calculated
For a helical coil, the tube length is the number of turns × √((π × D)² + P²), where D is the centreline (mean) coil diameter and P is the pitch, plus the straight connection legs. The outside surface area is π × tube outside diameter × length, the internal volume is π/4 × tube inside diameter² × length, and the tube mass is the density × π/4 × (outside diameter² − inside diameter²) × length.
Formulas used
All formulas give the developed length along the tube centreline. d is the tube outside diameter, t the wall thickness and dᵢ = d − 2t the inside diameter.
- Helical coil:
L = N × √((π × (D₀ − d))² + P²), where D₀ is the coil outside diameter over the tube, P the pitch and N the number of turns. This is the arc length of a helix: each turn unrolls into the hypotenuse of a triangle whose sides are the centreline circumference and the pitch. - Flat spiral (pancake) coil:
L ≈ N × π × (D_out + D_in) / 2, where D_out = outside diameter − d and D_in = centre opening + d are the outermost and innermost centreline diameters. This treats each turn as a circle at the average diameter, which is close for evenly spaced turns. - Serpentine coil:
L = n × S + (n − 1) × π × R, where n is the number of straight passes, S the straight length of each pass and R the centreline radius of the 180° return bends. - Surface, volume and mass:
A₀ = π × d × L,Aᵢ = π × dᵢ × L,V = π/4 × dᵢ² × L,m = ρ × π/4 × (d² − dᵢ²) × L, with ρ = 8,030 kg/m³ for 304 stainless steel and 8,940 kg/m³ for copper.
Worked examples
The examples use tube sizes that appear in the Uniinox custom coil catalog, but the coil dimensions are illustrative and are not catalog products. Straight legs are not included.
| Example | Tube length | Outside area | Internal volume | Tube mass |
|---|---|---|---|---|
| Helical, Ø22 × 1.0 mm 304, coil OD 420 mm, pitch 40 mm, 10 turns | 12.51 m | 0.865 m² | 3.93 L | 6.63 kg |
| Flat spiral, Ø12 × 0.8 mm 304, 300 mm outside, 100 mm centre opening, 6 turns | 3.77 m | 0.142 m² | 0.32 L | 0.85 kg |
| Serpentine, Ø9.52 × 0.7 mm copper, 8 passes of 600 mm, 15 mm bend radius | 5.13 m | 0.153 m² | 0.27 L | 0.89 kg |
Using the result in an enquiry
The tube length and mass help compare material use between designs, and the internal volume shows how much fluid the coil holds when it is filled or drained. The surface area is a geometry check only: the heat duty also depends on the fluids, flow rates, temperatures, tube material and fouling, so it cannot be read from the area alone.
When you send an enquiry, give the coil dimensions you calculated with, together with the operating conditions, connection details and quantity. Real coils also have straight legs, connection ends and forming allowances, so the purchased tube length is longer than the calculated coil length.
Related: How to specify a heat exchanger coil, Tube diameter and wall thickness, Tank heating and cooling coils
Frequently asked questions
Calculator questions
How do I calculate the tube length of a helical coil?
Multiply the number of turns by the length of one turn. One turn is the square root of (π × mean coil diameter)² + pitch², where the mean diameter is the coil outside diameter minus the tube outside diameter. Add the straight connection legs.
Does a larger surface area mean a larger heat duty?
Not by itself. The duty also depends on the fluids on both sides, their flow rates and temperatures, the tube material and fouling. Use the surface area as a geometry check, and send the operating conditions for a sizing review.
Should I use the coil outside diameter or the mean diameter?
This calculator asks for the outside diameter measured over the tube, the dimension usually shown on a drawing, and converts it to the centreline (mean) diameter by subtracting one tube outside diameter.
Primary sources
Technical references
- HelixWolfram MathWorld
Gives the parametric equations of a helix and its arc length, the basis of the helical-coil formula.
- Datasheet for 304 Stainless Steel Sheet, Coil and PlateUnited Performance Metals
Lists a density of 0.29 lb/in³ (8.03 g/cm³) for 304 stainless steel, used for the tube mass.
- Metals and Alloys - DensitiesEngineering ToolBox
Lists a density of 8,940 kg/m³ for copper, used for the tube mass.