THE METHOD, MADE CLEAR
A helix is longer than its rise.
Helixlength calculates the path along an ideal circular helix. It is useful for reproducing geometric material-length arithmetic when you know a constant diameter, a constant axial pitch and a number of turns.
What this calculator follows
Imagine a line running through the middle of a round cord or wire. That line winds around an axis while advancing along it. The calculator measures that centreline path. It does not measure just the distance between the ends along the axis, and it does not add a circumference and a pitch as if those two distances were travelled separately.
The model has a circular centreline of constant diameter and an unchanging pitch. A tapered wrap, variable-radius spiral, compressed decorative braid or irregular coil needs a different description. The result is geometric; it does not predict how a real material changes length when bent, stretched, heated or released.
Choose the right diameter reference
The diameter is measured across the coil, not from the axis to one side. For the round cross-section assumed here, let d be the cord or wire diameter. The relationships are:
Centreline diameter = inside diameter + d
Centreline diameter = outside diameter − d
Inside diameter = centreline diameter − d
Outside diameter = centreline diameter + d
For example, an inside diameter of 98 mm and a round wire diameter of 2 mm give a 100 mm centreline and a 102 mm outside diameter. Entering 102 mm with Outside selected must produce the same centreline and curve result. These are diameter differences: adding d to an inside radius would be a different operation.
The reference selector describes the number currently in Measured diameter. Changing that selector reinterprets the entered number; it does not silently convert it to another reference. The dimension-unit selector, in contrast, converts all five dimension fields while retaining their physical values.
Inside and outside references require a positive cross-section diameter. With Centreline selected, a zero cross-section diameter explicitly means an ideal line. Negative diameters, a nonpositive resulting centreline, or a round cross-section larger than the centreline diameter are rejected. A zero inside diameter is allowed as a limiting geometry, not as a practical winding recommendation.
Pitch is an axial advance
Pitch here is the centreline’s advance parallel to the axis after one complete 360-degree turn. It is not the sloping distance along the wire and not a clear gap between neighbouring surfaces. The total axial rise is pitch multiplied by turns. The same pitch value applies to fractional turns: 2.5 turns at 20 mm per turn rise by 50 mm.
Winding left-handed instead of right-handed changes the direction, not this length. The calculator accepts a nonnegative pitch and reports the magnitude of the axial rise. It has no handedness input because that would not change any result it calculates.
Unwrap one turn into a right triangle
The University of Texas helix derivation parameterises a constant-radius helix and obtains its arc length from a constant speed. With centreline diameter D, pitch p and N turns, the equivalent one-turn triangle has perpendicular legs πD and p.
Circumference C = πD
Curve per full turn = √(C² + p²)
Helical curve = N × √((πD)² + p²)
Axial rise = N × p
The implementation uses a numerical hypotenuse calculation for the square root. The diagram unwraps one complete turn and labels both legs and the curve. It excludes tails and allowance. It is an explanatory SVG, not a full-size cutting or fabrication template.
Worked example: the default five-turn helix
100 mm centreline, 20 mm pitch, five turns
A 100 mm centreline has a circumference of about 314.159265 mm. The curve per turn is √(314.159265…² + 20²), approximately 314.795241 mm. Five turns require approximately 1,573.976207 mm of ideal centreline, while the axial rise is only 100 mm.
The example adds two explicitly entered 100 mm straight tails, producing 1,773.976207 mm before allowance. Its illustrative 10% allowance is 177.397621 mm. Geometry plus that entered allowance is approximately 1,951.373828 mm, or 1.951373828 m.
The 10% is an invented demonstration choice, not a standard waste factor or an instruction for a material. The guide rounds numbers for readability; the calculation and reports retain their computed precision.
A triangle with a simple numerical check
Take an ideal centreline diameter of 300 ÷ π mm, making the circumference 300 mm. Choose a pitch of 400 mm per turn. The one-turn curve is exactly the familiar 3–4–5 hypotenuse scaled by 100: 500 mm. At 2.5 turns, curve length is 1,250 mm and rise is 1,000 mm. This demonstrates both fractional turns and the difference between curve and rise.
Entering the decimal approximation of 300 ÷ π necessarily introduces finite input precision. It should give a result close to those reference values, rather than establish a fabrication tolerance.
Zero pitch, zero turns and overlap
With zero pitch, one turn becomes a circle: its curve length is πD and its axial rise is zero. Half a turn is a semicircular arc with length πD ÷ 2. More than one zero-pitch turn numerically traverses the same circle repeatedly; the tool flags that as a retraced path, not separated turns of a physical winding.
With zero turns, helical length and rise are zero. Entered straight tails still contribute to the total, and your allowance still applies to those tails. This is a deliberate tails-only arithmetic case. A valid diameter is still required to define the otherwise unused helix.
If positive pitch is smaller than positive cord/wire diameter and at least one full turn is present, the tool flags the evident proximity of positions one revolution apart. Passing that simple check does not prove clearance. The calculator does not perform a full three-dimensional collision, bend-radius, manufacturing or assembly analysis.
Add straight lengths and allowance explicitly
Enter the two tails as straight material lengths you already know. The tool does not derive tail bends, hooks, joins or tangent transitions. Set either tail to zero if absent. Curve plus tails is the geometric subtotal; the separate allowance equals that subtotal multiplied by your percentage divided by 100.
Allowance changes the material arithmetic only. It does not enlarge the diameter, increase pitch, add turns or change rise. A 0% allowance preserves the geometric subtotal exactly. An allowance is not a substitute for a process-specific bend allowance or a tested production method.
Keep a record of the assumptions
Copy report, Text and CSV preserve entered references, dimensions, turns, tails, allowance and computed numbers in millimetres. The total also appears in metres in the text report. The SVG contains only the one-turn explanatory diagram. Unit changes support millimetres, centimetres and inches using 1 inch = 25.4 mm; cached underlying dimensions avoid drift from repeatedly converting a rounded screen display.
Blank or invalid inputs clear usable results, the diagram and exports. Restore example replaces current entries with the defaults. This release has no account, upload, saved-input link or persistent project history; reloading returns to the example. The calculation provides no spring strength, electrical rating, code assessment or load-capacity conclusion.