Coil Length Calculator
“Coil length” means two different jobs, and most calculators only do one of them. Winding a spring or a solenoid, you need the length of wire in the helix. Checking a spool, you need the length of material left on the roll, without unrolling it.
This tool does both. The helical tab uses the pitch-corrected helical path formula and reports total and per-turn length, with a mean-diameter helper for anyone measuring with calipers. The roll tab uses the annulus area method and needs only the outer diameter, core diameter, and material thickness.
Use this mode for springs, solenoid windings, heating coils, and any helix of wire or tubing.
Use this mode for wire, cable, rope, hose, or belt wound on a reel or spool. Measure the full roll: outside diameter, core (inside) diameter, and the thickness of the material.
Results are geometric estimates for uniform coils and tightly wound rolls. They do not include end leads, trimming allowance, or manufacturing tolerances.
Quick Answer
Key takeaways
- Pick the tab by the shape of the problem: a helix you are winding, or a roll you are measuring. The two formulas share nothing but the word coil.
- Helical length is per-turn length times turns, and per-turn length is the hypotenuse of circumference and pitch. For tight coils the pitch term nearly vanishes.
- Always use the mean diameter in the helix formula. Measuring the outside and forgetting the wire diameter is the single most common error in this calculation.
- Roll length is annulus area divided by material thickness. Thickness is the sensitive input: a 10% thickness error is a 10% length error.
- Quick Answer
- How to use the coil length calculator
- The two formulas, and why they look nothing alike
- Worked examples: one spring, one spool
- Quick reference: spring configurations at a glance
- Measuring without fooling yourself
- What other coil calculators miss
- Frequently Asked Questions
- Add This Calculator to Your Website
- References
How to use the coil length calculator
Start with the tab. Springs, solenoids, heating elements, and any wire wound as a screw shape belong under Helical coil. Cable, rope, hose, belt, or strip sitting on a reel belongs under Wound roll. Each tab keeps its own inputs, units, and result, so you can run both for the same workshop job, wire for the winding and a stock check on the spool it came from, without re-entering anything.
For the helical tab you need turns and a mean diameter. If your calipers only give you the outside of the coil, fill in the optional outer diameter and wire diameter instead and the tool converts: mean diameter equals outer diameter minus one wire diameter. Pitch is the axial distance one turn advances; set it to 0 for a tight coil with touching turns. Units convert internally, so measure in whichever unit your ruler uses.
The two formulas, and why they look nothing alike
A helical turn is not a flat circle. Unwrap one turn and it becomes the diagonal of a rectangle whose sides are the circumference and the pitch, so the Pythagorean theorem, the same result behind the arc length of a helix in the MathWorld helix reference, gives the per-turn length.
A wound roll is a different picture. Look at it end-on and the material forms a ring: an annulus with area π/4 x (OD² - ID²). Unrolled, that same material is a long rectangle with the same area, so dividing the area by the thickness gives the length. This annulus method is the standard belt-and-roll calculation documented in the ConveyorTek guide to calculating the length of a belt in a coil.
Worked examples: one spring, one spool
Both tabs are pre-filled with these cases, and every figure below is what the tool returns.
| Case | Inputs | Working | Result |
|---|---|---|---|
| Helical spring | 20 turns, mean diameter 30 mm, pitch 2 mm | Per turn: sqrt((π x 30)² + 2²) = 94.27 mm; total 20 x 94.27 | 1,885.38 mm |
| Wound cable roll | OD 50 cm, ID 10 cm, thickness 0.5 cm | π x (50² - 10²) / (4 x 0.5) = π x 2400 / 2 | 3,769.91 cm (37.70 m) |
| Tight coil shortcut | OD 10 mm, wire 2 mm, pitch 0 | Mean diameter 8 mm; per turn 8 x π | 25.13 mm per turn |
The pitch term deserves its reputation for being small. On the spring above it adds about 0.6 mm of wire across all 20 turns versus the pitch-free shortcut, because 2 mm of pitch is tiny next to a 94.25 mm circumference inside a square root. It starts to matter on open-wound coils and extension springs, where the pitch is a real fraction of the circumference. The same geometry underlies the generic arc length calculator, which covers the single-curve version of this unwrapping argument.
Quick reference: spring configurations at a glance
Lengths computed with the pitch-corrected helical formula, in millimetres.
| Turns | Mean diameter | Pitch | Wire length |
|---|---|---|---|
| 10 | 20 mm | 0 mm | 628.32 mm |
| 15 | 30 mm | 1 mm | 1,413.80 mm |
| 20 | 40 mm | 2 mm | 2,513.59 mm |
| 25 | 50 mm | 3 mm | 3,927.71 mm |
Measuring without fooling yourself
Mean diameter is the trap. The helix formula wants the diameter through the centre of the wire. Measure outside to outside and use that number directly and you overstate every turn by π times the wire diameter; on thick wire wound on a small core, that error is several percent of the whole job. The conversion the tool applies, mean equals outer minus wire diameter, is also the starting point in manufacturer design guides such as the Kanthal design calculations for wire elements, where coil geometry drives resistance and surface load.
Thickness is the roll's sensitive input. Length divides by thickness, so a cable that is really 0.55 cm where you entered 0.5 cm holds about 9% less material than the answer says. Measure with calipers in three places and average, and strip or account for insulation where the spec separates conductor from jacket. The same measure-twice discipline applies to flexible stock generally, whether it is the rope in the anchor chain rope length calculator or the linked stock in the chain length calculator.
Gaps read as material. The annulus method assumes a solid ring of material. A loosely wound roll carries air between layers, and the formula counts that air as cable. For inventory estimates that is acceptable; for a cut-to-length commitment, unwind and measure a sample or weigh the roll against a known weight per metre.
What other coil calculators miss
The tools reviewed for this page each cover a slice of the problem and leave the rest to you.
Miss 1: one intent only. The top roll-style tools take outer diameter, inner diameter, and thickness and stop there; they cannot help you wind anything. The top helical tools do the reverse. Putting both behind one tab switch sounds obvious until you notice how few pages bother.
Miss 2: the pitch-free shortcut presented as exact. Widely used helical tools compute wire length as π x D x N with no pitch term at all. For tight coils the error is trivial; for open coils it understates every job, and the page never says an approximation was made. The full helical path formula here is exact for a uniform helix, and the article quantifies when the shortcut is safe.
Miss 3: per-turn answers with the multiplication left to you. Several tools report one loop and stop. Total and per-turn both appear in the result here, because ordering wire needs the total and checking a winding machine needs the per-turn figure.
Miss 4: no mean-diameter help. Tools that demand a mean diameter from users holding calipers are asking for the one measurement nobody takes directly. The outer-plus-wire helper fields remove that conversion error at the source.
Frequently Asked Questions
Use the mean diameter: the distance from the centre of the wire on one side of the coil to the centre of the wire on the other side. If you can only measure the outside of the coil, enter the outer diameter and the wire diameter in the optional fields and the tool subtracts one wire diameter for you. Using the outer diameter as if it were the mean overstates the wire length, especially with thick wire.
Pitch is the axial distance the coil advances in one full turn, measured centre to centre between neighbouring turns. For tightly wound coils with touching turns, set it to 0; the pitch term inside the square root is then zero and the formula reduces to pi times diameter times turns. For extension springs and open coils, measure it with calipers, because there it genuinely lengthens each turn.
Because each turn of wire is a helix, not a flat ring. Unwrapped, one turn is the hypotenuse of a right triangle whose legs are the circumference, pi times the mean diameter, and the pitch. The square root is the Pythagorean theorem applied to that triangle, and it is the standard arc-length result for a helical curve.
Very accurate for tightly wound rolls of uniform material, because it works from the total cross-sectional area of material rather than counting layers. It reads high when there are air gaps between layers or the thickness varies along the roll, and it is only as good as the thickness measurement, which the result divides by.
No. A flat spiral, like a clock spring or a planar spiral antenna, grows outward in a plane and needs a spiral-length formula, which is a different calculation. This tool covers helical coils, the screw-like shape, and wound rolls. Using the helical mode on a flat spiral will give the wrong answer.
Use digital calipers or a micrometer, take three readings at different points around the wire, and average them. For enamelled magnet wire the insulation adds a small amount; strip a short section or check the manufacturer's bare-wire specification if the difference matters to your job.
Any one unit, as long as every input in the tab uses it. Each tab has its own unit selector, and the tool converts internally, so you can measure a spring in millimetres and a roll in centimetres on the same visit. Results come back in the selected unit, with metres added in the summary line.
Real coils often end with a partial turn, for example 20.5 turns on a spring with ground ends or a winding that stops mid-turn for a lead. The tool accepts fractional turns and prorates the length exactly, which is more faithful than forcing you to round to 20 or 21.
Add This Calculator to Your Website
References
- Weisstein, Eric W., "Helix," MathWorld, Wolfram: the helical curve and its arc-length result, which unwraps one turn into the hypotenuse of the circumference and pitch, the basis of the helical mode. MathWorld: Helix. Accessed October 2026.
- ConveyorTek, "Calculating the Length of a Belt in a Coil": the annulus-area method for material length on a wound roll, L = (D² - d²) x 0.785 / thickness, equivalent to the pi x (OD² - ID²) / (4t) form used by the roll mode. ConveyorTek: Calculating the Length of a Belt in a Coil. Accessed October 2026.
- Kanthal (Alleima), "Design Calculations and Standard Tolerances" for resistance wire elements: manufacturer design practice for coiled wire, including mean coil diameter geometry and stretched coil length, used here for the measurement guidance. Kanthal: Design Calculations of Wire Elements. Accessed October 2026.