Calculate the length of wire in a coil from its turns and coil diameter, or the length of rolled strip, film or foil from its diameters and thickness.
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Coil Length Formula
The widget supports two distinct models. For a tightly wound strip, sheet, film, paper or foil roll, L = π(D² − d²)/(4t), where D is outer diameter, d is core diameter and t is effective layer thickness. The inverse modes calculate D = √(d² + 4tL/π) or t = π(D² − d²)/(4L). Width cancels. Use uniform effective thickness and account for liners, compression or gaps when interpreting the estimate.
For a constant-diameter helix, total wire or tube length = N × √((π × mean diameter)² + pitch²) + two end leads. Pitch is axial advance per turn and each lead is the entered straight length at one end. Fractional turns are allowed. The following circumference formula is the zero-pitch wire-length special case, not the rolled-strip formula.
- CL = Coil Length per turn (wire length consumed per revolution)
- OD = Outer Diameter (measured to the outside surface of the wound wire)
- WD = Wire Diameter (cross-sectional diameter of the wire)
The expression (OD - WD) gives the mean diameter of the coil, which is the average of the outer and inner diameters. For a single-layer coil, the inner diameter equals OD minus twice the wire diameter, making the mean diameter exactly OD - WD. Multiplying by pi converts that diameter into the circumference the wire travels per turn. To find total wire length for a multi-turn coil, multiply the result by the number of turns.
Mean Diameter and Why It Matters
The mean diameter is the geometric center of the wire cross-section as it travels around the coil. Engineers use the mean diameter, not the outer diameter, for wire length calculations because the outer surface of the wire travels a longer path than the inner surface. Using OD alone overestimates wire consumption; using the inner diameter alone underestimates it. The mean diameter produces the true average path, which is what determines the actual wire used.
For a coil wound from 0.5 mm wire with a 20 mm outer diameter, the mean diameter is 19.5 mm, and the circumference per turn is approximately 61.26 mm. Over 500 turns, that is 30.63 meters of wire. A designer who neglected to account for wire diameter and used the outer diameter instead would overestimate wire usage by about 0.79 meters on this modest coil, a meaningful error when specifying magnet wire by the kilogram.
Coil Length, Resistance, and Electrical Performance
Wire resistance scales directly with total wire length, making coil length per turn the foundational quantity in predicting electrical behavior. Copper wire resistance is governed by R = (resistivity x length) / cross-sectional area. At 20 degrees Celsius, copper has a resistivity of 1.72 x 10-8 ohm-meters. For common AWG sizes wound into coils, typical resistance per meter values are:
| AWG | Wire Diameter (mm) | Resistance per Meter (ohms/m) | Common Coil Application |
|---|---|---|---|
| 24 | 0.511 | 0.0843 | Small transformers, relays |
| 28 | 0.321 | 0.2139 | Inductors, solenoid coils |
| 32 | 0.202 | 0.538 | High-impedance pickup coils |
| 36 | 0.127 | 1.361 | Miniature transformers |
| 40 | 0.0799 | 3.441 | Fine-wire sensors, precision coils |
For an idealized constant-diameter winding with a finished outer diameter of 15 mm and 0.321 mm AWG 28 wire, the mean circumference is (15 − 0.321) × π ≈ 46.13 mm per turn. At 1,000 turns, wire length is about 46.13 m and resistance at the stated rate is about 9.87 ohms. A bobbin outer diameter instead requires adding the wire diameter to obtain the first layer’s mean diameter; multiple layers require separate diameters. This resistance figure directly governs the coil's current draw, heat generation, and time constant when combined with inductance.
Coil Types and Their Geometric Requirements
Different coil types use wire length per turn in fundamentally different ways depending on what the coil is designed to accomplish.
Inductive Coils (Solenoids, Inductors, Transformers)
Inductance scales with the square of the number of turns and inversely with coil length (the axial dimension). Wire length per turn determines how many turns fit within a given wire budget or resistance budget. A coil designer working toward a target inductance of 100 microhenrys must balance turn count, core permeability, and wire resistance simultaneously. Knowing the wire length per turn lets the designer calculate DC resistance before winding begins, avoiding the discovery that a target inductance requires resistance incompatible with circuit limits.
Heating Element Coils
Resistance heating elements, such as those in electric ovens, industrial furnaces, and 3D printer hot ends, are wound coils of high-resistivity alloys like Nichrome (NiCr) or Kanthal. The power output of a heating element is P = V squared divided by R, and the resistance R depends entirely on total wire length and wire cross-section. A Nichrome wire with a resistivity of 1.10 x 10-6 ohm-meters wound into a coil with 25 mm OD and 1 mm wire diameter produces a mean circumference of (25 - 1) x pi = 75.4 mm per turn. At 100 turns, that is 7.54 meters of wire, yielding an approximate cold resistance of 10.56 ohms for the stated 1 mm wire and resistivity. At 120 V, the idealized V²/R value is about 1,364 W. Actual alloy, operating temperature, heat transfer and electrical safety require a separate design assessment.
Spring Coils
Mechanical springs are geometrically identical to electrical coils. The coil length per turn determines the wire volume per turn, which combined with material density gives the mass per turn. A compression spring wound from 3 mm steel wire with a 30 mm outer diameter has a mean diameter of 27 mm and a circumference of 84.82 mm per turn. At a steel density of 7,850 kg/m3, each zero-pitch turn contains approximately 4.71 grams of steel. For automotive valve springs, which typically have 7 to 9 active coils and must meet precise weight specifications, this calculation directly influences material selection and manufacturing tolerances.
Coil Winding Industry Context
The global coil winding machine market was valued at approximately 4.21 billion USD in 2024 and is projected to reach 10.52 billion USD by 2037, growing at a compound annual rate of around 7.3%. This growth is driven by electric vehicle motor production, renewable energy generator windings, and consumer electronics miniaturization. The electrical coil winding services segment alone, which includes transformers, motors, and custom inductors, was valued at 5.46 billion USD in 2025 and is expected to reach 7.98 billion USD by 2035.
Nearly 60% of coil winding operations have adopted automated CNC winding solutions as of 2024. These automated systems require precise geometric inputs, including mean coil circumference, to calculate wire feed rates, tension settings, and material consumption per batch. The coil length per turn figure calculated here is a required input parameter for most industrial winding programs.
Pitch and Helical Correction
The formula CL = pi x (OD - WD) assumes the wire wraps in a flat plane, which is an approximation. In reality, each turn of a coil advances axially by one pitch distance (the center-to-center spacing between adjacent turns). The true wire length per turn follows a helical path, calculated as the square root of the sum of the squared circumference and squared pitch: CLhelix = √((pi x meandiameter)2 + pitch2). For tightly wound coils where the pitch equals the wire diameter, the helical correction is very small. A coil with a 20 mm mean diameter and 0.5 mm pitch produces a planar circumference of 62.83 mm and a helical circumference of 62.83 mm as well, since the pitch term (0.5 mm squared = 0.25) is negligible against the circumference squared (62.83 squared = 3947.6). The two lengths are close but not equal: approximately 62.831853 mm and 62.833842 mm, a 0.003166% increase. Whether that matters depends on the required precision; no universal pitch-to-diameter threshold applies.
Coil Length in Multi-Layer Windings
For multi-layer coils, each successive layer has a larger outer diameter. The first layer sits on the bobbin at the inner diameter; each additional layer adds two wire diameters to the outer diameter of the previous layer. The mean circumference increases with each layer, so wire consumption per turn grows as the winding builds outward. A transformer secondary with 10 layers of 0.5 mm wire starting from a 20 mm bobbin outer diameter will have layer mean diameters ranging from 20.5 mm (layer 1) to 29.5 mm (layer 10), with circumferences from 64.4 mm to 92.7 mm per turn. Total wire consumption cannot be estimated from a single coil length figure in this case; it requires summing the circumference across all layers, weighted by the number of turns per layer.
