Coil Geometry Calculator

Before ordering wire, it pays to know what a winding actually becomes: how far it builds out radially, how many meters of conductor it swallows, what it weighs, and what resistance the power supply will see hot. This calculator models a conventional layer-wound solenoid coil. A cyclotron magnet uses two such coils, one per pole — the results below are for one coil.

Half cross-section through one coil (axisymmetric about the dash-dot axis; the bore is broken — its width is not to scale). Each cell is one conductor at the winding pitch, in layers (radial) × turns per layer (axial). Window and conductor grid drawn to scale. Dimensions update with the inputs.

Results

Winding pitch (insulated size)	—
Turns per layer	—
Coil outer diameter	—
Coil axial height	—
Conductor length	—
Resistance at 20 °C	—
Resistance at operating temperature	—
Copper mass	—

The math

The winding pitch is the bare size plus insulation on both sides: s = s_bare + 2t_ins. With N turns in n_L layers, each layer carries ⌈N/n_L⌉ turns; layer k (counting from 0) winds at mean diameter

D_k = D_inner + (2k + 1)·s

Conductor length is the layer-by-layer sum ℓ = Σ (turns in layer k) · πD_k, the outer diameter is D_inner + 2n_Ls, and the axial height is (turns per layer) · s. Resistance and mass follow from the bare copper cross-section A (side² for square, πd²/4 for round):

R = ρℓ/A, ρ(T) = ρ₂₀ [1 + α(T − 20 °C)], m = δAℓ

with annealed-copper values ρ₂₀ = 1.724 × 10⁻⁸ Ω·m (100% IACS), α = 0.00393 K⁻¹, δ = 8960 kg/m³. Magnet coils run warm: expect roughly +24% resistance at 80 °C over the nameplate 20 °C value, and size the power supply for the hot resistance.

Assumptions and limits

Ideal square-packed winding: every turn lands at exactly one pitch. Real coils wind slightly proud — add a few percent to the radial build, more for round wire wound loose.
Round-wire orthocyclic (hexagonal) packing, bobbin flanges, leads, and interlayer cooling plates are not modeled.
Length uses the mean diameter of each layer; helical pitch adds a negligible √(1 + (s/πD)²) correction for any sane geometry.

Worked check

300 mm ID, 500 turns of 2 mm square wire with 0.1 mm insulation per side (pitch 2.2 mm) in 10 layers: 50 turns/layer, OD = 344 mm, height = 110 mm, ℓ = 506 m, R₂₀ = 2.18 Ω, R₈₀ = 2.69 Ω, mass = 18.1 kg. (Cross-check the mass: 4 mm² × 506 m × 8960 kg/m³ = 18.1 kg.)

Sources

Copper properties: International Annealed Copper Standard (IACS); CRC Handbook of Chemistry and Physics, resistivity of metals.
Winding geometry: standard practice, e.g. D. B. Montgomery, Solenoid Magnet Design, Wiley-Interscience, 1969, ch. 1.

Educational reference, not an operating procedure: results reflect the stated model and assumptions. Verify anything safety-critical against primary sources, and read the safety fundamentals before applying numbers to real hardware.