EI Core Inductance Capacity Calculator

For EI cores with spacers between the E and I pieces, apparent permeability is calculated using:

μ_app = μ_material / (1 + (l_gap/l_c) × μ_material)

Where:

μ_material = ungapped permeability of the core material
l_c = magnetic path length (6 × tongue for standard EI)
l_gap = total magnetic gap = 2 × spacer thickness + 0.08 mm — the flux crosses the gap twice, once from E to I and once from I back to E, and the butt joint leaves a residual gap of its own even with no spacer fitted

Material values used:

M6 (GOES) — grain-oriented electrical steel, μ ≈ 30,000
M19 (NOES) — non-oriented electrical steel, μ ≈ 6,000
M27 (NOES) — non-oriented, slightly less silicon, μ ≈ 5,000
49 % nickel — AL4750 and similar, μ ≈ 45,000
80 % nickel — mumetal, permalloy, μ ≈ 150,000

These are representative figures at moderate flux, shared with the choke calculator so the two agree. Relative permeability is not a single number — it swings by an order of magnitude with flux level, anneal and rolling direction — but as the note below says, the gap decides μ_app in any practical build, so the choice barely reaches the answer.

This is capacity, not a design. Each cell is the most turns that will fit inside the fill limit, and the inductance that follows. The choke calculator asks the opposite question — how many turns a target inductance needs — so the two will not print the same number for the same core even though they now share their materials, their 6T path and their gap treatment, joint residual included.

Where they meet is worth checking. On an EI-87 with a 1″ stack, M19 and a 14 mil spacer, both put μ_app at 164. This page then fits 186 turns of 19 AWG at an 85 % limit, six whole layers, for 28.7 mH. The choke calculator needs 206 turns to reach 35 mH, which is seven layers and 85.3 % — just past the limit set here. Raise the fill limit to 86 % and this page fits the seventh layer too. Layers are whole numbers, so a percent either way moves a whole layer.

Note: For practical gap sizes (>5 mil), the gap dominates and the formula simplifies to μ_app ≈ l_c/l_gap regardless of material. Material choice matters more for small gaps where the core's intrinsic permeability becomes significant.

Why μ_app varies by core size: Larger cores have longer magnetic paths (l_c), so the same gap produces a higher μ_app. In gap mode, the matrix calculates μ_app individually for each core (shown in the left column). The "Reference Core" selector just controls which value is displayed in the green box above.

Formula: L = N² × μ₀ × μ_app × A_c / l_c

Where:
• N = maximum turns (from winding capacity)
• μ₀ = 4π × 10⁻⁷ H/m
• A_c = tongue × stack height × stacking factor
• l_c = 6 × tongue (standard EI path length)

Random Winding Factor: Accounts for imperfect wire packing when hand-winding coils.

With perfect machine winding, each layer is exactly one wire diameter thick. Hand winding produces gaps, crossovers, and slight misalignment that increase the effective height of each layer.

Typical values:

1.0 — Perfect layer winding (machine wound or very careful technique)
1.1–1.15 — Good hand winding with attention to layer alignment
1.2–1.3 — Loose or scramble winding with significant gaps

The factor multiplies wire diameter to get effective layer height: Layer height = Wire diameter × Random factor

Circular Mils per Amp (CM/A): A measure of current-carrying capacity based on wire cross-sectional area.

Circular mils = (bare wire diameter in mils)². For example, 20 AWG (32 mils) = 1,024 circular mils.

Typical CM/A guidelines for magnet wire:

500–700 CM/A — Continuous duty, enclosed, limited cooling
300–500 CM/A — Intermittent duty or well-ventilated
<300 CM/A — May overheat in continuous operation

The CM/A values shown in the table headers update based on your DC Current input, helping you verify wire sizing is appropriate for your application.