Free Inductance Calculator (Air‑Core & Ferrite Core Options)Inductance is one of the fundamental properties of electrical circuits. Whether you’re designing RF filters, power converters, antennas, or hobbyist coils, knowing the inductance of a coil is critical for predicting circuit behavior. A free inductance calculator that supports both air‑core and ferrite‑core options saves time and reduces guesswork. This article explains how such a calculator works, the key equations, practical considerations when choosing cores and winding techniques, examples, and how to implement a simple calculator yourself.
What the calculator does
A good inductance calculator accepts coil geometry and material details and returns:
- Inductance (L) in henries (H), millihenries (mH), or microhenries (µH)
- Estimated self‑resonant frequency (SRF) — approximate
- DC resistance (Rdc) estimate based on wire gauge and length (optional)
- Core effective permeability (µeff) for ferrite cores (if provided)
- Warnings about assumptions (e.g., tight winding, uniform coil)
Key coil parameters the calculator needs
- Number of turns (N)
- Coil length (l) — axial length of the winding
- Mean coil diameter (D) or inner and outer diameters to compute mean
- Wire gauge or diameter (for fill factor and resistance)
- Core type: air or ferrite (or other magnetic material)
- Core geometry (if ferrite): tubular, toroidal, rod — core dimensions and relative permeability (µr)
- Winding spacing (bunched vs. single‑layer spaced)
- Frequency (for SRF estimate and skin/ proximity effects)
Core formulas
Below are commonly used approximations a calculator uses. They trade off complexity and accuracy; the exact method depends on coil shape and desired precision.
- Wheeler formula — single‑layer air‑core solenoid (good general-purpose) For a single‑layer solenoid with length l and average diameter D, inductance L (in µH) can be estimated by:
L ≈ (D^2 * N^2) / (18D + 40l)
where D and l are in inches. Converting to SI (meters) and henries requires unit adjustments.
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Modified Wheeler for multilayer and short coils For coils where length is comparable to diameter, other Wheeler variants or the Rosa formula provide better results.
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Nagaoka coefficient — corrects for finite coil length L = µ0 * N^2 * A * k_N / l_eff
where µ0 is the vacuum permeability, A is cross‑sectional area, and k_N is the Nagaoka factor (depends on coil aspect ratio).
- Toroidal core (ferrite) — approximate formula For a toroid: L = (µ0 * µr * N^2 * A) / (2π * r_mean)
where A is cross‑sectional area, r_mean is mean radius, and µr is relative permeability of the core material. This assumes magnetic path is mostly confined in the core.
- Rod core (long solenoid on rod) Use effective permeability µeff to account for leakage and air gaps: L = µ0 * µeff * N^2 * A / l
µeff depends strongly on the core shape, relative permeability, and whether there are air gaps.
- Self‑resonant frequency (SRF) — rough estimate SRF ≈ 1 / (2π * sqrt(L * Cstray))
Estimate stray capacitance Cstray from empirical formulas or a small default value (a few pF for simple coils).
- DC resistance (Rdc) Rdc = ρ * length_of_wire / A_conductor
For copper, ρ ≈ 1.724×10^−8 Ω·m at 20°C. Use wire AWG tables to get conductor area and diameter.
Air‑core vs. Ferrite core — practical tradeoffs
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Air‑core coils
- Advantages: Linear inductance vs. current (no saturation), low core losses at high frequency, predictable behavior.
- Disadvantages: Lower inductance per turn; larger physical size for the same L.
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Ferrite core coils
- Advantages: Much higher inductance per turn (smaller coils), compact; good for low‑frequency power inductors and EMI components.
- Disadvantages: Permeability is frequency‑dependent; cores can saturate with DC bias; core losses at high frequency; effective permeability less than µr due to fringing and gaps.
Practical tips when using a calculator
- Always enter the mean diameter (average of inner and outer diameters) for best Wheeler estimates.
- For multi‑layer coils, consider using a multilayer formula or split into equivalent single layers and sum appropriately.
- For ferrite cores, use the manufacturer’s µr and AL value (nH/turn^2) if available — AL values are the simplest input: L(nH) = AL(nH/turn^2) * N^2.
- Include wire insulation thickness when computing packing and coil length.
- At high frequencies, account for skin effect: use litz wire or fewer turns of thicker conductor for power applications, or compute AC resistance using skin depth δ = sqrt(2ρ/(ωµ0)).
- Check for core saturation: estimate peak flux density B ≈ (µ0 * µr * N * I) / l_magpath for toroids/rods and compare to core Bs rating.
Example calculations
Example 1 — Single‑layer air‑core solenoid (approx using Wheeler)
- N = 50 turns
- Mean diameter D = 20 mm (0.787 in)
- Length l = 25 mm (0.984 in) Using Wheeler (in µH with inches): L ≈ (D^2 * N^2) / (18D + 40l) Convert and compute in the calculator for a numeric result (calculator automates unit conversions).
Example 2 — Ferrite toroid using AL value
- AL = 250 nH/turn^2
- N = 10 turns L = AL * N^2 = 250 nH * 100 = 25,000 nH = 25 µH
How to implement a simple web calculator
- Inputs: N, D or inner/outer diameters, length, wire gauge, core type, AL or µr if ferrite.
- Convert all units to SI internally.
- Choose formula based on core type and coil geometry (e.g., Wheeler for single‑layer air core, AL for ferrite).
- Compute L, Rdc, approximate SRF.
- Display results with unit options and warnings about assumptions.
Sample pseudocode (JavaScript):
// Inputs: N, D_m, l_m, coreType, AL_nH_per_turn2 (optional) function wheelerAirCoreInductance(N, D_m, l_m) { // convert to inches for Wheeler formula const inch = 0.0254; let D_in = D_m / inch; let l_in = l_m / inch; let L_uH = (D_in*D_in * N*N) / (18*D_in + 40*l_in); return L_uH * 1e-6; // convert µH to H } function ferriteALInductance(N, AL_nH) { return (AL_nH * N*N) * 1e-9; // nH to H } Common mistakes to avoid
- Using the wrong diameter (outer instead of mean) — overestimates inductance.
- Ignoring wire insulation and packing when computing coil length.
- Applying high‑frequency assumptions at low frequencies and vice versa.
- Assuming ferrite µr is constant across frequencies and flux densities.
When to measure instead of calculating
Calculations are approximations. Measure when:
- High accuracy is required (RF filters, tuned circuits).
- Complex core geometries or significant fringing fields exist.
- You need exact self‑resonant frequency.
A handheld LCR meter or impedance analyzer gives the most reliable results.
Summary
A free inductance calculator that supports both air‑core and ferrite‑core options is a practical tool for designers and hobbyists. Use Wheeler or Nagaoka corrections for air cores, AL values or toroidal formulas for ferrite, and mind practical issues like core losses, saturation, and skin effect. For final designs and critical frequencies, verify with measurements.
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