Inductance Calculator

Compute coil inductance using L = μ₀·μ_r·N²·A / l. Choose a core material (relative permeability μ_r), enter the number of turns, core cross-sectional area and magnetic path length. Optionally, add frequency to get reactance (X_L) and estimate Q with series resistance.

Core Material (μ_r)

Custom μ_r (if selected)

Turns N

Magnetic Path Length l

For a toroid, l ≈ 2π·r_mean. For a long solenoid, use core length.

Core Cross-Section Area A

A = width × height of the core cross-section.

Frequency (optional)

Used to compute reactance X_L = 2πfL.

Series Resistance R_s (optional)

If provided with frequency, Q ≈ X_L/R_s.

Inductance Calculator – Compute L, Reactance, and Q from Core Geometry

The inductance calculator provides a rigorous way to estimate the inductance of a coil based on magnetic path length, cross-sectional area, number of turns, and relative permeability of the core. It implements the classic solenoid approximation L = μ₀ μ_r N² A / l and optionally evaluates AC reactance X_L = 2π f L and a quality-factor estimate Q ≈ X_L/R_s. This makes the tool useful for prototyping chokes, RF coils, filters, and energy-storage inductors where a quick yet principled estimate is required before detailed electromagnetic modeling.

How the Inductance Formula Works

Inductance measures the ability of a conductor to store energy in its magnetic field per unit of current. For a uniform magnetic circuit, the inductance calculator uses:

L = μ₀ · μ_r · N² · (A / l)

Here μ₀ = 4π × 10⁻⁷ H/m is the permeability of free space, μ_r is the core’s relative permeability, N is the number of turns, A is the core cross-section, and l is the effective magnetic path length. The expression follows directly from magnetic circuit analogies in which reluctance ℜ = l / (μ A) and inductance L = N²/ℜ. Although exact only for idealized geometries, it provides reliable first-order estimates across a wide range of practical coils.

Inputs to the Inductance Calculator

Core Material (μ_r): Select air (≈1), powdered iron (≈10–60), ferrite (≈200–2000), or silicon steel (≈4000). A custom μ_r option is available when you have a specific core grade.
Turns N: Increasing turns raises inductance quadratically (N²), a powerful design lever constrained by winding resistance and window fill.
Magnetic Path Length l: Effective path around which flux travels. For toroids, l ≈ 2π r_mean; for a long solenoid with a straight core, approximate with the core length.
Cross-Section A: Core area perpendicular to flux. Larger A reduces magnetic reluctance, increasing L.
Frequency (optional): Used to compute AC reactance X_L = 2π f L.
Series Resistance (optional): If provided with frequency, Q ≈ X_L/R_s is reported (simple copper-loss estimate).

Design Intuition

For a fixed geometry and material, inductance scales with the square of turns. Doubling N quadruples L but also increases copper length (and resistance), potentially lowering Q at high frequency. Meanwhile, increasing μ_r via a magnetic core concentrates flux and boosts L without adding turns. The inductance calculator exposes these trade-offs so that you can navigate toward a solution that balances size, loss, and bandwidth.

Example 1 — Air-Core RF Coil

Assume an air coil with N = 10, A = 25 mm² = 25×10⁻⁶ m², and an effective path length l = 60 mm = 0.06 m. With μ_r = 1, the inductance calculator returns L ≈ μ₀·N²·A/l ≈ 4π×10⁻⁷ × 100 × (25×10⁻⁶/0.06) ≈ 0.52 µH. At 10 MHz, X_L ≈ 2π f L ≈ 32.7 Ω — typical for a small RF inductor used in matching networks.

Example 2 — Ferrite Choke

Consider a ferrite core with μ_r = 800, A = 1 cm² = 1×10⁻⁴ m², l = 10 cm = 0.1 m, and N = 50. The inductance calculator gives L ≈ μ₀ μ_r N² A / l ≈ (4π×10⁻⁷)·800·2500·(1×10⁻⁴)/0.1 ≈ 0.025 H (25 mH), suitable for line chokes in EMI filters at low kHz.

Choosing a Core Material

Magnetic materials differ in initial permeability, saturation flux density, loss characteristics, and temperature stability. Air is linear and lossless but yields the lowest L. Powdered iron offers moderate μ_r, distributed gaps (stable energy storage), and better linearity under DC bias than high-μ ferrites. Ferrites provide high μ_r and compact inductors but exhibit frequency-dependent losses and lower saturation flux density. Silicon steel delivers very high μ_r and saturation but is heavy and suited to line-frequency magnetics. Use the inductance calculator to quantify L, then validate material suitability from the manufacturer’s datasheet (B-H curves, loss vs frequency).

Magnetic Path and Area for Common Geometries

Toroid: l ≈ 2π r_mean, A ≈ (h · t), where h is height and t = r_outer − r_inner is radial thickness. The inductance calculator accepts A and l directly — compute from dimensions beforehand.
Long Solenoid: l ≈ core length and A equals cross-section of the core (e.g., πr² for a cylinder).
E-I Cores: Manufacturers provide effective A_e and l_e; enter those into the calculator along with N and μ_r.

Reactance and Impedance

At frequency f, inductive reactance is X_L = 2π f L. The inductance calculator reports X_L when a frequency is provided. Inductor impedance is Z = R_s + jX_L. Minimizing copper resistance raises Q and reduces loss. At high frequency, skin effect and proximity effect further increase R_s, so the simple Q estimate may be optimistic; still, it is a helpful first-look metric.

Winding Considerations

Wire Gauge & Resistance: Thicker wire lowers R_s and improves Q but increases winding area.
Window Fill: Practical coils cannot pack indefinitely many turns; insulation and bobbin geometry impose limits.
Parasitics: Inter-turn capacitance forms a self-resonant LC; above the self-resonant frequency (SRF), the inductor behaves capacitively.

DC Bias and Saturation

Energy-storage inductors carry DC plus ripple current, moving the operating point along the B-H curve. High μ_r materials saturate at relatively low H fields, dropping effective inductance. The inductance calculator estimates L at small-signal conditions; use core vendor charts to account for bias derating when necessary.

Losses and Temperature

Core loss depends on frequency, flux density, and material. Copper loss scales with I²R and increases with temperature due to resistivity. Ferrite μ_r is temperature-dependent. While the inductance calculator focuses on L, preliminary Q, and X_L, final designs should be checked against thermal limits and efficiency goals.

Validation on the Bench

Inductance can be measured via LCR meters, impedance analyzers, or by stepping current and integrating voltage (V = L di/dt). Compare measured L with the inductance calculator output; differences typically arise from fringing fields, non-uniform flux, or inaccurate A and l estimates.

Typical Ranges and Rules of Thumb

Air-core RF coils: tens of nH to a few µH.
Ferrite chokes: tens of µH to tens of mH.
Power inductors for DC-DC: few µH to few mH, with gapped ferrites or powdered iron.

Worked Calculation — Design Flow

Choose geometry and material from mechanical constraints and frequency.
From datasheets, obtain effective A and l (A_e, l_e for standard cores).
Use the inductance calculator to find L for candidate N and μ_r.
Iterate N to meet target L while keeping R_s and window fill within limits.
Check X_L at operating frequency and estimate Q; refine wire gauge as needed.

Limitations of the First-Order Model

Assumes uniform flux and negligible fringing.
Neglects stacking factors, air gaps (unless embedded in μ_r/l), and frequency-dependent μ_r.
Q estimate includes only series resistance; core loss not included.

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References & Further Reading

Disclaimer: The inductance calculator provides engineering estimates for initial design. Always verify results against component datasheets and laboratory measurements before production use.