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Toroid Inductance Calculator

Enter the turns, permeability and core dimensions to compute the toroid's inductance.

How it is calculated

The inductance of a toroid with a rectangular cross-section is L = μ0 · μr · N² · h · ln(b ÷ a) ÷ (2π), where μ0 = 4π × 10⁻⁷ H/m, μr is the relative permeability of the core (1 if left empty), N is the number of turns, h is the core height and a and b are the inner and outer radii. The three sizes are entered in millimetres and converted to metres inside the tool. The outer radius must be larger than the inner one, turns must be at least 1, and the other values must be positive. The answer is given in microhenries, millihenries and in henries in scientific notation. It assumes the field stays inside the core and ignores the wire, gaps and saturation.

Worked example

A ferrite ring has an inner radius of 6 mm, an outer radius of 12 mm, a height of 5 mm and μr = 75, wound with 30 turns. Then ln(12 ÷ 6) = ln 2 = 0.6931. L = 4π × 10⁻⁷ × 75 × 30² × 0.005 × 0.6931 ÷ (2π) = 2 × 10⁻⁷ × 75 × 900 × 0.005 × 0.6931 = 4.6787 × 10⁻⁵ H. That is 46.787 µH, or 0.0468 mH. Doubling the turns to 60 would quadruple it to about 187 µH.

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Common mistakes

  • Entering diameters instead of radii: the inner and outer fields are radii, so a ring labelled 12 mm inner and 24 mm outer diameter needs 6 and 12.
  • Entering sizes in centimetres or metres: the fields are in millimetres, and only the ratio b ÷ a does not depend on the unit, while the height does.
  • Using the initial permeability of the material as the working value: μr changes with frequency and with the DC current in the winding, so the real inductance can be lower than calculated.
  • Expecting inductance to grow in proportion to the turns: it grows with the square of the turns, so 30 turns to 60 turns is four times as much, not two.

About this calculator

A toroidal inductor — wire wound N times around a donut-shaped core — has inductance given by L = (μ·N²·h) / (2π) · ln(b/a), where μ is the core material's permeability, h is the core's height, and a and b are its inner and outer radii. The logarithmic term captures how the magnetic field strength falls off with distance from the center of the ring.

Toroid cores confine their magnetic field almost entirely within the donut shape, which means far less stray flux and electromagnetic interference than an equivalent solenoid — the reason toroidal ferrite and powdered-iron cores are the standard choice for switch-mode power supply chokes, EMI/RFI filters, and compact transformers in consumer electronics and audio equipment.

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Comments (1)

  • Editorial team

    Datasheets usually list outer and inner diameters, while this tool wants radii in millimetres, so halve them: a ring with an outer diameter of 24 mm and an inner diameter of 12 mm means 12 and 6. To compare with a maker's inductance index in nH per turn squared, divide the result by the turns squared; the example ring of 30 turns works out to about 52 nH. Which core material and size are you winding?

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