Toroid Inductance Calculator
A toroidal inductor wraps wire around a ring-shaped core, confining nearly all of the magnetic field inside the ring. Inductance is set by the core material and dimensions and by the number of turns squared. This calculator computes the inductance directly from the geometry: the relative permeability of your core, the ring height, and its inner and outer diameters, multiplied by turns squared. It returns inductance in microhenries, the resulting AL value, and the turns needed for a target. Supply the permeability from your core datasheet, since it varies by material.
Toroid inductance formula
mu0 = 4 * pi * 1e-7 (H/m)
AL = mu0 * mu_r * h * ln(OD/ID) / (2 * pi) [henries per turn^2, SI units]
L = AL * N^2
Convert mm dimensions to metres before applying
AL(nH) = AL(H) * 1e9
The natural log of the outer-to-inner diameter ratio accounts for the field varying across the ring. Supply mu_r from your core datasheet.
Toroid design context
- Inductance scales with the square of the number of turns, so small turn changes have a large effect.
- Toroids contain their flux internally, radiating far less than solenoids.
- The AL value bundles material and geometry; using it directly is the most reliable method.
- Relative permeability depends entirely on the core material, so it is a user input.
- High-current designs must check the saturation curve; AL is a small-signal figure.
Toroid inductance: frequently asked questions
How is toroid inductance calculated from the AL value?
Manufacturers print an AL value (inductance per turn squared) for each toroid core. Inductance equals AL times the number of turns squared. With AL in nanohenries per turn squared, L (nanohenries) = AL times N squared. This is the most reliable method because AL already captures the core material and geometry.
How do I find the number of turns for a target inductance?
Rearrange the AL formula: N = square root of (L divided by AL), using the same units for L and AL. For example, a target of 100 microhenries (100,000 nH) on a core with AL of 250 nH per turn squared needs the square root of 400, which is 20 turns.
What if I do not know the AL value?
You can compute it from geometry: AL (henries per turn squared) = (mu0 times mu_r times height times ln(outer radius / inner radius)) divided by (2 times pi), where mu0 is 4 pi times ten to the minus seven. You supply the relative permeability mu_r of the core material from its datasheet, since it is not universal.
Why are toroids preferred over straight solenoids?
A toroid confines almost all of its magnetic flux inside the ring, so it radiates very little and is less affected by nearby components. This makes toroids the standard choice for power inductors, common-mode chokes, and EMI filters.
Does core saturation affect inductance?
Yes. As current rises and the core approaches saturation, the effective permeability falls and so does inductance. The AL value is specified at low signal levels, so high-current designs must check the manufacturer's saturation curve, which this calculator does not model.
Official sources
- NIST: vacuum permeability and fundamental constants.
- IEEE Standards Association: magnetics and inductance standards.
Reviewed by the CalculatorHub team, edited by James Graham, 17 June 2026. See our methodology.