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Ferrite toroid coil calculator

When you need this

When you have to wind a coil on a toroid of known size and permeability — and check at the same time whether the winding will fit through the hole.

OD 22 mmID 11 mmh 5 mmsection
OD — outer diameter, ID — inner, h — height, C — chamfer
Required inductance L (µH)
Toroid outer diameter OD (mm)
Toroid inner diameter ID (mm)
Toroid height h (mm)
Chamfer C (mm)
Ferrite permeability μr
Wire diameter d (mm)
Result
Number of turns N
Inductance factor AL
Wire length Lw
Number of winding layers

📐 Formulas​

The inductance of a toroid does not depend on the wire diameter or on how the turns are spread around the ring: the whole flux is closed inside the core. The relation L ↔ N is therefore exactly quadratic and is solved directly, without iteration.

The chamfer reduces the cross-section of the magnetic path, which is accounted for as a correction to the height:

r  = C / √2
k  = 0.8584·r² / (h·(OD − ID)/2)
he = h·(1 − k)

The inductance factor follows directly from Ampère's circuital law for a toroid:

AL [nH/N²] = 0.2 · μr · he · ln(OD/ID)        dimensions in mm

Number of turns:

L [nH] = AL · N²      →      N = √( L[nH] / AL )

The wire length comes from a layer-by-layer model: the turns lie close together around the inner circumference, and the «window» of the toroid narrows by one wire diameter each layer.

turns per layer: nₖ = π·(IDₖ − d)/d
length of a turn: pₖ = (ODₖ − IDₖ) + 2·hₖ + 2·d

Notation:​

  • L — inductance [µH]
  • OD — outer diameter of the toroid [mm]
  • ID — inner diameter [mm]
  • h — height of the toroid [mm]
  • C — chamfer [mm]
  • μr — relative permeability
  • AL — inductance factor [nH/N²]
Limits of the calculator:
  • Not for power chokes in switching supplies: there it is core saturation that decides, not permeability, and the core is chosen by its L·I² energy
  • At radio frequencies the permeability of ferrite depends strongly on frequency — that needs a separate calculation
  • The real μr of a particular core can differ from the datasheet value by tens of per cent because of batch spread and ageing
  • The model assumes the winding is spread evenly around the ring

🎯 Where it is used​

  • Tuned-circuit coils and chokes at low frequencies.
  • Broadband transformers and baluns.
  • Checking that the winding will fit before you cut the wire.
Practical notes:
  1. A toroid of OD 22 / ID 11 / h 5 at μr = 1000 gives AL = 693 nH/N² — a handy benchmark for checking the order of magnitude.
  2. Wind evenly around the whole ring: turns bunched into one sector give less inductance than calculated.
  3. If the real permeability of the core is unknown, measure it first with the separate calculator — that is more accurate than taking the datasheet figure.

© 2026 UR3PKI · CyberDev.Space · Content licensed under CC BY-NC-SA 4.0.

How to cite this calculator
UR3PKI. «Ferrite toroid coil calculator». CyberDev.Space. https://cyberdev.space/en/radio/calculators/coils/ferrite_toroid (licence CC BY-NC-SA 4.0).

The licence lets you use this material freely, including in teaching materials, but only with attribution to the author and a link to the source.

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