Toroid Inductor Turns Calculator (AL Value)
Toroid Inductor Turns Calculator (AL Value)
Turns for a target inductance on a ring core from its Aₗ value, both directions, with the flux-density check that decides whether the design works at your peak current, the Aₗ tolerance band the core is really built to, and whether the wire fits the window.
Turns on a ring core
a 1,000 µH choke on a ring core with Aₗ 2,350 nH/turn² ±25%, Aₑ 48.9 mm², Bₛₐₜ 320 mT, 0.25 A peak, 14 mm hole, 22 AWG
Aₗ, turns and flux
- AL
- inductance factor, nH per turn squared (= mH per 1000 turns); a property of the core
- Ae
- effective cross-sectional area of the core, in m²
- Bpk
- peak flux density; it comes from the flux linkage L·I = N·B·Aₑ, so it needs no permeability
- Ipk
- peak current, not RMS and not average
Worked example
a 1,000 µH choke on a ring core with Aₗ 2,350 nH/turn² ±25%, Aₑ 48.9 mm², Bₛₐₜ 320 mT, 0.25 A peak, 14 mm hole, 22 AWG
N = √(L ÷ Aₗ) = √(1,000 µH ÷ 2,350 nH) = 20.628 turns, so wind 21
21² × 2,350 nH = 1.036 mH, which is the inductance those whole turns actually give
The ±25% Aₗ tolerance puts the wound part anywhere between 777 µH and 1.3 mH
B = L·I ÷ (N·Aₑ) = 1.036 mH × 0.25 A ÷ (21 × 48.9 mm²) = 252.3 mT, 78.8% of Bₛₐₜ — it would saturate at 317 mA peak
22 AWG is 0.644 mm, so 65 turns fit in one layer round the hole and the 21 turns fill 4.4% of it; 35.4 mm per turn is 0.743 m of wire and 39.3 mΩ
How tightly the Aₗ of a core is actually held
| Core type | Typical Aₗ tolerance | Why |
|---|---|---|
| Ungapped ferrite ring (power and EMI grades) | ±20% to ±30% | Aₗ follows the ferrite’s own permeability, which is a property of the fired batch. Fair-Rite publishes ±25% on most of its toroids, and +25/−30% or ±30% on the highest-permeability grades. |
| Gapped ferrite (ground centre leg or ring) | ±3% to ±10% | The gap’s reluctance dominates, and the gap is a machined dimension. Magnetics grinds gapped cores to ±3% for a gap-to-gap pair. |
| Iron powder, RF grades | ±5% | The distributed gap in the binder sets the permeability, so it is far more repeatable than ferrite (Micrometals). |
| Iron powder, power-conversion grades | ±10% | Same mechanism, looser grading (Micrometals). |
Winding a ring core to an inductance
A ring core is sold with an Aₗ value: the inductance one turn would give, in nanohenries. Because inductance goes with the square of the turns, L = Aₗ × N² and N = √(L ÷ Aₗ). Aₗ is sometimes printed as millihenries per 1000 turns, which is the same number — 2350 nH/turn² is 2350 mH/1000 turns. That is the whole of the easy part, and it is where most calculators stop.
The flux check is what decides whether the design works. Every turn you add raises the inductance by the square, but the flux density at a given peak current only falls in proportion to the turns: B = L·I ÷ (N·Aₑ), which is just the flux linkage L·I = N·B·Aₑ rearranged, so it needs no permeability and no reluctance. If B reaches the core’s saturation flux density the inductance collapses, the current stops being limited by the inductor and the switch sees the full short-circuit di/dt. Read Bₛₐₜ at the temperature you will actually run: power ferrite is around 500 mT at 25 °C and 320–390 mT at 100 °C, so a design checked cold can saturate hot. Use the PEAK current, including ripple — the average tells you nothing about saturation.
Ferrite or iron powder. Ferrite has a high permeability, so you need few turns and the copper loss is low, but it saturates sharply at a few hundred millitesla and its Aₗ is held only to about ±25% because Aₗ follows the permeability of the fired batch. Iron powder has a distributed gap: its permeability is an order of magnitude lower, so it wants many more turns for the same inductance, but it saturates gradually rather than suddenly, tolerates DC bias far better, and is graded to ±5% or ±10%. Its core loss at high frequency is much worse, and some grades age thermally. In one sentence: ferrite for switching transformers and EMI chokes, iron powder for DC-biased power inductors where a soft roll-off is safer than a cliff. A gapped ferrite gets you both the tight tolerance and the bias handling, at the cost of turns and of fringing flux near the gap.
Getting the winding on. The hole has to take the wire twice — once going in, once coming back — and the turns crowd on the inside diameter, so the first layer runs out at roughly π(ID − d) ÷ d turns. Past about 40% window fill a toroid is hard to wind by hand and later turns start riding on earlier ones, which lengthens the mean turn and raises both resistance and self-capacitance. The wire figures here use the same ASTM B258 diameter law and the same 17.241 Ω·mm²/km copper constant as the AWG wire size calculator. For a switching transformer rather than a single winding, the SMPS transformer calculator sizes the core by area product instead, and for a coil with no core at all see the air-core inductor calculator.
Frequently asked questions
How do I work out the turns on a toroid?
N = √(L ÷ Aₗ), with Aₗ in nanohenries per turn squared from the core datasheet. 1000 µH on a core with Aₗ = 2350 nH needs √425.5 = 20.63, so wind 21 turns — which gives 1.036 mH, not 1.000 mH.
What is the AL value of a core?
The inductance one turn on that core would produce, in nH. It bundles the core’s permeability, area and magnetic path length into one number, so you never need any of them separately to get the turns.
How do I know if the core will saturate?
B = L × Iₚₖ ÷ (N × Aₑ). Compare it with the datasheet Bₛₐₜ at your operating temperature. Above it the inductance disappears and the current is limited only by the winding resistance.
Why is my wound inductor’s value wrong?
Almost always the Aₗ tolerance. An ungapped ferrite ring is commonly ±25%, so a 21-turn winding calculated for 1.036 mH can legitimately measure anywhere from 777 µH to 1.30 mH. Gapped cores hold ±3–±10% and iron powder ±5–±10%.
Ferrite or iron powder for a power inductor?
Iron powder if the inductor carries DC bias and you want a gentle roll-off instead of a cliff; ferrite if the frequency is high and core loss matters more than bias handling. Ferrite needs far fewer turns for the same inductance.
Related calculators
References
- Ferroxcube. TN25/15/10 ferrite toroid data sheet, September 2008. Aₑ 48.9 mm², lₑ 60.2 mm, Aₗ 2350 nH ±25% in 3C90; 3C90 B ≥ 320 mT at 250 A/m, 25 kHz, 100 °C — the worked example’s core.
- Fair-Rite Products. Toroid product listings, fair-rite.com. Published Aₗ tolerances by material: ±25% on grades 52, 61, 77, 78 and 80, ±20% to +20/−25% on 43, +25/−30% on 75 and ±30% on 76.
- Micrometals. Product Tolerance Guide. Aₗ held to ±5% on RF materials and ±10% on power-conversion materials for iron powder cores.
- Magnetics (Spang). Ferrite Cores catalogue, 2022. Aₗ defined as mH per 1000 turns or nH/T²; gapped cores ground to ±3% for a gap-to-gap pair and ±3% to ±10% for ungapped-to-gapped combinations.
- McLyman CWT. Transformer and Inductor Design Handbook, 4th ed. CRC Press, 2011. Window utilisation, mean length of turn and the flux-linkage form of the flux-density check.