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Toroid and coil calculator

Choose a core and either the inductance you want or the turns you've wound. You get the other one, the wire length to cut and how many turns fit. Below that are an air-core coil calculator and an LC resonance calculator.

Toroid

–
0.56 mm is 24 SWG / 23 AWG
Turns––
Wire to cut–Including 5 cm for each lead
Fits in one layer––
Reactance––

Air-core coil

Centre of the wire to centre
Inductance–Wheeler's formula
Turns for target–Same diameter and length
Wire needed–Plus leads

LC resonance and reactance

Fill in any two of the three. The empty one is calculated, or with all three filled, the one you changed least recently.

Result––
Inductive reactance–XL = 2πfL
Capacitive reactance–XC = 1 ÷ 2πfC

Core data

CoreMaterialALOD × ID × H (mm)Turns for 1 µHBest for

Turns on a toroid

A toroid's inductance rises with the square of the number of turns, scaled by the core's AL value. Amidon quotes AL in two different units, which catches a lot of people out:

Iron powder (T cores): L (µH) = AL × N² ÷ 10,000 (AL in µH per 100 turns)
Ferrite (FT cores): L (µH) = AL × N² ÷ 1,000 (AL in mH per 1,000 turns)

On a toroid, every pass of the wire through the centre hole counts as one turn. A wire passed through once and back out is one turn, not two. AL values have a tolerance of around ±10% for iron powder and ±25% for ferrite, so measure the finished coil and add or remove a turn if needed. Spreading the turns out lowers the inductance slightly, and squeezing them together raises it.

Iron powder or ferrite?

Iron powder cores (T-50-2, T-68-6 and so on) are stable and low-loss, with a high Q, so they're used for tuned circuits, filters and traps. Mix 2 (red) suits 1 to 30 MHz and mix 6 (yellow) 2 to 50 MHz. Mix 10 (black) goes higher, and mix 1 (blue) lower.

Ferrite cores (FT-37-43 and so on) have a much higher AL, so you need fewer turns. They're lossy, which makes them ideal for chokes, baluns and broadband transformers but poor for tuned circuits. Mix 43 is the HF workhorse for chokes and ununs, and mix 61 is lower loss and suits transformers from about 10 to 200 MHz.

Air-core coils

For a single-layer air-core coil, Wheeler's formula is accurate to within about 1% when the coil is longer than about 0.4 times its diameter:

L (µH) = r² N² ÷ (9r + 10ℓ) with r and ℓ in inches
L (µH) = d² N² ÷ (18d + 40ℓ) with d and ℓ in inches

The calculator converts from millimetres for you. Measure the diameter from the centre of the wire on one side to the centre on the other.

LC resonance

An inductor and capacitor resonate where their reactances are equal:

f = 1 ÷ (2π √(LC))

That's the basis of every trap, tuned circuit and filter. A trap for a trap dipole is a parallel LC circuit that resonates on the higher band.

Questions

How many turns on a T-50-2 for 1 µH?

About 14 turns, since a T-50-2 has an AL of 49 µH per 100 turns. 20 turns gives about 2 µH.

What's the difference between T and FT cores?

T cores are iron powder, which is stable and low-loss for tuned circuits. FT cores are ferrite, which has a much higher permeability and suits chokes and broadband transformers.

Does each pass through the toroid count as a turn?

Yes. Every time the wire passes through the centre hole counts as one turn.

What colour is a mix 2 toroid?

Red. Mix 6 is yellow, mix 1 blue, mix 10 black and mix 7 white. Ferrite cores are usually uncoated grey.