# Calculate the number of turns in air core inductor

Coil specification:

• Air core coil
• Length 790 mm
• Diameter 290 mm
• Wire guage 18 - 1 mm diameter

I need the number of turns to get an inductance of 150 mH.

While searching for calculating the number of turns, I found a lot of different formulas.

I know that we can calculate the inductance with the formula

$$L = \frac{\mu_0 N^2 A}{d}.$$

If I use it to get the number of turns, it gives 4 turns only.

I am also confused how this formula can calculate the inductance and not the turns.

• Is it Tesla coil? Change AWG for single layer @Dave Tweed suggestion. Weight 8 kg wire. Commented Aug 9, 2022 at 14:54
• It is multilayer for solenoid coil
– Tito
Commented Aug 9, 2022 at 14:57
• What frequency range is this operating at? Commented Aug 9, 2022 at 16:04
• Main power Ac 220v - 50 hz
– Tito
Commented Aug 9, 2022 at 18:22
• If the ratios of your dimensions are not fixed, then length = 81% of diameter gives you maximum inductance for a given length of wire in a single layer solenoid. Commented Aug 9, 2022 at 18:49

Air core coil

Length 790mm

Diameter 290mm

Let me mention that air's magnetic permeability ($$\\mu_0\$$) is $$\4\pi\times 10^{-7} \frac{H}{m}\$$ and not unity.

Let's also start with the correct formula (and not what you wrote in the question): -

$$L = \dfrac{\mu_0\cdot N^2\cdot A}{\ell}$$

Where $$\l\$$ is the length of the solenoid. The enclosed area of a round solenoid is $$\A = \pi d^2 / 4\$$ for diameter $$\d\$$.

So, rearrange the formula to get: -

$$N = \sqrt{\dfrac{0.15\text{ H} \times 0.79\text{ m}}{4\pi\times 10^{-7} \frac{H}{m} \times 0.06605\text{ m}^2}} = 1195 \text{ turns}$$

Calculator double check: -

When I enter 1 for relative permeability the calculator inherently knows about $$\4\pi\times 10^{-7} \frac{H}{m}\$$.

I also confused how this formula can calculate the inductance and not the turns

It can calculate turns but you need to factor-in the correct value for the permeability of free-space. Good luck winding 1145 turns along a distance of 790 mm; I'd be considering a two-layer winding.

• For a single layer, he'll have to switch to AWG 22 wire. It will require about 1.1 km of wire, with a resistance of 56 ohms. Commented Aug 9, 2022 at 14:52
• It is multilayer coil for solenoid
– Tito
Commented Aug 9, 2022 at 15:14
• @Tito yes, that is what I suggested. Please take the 2 minute tour to understand why folk give their help for free. I'm saying this because you haven't previously formally selected any answers to your questions. I'm sure this is an oversight of course so, now is the time to remedy this. Any answers that need clarification just raise a new comment. Commented Aug 9, 2022 at 15:17
• @tito your question says Diameter 290mm and that is 29 cm. Commented Aug 9, 2022 at 15:18
• The errors you will get will be mainly due to the outer layer not fully coupling to the inner layer. You might need more like 5000 turns but that is just a broad estimate on my part. When layers don't couple properly the $N^2$ factor becomes more like $N^{1.5}$ for instance. Commented Aug 9, 2022 at 15:39