If you’ve ever worked on electronics projects—whether building a DIY guitar pedal, a custom audio amplifier, or a renewable energy system—you’ve probably come across air core inductors. These simple, air-wound coils are workhorses in high-frequency circuits, filtering noise, tuning radio signals, and storing energy in switching power supplies. As a supplier who’s spent years talking to engineers, hobbyists, and product designers, one question comes up again and again: “How do I calculate the right inductance for my project?” Air Core Inductor
It’s not a trivial task. Too little inductance, and your circuit will underperform; too much, and you’ll waste space, money, and power. The good news is that the formula for air core inductance is well-established, and with a few key measurements, you can get an accurate estimate without fancy lab equipment. In this post, I’ll break down everything you need to know, from the basic formula to the small tweaks that make a big difference in real-world applications.
First, let’s start with the basics: what is inductance, anyway? Inductance is a coil’s ability to store energy in a magnetic field when current flows through it. For air core inductors, there’s no ferromagnetic core to boost that field—meaning the inductance depends entirely on the coil’s shape, size, number of turns, and the material of the wire. That’s different from iron core inductors, where the core’s magnetic properties are the biggest factor, but it also makes air core inductors more predictable, which is why they’re so popular for precision applications.
The most widely used formula for a single-layer air core inductor comes from the work of Harold A. Wheeler, a prolific engineer who specialized in radio-frequency components. His 1928 Wheeler’s Formula for single-layer coils remains the industry standard today, trusted by designers and manufacturers alike. The simplified version for inductance (in microhenries, or μH) is:
L = ( (N² × d²) / (18 × d + 40 × l) )
Let’s define each variable to make sure we’re all on the same page:
- L is the inductance, in microhenries (μH)
- N is the total number of turns of wire in the coil
- d is the diameter of the coil, measured in inches, from one side of the coil’s winding to the other (not the wire’s diameter, the whole coil)
- l is the length of the coil, also in inches, measured along the axis of the coil (from the first turn to the last turn, not counting wire insulation length)
Wait, I know what some of you are thinking—metric units? Most of the world uses centimeters or millimeters, and it’s annoying to convert. There’s a metric version of Wheeler’s Formula that’s just as easy to use, especially if you’re working with smaller coils:
L = ( (N² × d²) / (22 × d + 30 × l) )
Here, d and l are in centimeters, and L is still in microhenries. I’ve used both formulas for decades, and the key is to make sure your units are consistent—mixing inches and centimeters will give you a wildly wrong number.
Let’s test this with a real example to see how it works. Suppose you’re building a radio tuner and need a 5 μH single-layer air core inductor. Let’s pick a coil diameter of 1 inch (that’s a common size for small RF coils) and a coil length of 0.5 inches. We can rearrange the formula to solve for N, instead of L:
Rearranged Wheeler’s Formula (for N):
N = sqrt( L × (18d + 40l) / d² )
Plug in the numbers: L = 5 μH, d = 1 in, l = 0.5 in.
N = sqrt( 5 × (18×1 + 40×0.5) / (1²) )
N = sqrt(5 × (18 + 20) ) = sqrt(5 × 38) = sqrt(190) ≈ 13.78 turns.
That means you’d need about 14 turns of wire, right? In practice, you’d adjust slightly to get exactly 5 μH, but that’s a great starting point.
Now, let’s talk about common mistakes that throw off your calculation. First, measuring the wrong diameter. A lot of folks measure the diameter of the wire, not the entire coil. That’s a huge error—if your wire is 0.01 inches thick, but your coil is wound around a 1-inch form, the actual coil diameter is 1 inch, not 1.01 inches. Another common mistake is counting the length wrong. If your coil has 14 turns spaced evenly, and each turn is 0.035 inches apart, your total length is 14 × 0.035 = 0.49 inches, which is almost exactly the 0.5 inches we used earlier. Skip that, and you’ll end up with an inductor that’s shorter or longer than you planned.
What if your inductor isn’t single-layer? A lot of air core inductors are multi-layer, for higher inductance in a smaller footprint. The formula gets a bit more complex there—Wheeler also developed a formula for multi-layer coils, which accounts for the number of layers, the spacing between layers, and the coil’s dimensions. The multi-layer formula (still in μH, inches) is:
L = ( (N² × d²) / (18d + 40l) ) × ( (a + 1) / (9a + 10b) )
Where:
- a is the ratio of the coil’s width to its diameter (width is the distance between the first and last layer, divided by two)
- b is the ratio of the total length of the coil (l) to the diameter (d)
This formula is a great middle ground for hobbyists who use multi-layer coils, but if you’re designing for commercial applications, you’ll want to work with a supplier who can run more precise calculations, because small variations in layer spacing can add up.
Another factor that’s easy to overlook: wire type. The formula we use assumes solid, round copper wire, which is the standard for most air core inductors. If you’re using stranded wire, wire with insulation that’s very thick, or even flat wire, you’ll need to adjust the calculation. Stranded wire has a slightly lower inductance than solid wire of the same gauge, because the strands are spaced apart, which reduces the magnetic field strength. Flat wire, on the other hand, can have higher inductance because it packs more turns into the same space, as long as you’re winding it tightly without gaps.
Also, the core material (even though it’s air!) matters a little. Wait, air is air, right? Mostly, but the humidity and even the temperature can have a tiny effect on permeability. Most of the time, that effect is negligible—less than 1% change in inductance for most applications—but if you’re building a high-precision circuit, like a test instrument or a satellite component, you might want to account for temperature coefficients. At our company, we test every inductor we ship to make sure it meets your specified inductance within ±1% tolerance, so you don’t have to worry about that.
Let’s talk about when to trust the formula, and when to measure. The formula is a great starting point, but there’s no substitute for measuring the actual inductance once you wind the coil. You don’t need a fancy LCR meter—though they’re great to have—even a digital multimeter with an inductance setting will work for most hobbyist projects. For commercial applications, we always test each batch of inductors with a precision LCR meter to ensure accuracy, because even a small difference in winding tension, wire gauge, or turn count can shift the inductance by a few percent.
I’ve seen too many customers wind their own coils using the formula, only to find that their hand-wound inductor is off by 5% or more. Why? Because when you wind by hand, it’s hard to get evenly spaced turns, or to keep the wire tight enough that the coil length matches your calculation. That’s where working with a supplier comes in. We use automated winding machines that can space turns to within 0.001 inches, ensuring consistency across every inductor we make.
Now, let’s cover a few use cases to put this all together. If you’re building a wireless charger, you’ll need an air core inductor that operates at high frequency (100 kHz or higher), so the formula will work as long as you account for skin effect—another factor that affects inductance at high frequencies. Skin effect is when AC current flows only on the surface of the wire, so you might need a thicker wire or Litz wire (stranded wire designed to reduce skin effect) for high-frequency applications. For audio crossover networks, you’ll need a higher inductance, usually with thicker wire to handle higher currents, and the formula still applies, though you’ll want to use a single-layer coil to avoid parasitic capacitance.
What about shielding? Air core inductors don’t have a core, so they don’t have the same magnetic interference issues as iron core inductors, but if you’re placing them near other components, their magnetic field can affect nearby circuits. For that, you can add a shielding can around the inductor, though that will slightly reduce the inductance—you’ll want to adjust your calculation to account for that, or simply test the final product once it’s shielded.
I know this can feel overwhelming if you’re new to working with inductors, and that’s why our team is here to help. We’ve supported everyone from student engineers building a capstone project to Fortune 500 companies designing commercial electronics, and we can help you calculate the right inductance for your specific needs. Whether you need a single custom inductor for a prototype or 10,000 units for a production run, we can work with you to get the dimensions, turn count, and inductance exactly right.
If you’re still working through the numbers, or if you have questions about how a change in wire gauge or coil size will affect your inductance, don’t hesitate to reach out. We’re always happy to walk through the calculation with you, suggest materials that work for your application, and make sure you get the right product on time.
Low-voltage Transformer References
- Wheeler, H. A. (1928). Simple Inductance Formulas for Radio Coils. Proceedings of the IRE, 16(10), 1398-1400.
- Terman, F. E. (1943). Radio Engineers’ Handbook. McGraw-Hill Book Company.
- El-Deeb, A. Z., & El-Hawary, M. E. (1994). Inductance Calculation of Multi-Layer Air-Core Inductors. IEEE Transactions on Power Electronics, 9(3), 307-312.
- Frequency Effects in Wire for Inductors (2007). Coilcraft Application Note AN07.
Dongguan Hensiron Electric Co., Ltd.
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E-mail: jessica@dghensiron.com
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