Calculator
Example Data Table
| Method | Turns | Main size | Length | Depth or height | µr | Example result |
|---|---|---|---|---|---|---|
| Long solenoid | 100 | 20 mm radius | 50 mm | Not used | 1 | About 0.316 mH |
| Wheeler single layer | 20 | 10 mm radius | 30 mm | Not used | 1 | About 4.04 µH |
| Toroid | 50 | 25 mm mean radius | Not used | 8 mm by 10 mm core | 100 | About 0.160 mH |
Formula Used
Long solenoid: L = µ0µrN²A / l, where A = πr².
Wheeler single layer: L(µH) = r²N² / (9r + 10l), where r and l are in inches.
Wheeler multilayer: L(µH) = 0.8r²N² / (6r + 9l + 10d), where r, l, and d are in inches.
Toroid: L = µ0µrN²A / (2πr), where A is core section area and r is mean radius.
Extra electrical values: XL = 2πfL, E = 0.5LI², τ = L/R, and Q = XL divided by wire resistance.
How to Use This Calculator
- Select the coil method that matches your winding shape.
- Enter turns, radius or diameter, and the needed dimensions.
- Use effective relative permeability for the real core material.
- Add frequency and current to estimate reactance and energy.
- Choose wire gauge and material for resistance and Q estimates.
- Press Calculate, then download CSV or PDF when needed.
Article
Understanding Coil Inductance
Coil inductance shows how strongly a winding stores magnetic energy. A higher value means the coil resists rapid current change. This calculator supports long solenoids, Wheeler air coils, multilayer coils, and toroids. It also estimates wire length, copper loss, reactance, Q factor, and stored energy.
Why Geometry Matters
Inductance depends on turns, radius, length, winding depth, and core material. Turns have a square effect. Doubling turns can raise inductance by four times, when geometry stays fixed. Radius increases magnetic area. Longer coils usually lower inductance because the magnetic path spreads out. A toroid keeps flux inside a closed core, so leakage is often lower.
Core And Wire Choices
The relative permeability field represents the effective magnetic gain of the core. Air is close to one. Ferrite and iron powder can be much higher, but real values change with frequency, flux level, and bias current. Wire resistance matters too. Thin wire raises resistance and heat. Thick wire lowers loss, but it uses more winding space.
Practical Design Notes
Use the solenoid method for coils that are longer than their diameter. Use Wheeler single layer for short air coils. Use Wheeler multilayer when the winding has noticeable radial depth. Use the toroid option for closed ring cores with a rectangular cross section. Add a correction factor when test data or a data sheet suggests one.
Result Interpretation
The calculated inductance is an engineering estimate. Construction details can move the real value. Spacing, insulation, lead length, nearby metal, and winding tension all affect the final coil. At high frequency, parasitic capacitance also becomes important. Measure the finished coil when precision matters.
Electrical Performance
The reactance value shows opposition at the chosen frequency. The time constant shows current rise speed through an external resistance. Stored energy helps check switching circuits, relays, filters, chokes, and resonant designs. Compare results against current rating, temperature rise, and core saturation limits before building.
For better builds, keep leads short and stable. Wind turns evenly. Avoid sharp bends that damage enamel. Record every dimension before testing. Then compare the measured value with the estimate. This habit improves future designs and makes troubleshooting faster. It also helps you choose better cores and wire gauges. With less rework.
FAQs
What is coil inductance?
Coil inductance is the ability of a winding to store magnetic energy and oppose current changes. It is measured in henries. Most small coils are shown in millihenries or microhenries.
Which method should I select?
Use solenoid for long cylindrical coils. Use Wheeler single layer for compact air coils. Use Wheeler multilayer for thick windings. Use toroid for ring cores with a closed magnetic path.
What is effective relative permeability?
It is the practical magnetic gain of the core inside your coil. Air is about 1. Real ferrite or iron powder values depend on material, gap, bias, and frequency.
Why does turn count matter so much?
Turn count is squared in the main inductance formulas. This means small turn changes can strongly change inductance, especially when the coil shape stays the same.
Does wire gauge affect inductance?
Wire gauge mainly affects resistance, heat, and winding space. It can slightly change geometry when wire thickness changes the finished coil size or winding depth.
Can this replace a real LCR meter?
No. It gives a design estimate. Real coils include parasitic capacitance, uneven spacing, lead effects, nearby metal, and core behavior. Measure the built coil for precision.
What does Q factor mean here?
Q factor compares inductive reactance with wire resistance at the entered frequency. Higher Q usually means lower loss, but core loss and skin effect are not fully modeled.
Why include a correction factor?
The correction factor lets you tune results from test data, datasheets, magnetic gaps, winding spacing, or empirical adjustments. Keep it at 1 when no correction is known.