Calculator Inputs
Example Data Table
| Shape | Turns | Outer Diameter | Trace Width | Spacing | Frequency | Expected Use |
|---|---|---|---|---|---|---|
| Circular | 8 | 40 mm | 0.6 mm | 0.3 mm | 13.56 MHz | Wireless sensing coil |
| Square | 10 | 32 mm | 0.4 mm | 0.25 mm | 1 MHz | Printed board inductor |
| Octagonal | 6 | 25 mm | 0.5 mm | 0.2 mm | 100 kHz | Compact sensor winding |
Formula Used
L = μ0 × n² × davg × c1 / 2 × [ ln(c2 / ρ) + c3ρ + c4ρ² ]
In this formula, L is inductance in henries, μ0 is the permeability of free space, n is turns, davg is average diameter, and ρ is fill ratio. Shape coefficients change for circular, square, hexagonal, and octagonal spirals.
LµH = r² × n² / (8r + 11w)
Here, r is average radius in inches and w is radial winding width in inches. The calculator also estimates reactance with XL = 2πfL. It estimates quality factor with Q = XL / RAC.
How to Use This Calculator
- Select the spiral shape that best matches your layout.
- Choose the calculation method or compare both methods.
- Enter turns, outside diameter, trace width, and spacing.
- Use manual inner diameter when your layout already has a fixed opening.
- Enter conductor thickness, material, frequency, current, and temperature.
- Press the calculate button and review inductance, resistance, reactance, and quality factor.
- Download the result as CSV or PDF for design records.
Spiral Coil Design Guide
Why Spiral Coil Inductance Matters
A spiral coil packs useful inductance into a flat shape. It is common in sensors, wireless links, printed boards, and small power circuits. The design looks simple. Yet the result changes quickly when turns, spacing, outer size, and inner size change. This calculator helps you compare those changes before you draw the final layout.
Geometry Controls the Result
Planar spiral inductance depends mainly on average diameter, number of turns, and fill ratio. Average diameter represents the middle magnetic path. Fill ratio shows how much of the available area is occupied by winding. More turns usually raise inductance strongly, because the turn count is squared in the main formula. A larger outside size also raises inductance. Narrow spacing can increase turns, but it may raise resistance and parasitic capacitance.
Resistance and Frequency Matter
Inductance is only one part of coil behavior. At a chosen frequency, the coil creates inductive reactance. Higher frequency gives higher reactance. The conductor also has resistance. Thin traces and long paths increase that resistance. The quality factor compares reactance with resistance. A higher value often means a sharper and more efficient coil. Skin depth is included as a simple warning for high frequency work. When the conductor is much thicker than skin depth, alternating current may not use the full thickness.
Practical Design Notes
Use realistic dimensions from your layout tool. Keep all units consistent. Select a shape that matches your intended pattern. The modified Wheeler expression is useful for quick checks. The current sheet method is often better for integrated and printed spirals. Neither method includes every board effect. Nearby ground planes, shields, magnetic parts, solder mask, and components can shift the measured value. Temperature can also change loss, especially in copper traces. Wider conductors reduce loss, but they may reduce available turns. Check both choices together.
Accuracy Limits
Treat the answer as an engineering estimate. Build a margin into sensitive circuits. For radio, resonance, and precision sensing, measure a sample coil with the final stackup. Then adjust the design. This workflow saves board spins and reveals hidden losses early. Document each version carefully, so later tuning stays clear and repeatable.
FAQs
What is a spiral coil?
A spiral coil is a flat winding that turns inward or outward from a center point. It is often used on circuit boards, sensor plates, wireless power pads, and compact inductive links.
Which formula should I use?
Use the current sheet method for most printed spiral estimates. Use the Wheeler option for fast comparison. Compare both when you want to see how sensitive the layout is to formula choice.
Why does turn count affect inductance so much?
Turn count is squared in the main formula. Doubling turns can raise inductance strongly. It also increases length and resistance, so the best design balances inductance and loss.
What is fill ratio?
Fill ratio compares winding width with overall coil size. A higher fill ratio means the spiral uses more of the available area. It changes the magnetic path and affects inductance.
Does this calculator include parasitic capacitance?
No. It focuses on inductance, resistance, reactance, skin depth, and quality factor. High frequency designs should also check parasitic capacitance and self-resonant frequency separately.
Why is AC resistance higher than DC resistance?
At higher frequency, current crowds near conductor surfaces. This is called skin effect. The calculator uses a simple skin depth estimate to show possible resistance increase.
Can I use this for PCB coils?
Yes. Enter board trace width, spacing, copper thickness, and outside size. For final products, measure a sample because board stackup and nearby copper can shift results.
Why should I measure the finished coil?
Real coils include solder mask, nearby planes, component bodies, tolerance, and layout effects. Measurement confirms the final value and helps tune precision or radio circuits.