Calculator
Example Data Table
| Geometry | Turns | Outer Diameter | Inner Diameter | Method | Estimated Inductance | Typical Use |
|---|---|---|---|---|---|---|
| Circular | 5 | 50 mm | 10 mm | Classic Wheeler | About 0.65 µH | RF tank circuit |
| Square | 6 | 40 mm | 8 mm | Shape coefficient | About 1.20 µH | PCB spiral inductor |
| Octagonal | 4 | 25 mm | 5 mm | Shape coefficient | About 0.32 µH | Compact matching network |
Formula Used
The classic Wheeler flat spiral equation is:
L = N²r² / (8r + 11w).
In this equation, L is inductance in microhenries.
N is the number of turns.
r is the average radius in inches.
w is the radial winding depth in inches.
The average radius is found from the outer and inner diameters.
The radial winding depth is half of the outer diameter minus the inner diameter.
The calculator also includes a shape coefficient mode:
L = K1µ0N²davg / (1 + K2ρ).
This helps estimate circular, square, hexagonal, and octagonal layouts.
Resistance uses R = ρl / A.
Reactance uses XL = 2πfL.
Q factor uses Q = XL / Rac.
Self resonance uses f = 1 / (2π√LC).
How to Use This Calculator
- Select the spiral geometry that best matches your design.
- Choose the formula method. Use classic mode for round coils.
- Enter turns, outer diameter, and inner diameter.
- Add conductor width, spacing, and thickness.
- Select the material and operating frequency.
- Enter current and parasitic capacitance if known.
- Press the submit button to view results above the form.
- Use the CSV or PDF button to save the calculation.
Understanding Wheeler Spiral Coil Design
Why Spiral Coils Matter
A flat spiral coil is useful when space is limited. It can be etched on a board. It can also be wound from wire or copper strip. Designers use it in RF filters, wireless power pads, sensors, matching networks, and resonant circuits. The main goal is simple. You need enough inductance without wasting area. You also need low resistance and stable behavior at frequency.
What Wheeler Helps Estimate
Wheeler formulas give a fast inductance estimate. They are popular because they use easy dimensions. Turns, average radius, and winding depth drive the answer. More turns increase inductance strongly. A larger diameter also increases inductance. A wider winding depth can reduce the gain from added turns. This is why compact coils need careful balance.
Important Design Factors
Inductance is only one part of the design. The conductor has resistance. That resistance creates heat and reduces Q. At higher frequency, skin effect increases effective resistance. The coil also has stray capacitance. When inductance and stray capacitance resonate, the coil reaches self resonance. Above that point, the coil may stop behaving like a clean inductor.
Practical Layout Advice
Keep spacing consistent between turns. Use wider copper when current is high. Use thicker copper when loss must stay low. Avoid very high fill ratios when accuracy matters. Leave room for terminals and mounting. Keep nearby metal away from sensitive RF coils. After building the coil, measure it with an LCR meter. Real layouts include pads, solder, dielectric effects, and nearby parts. Measurement gives the final answer.
Using Results Safely
Treat this calculator as a design guide. It is best for early sizing and comparison. Use the output to compare turns, diameters, spacing, and materials. Then prototype the best option. Small changes can shift inductance and Q. A measured coil is always the strongest reference.
FAQs
What is Wheeler formula used for?
It estimates inductance for air core coils and flat spiral coils. It is useful during early design when exact measurement is not available.
Does this calculator work for PCB spiral inductors?
Yes. Enter the board trace width, spacing, thickness, and diameters. Use shape coefficient mode for square, hexagonal, or octagonal PCB spirals.
Which unit should I use?
You can use millimeters, centimeters, or inches. The calculator converts values internally, so choose the unit that matches your drawing.
Why does resistance matter?
Resistance causes voltage drop, heat, and lower Q factor. A low resistance coil usually performs better in resonant and RF circuits.
What is fill ratio?
Fill ratio compares winding depth with average diameter. Very high values may reduce formula accuracy and make the coil harder to build.
What is self resonant frequency?
It is the frequency where coil inductance resonates with stray capacitance. Near this point, the coil may not behave like a normal inductor.
Why is the Q factor estimated?
Q depends on AC resistance, skin effect, layout, material, and nearby objects. This tool gives a practical estimate, not a lab measurement.
Should I measure the finished coil?
Yes. Formula results are estimates. Measure the final coil with suitable test equipment, especially for RF, power, or precision circuits.