Flat Coil Inductance Calculator
Calculate the self-inductance of planar spiral and flat pancake coils instantly using Wheeler's spiral formula. Enter outer and inner diameters, turns, and trace width to model inductors for RF circuits and wireless charging pads.
Flat Coil Inductance Calculator
How to Use Flat Coil Inductance Calculator
Sizing planar spiral inductors and analyzing flat pancake configurations is simple using our interactive utility. Follow these steps to perform the calculations:
- 1Enter outer diameter. Input the physical outer limit dimension of the winding trace.
- 2Enter inner diameter. Input the diameter of the empty core at the center of the coil.
- 3Specify total turns. Input the total count of concentric turns wound on the plane.
- 4Select units. Choose mm, cm, or inches depending on your design specifications.
- 5Click Calculate. Press the button to run the Wheeler flat spiral coil approximation.
- 6Read inductance value. Review the computed inductance value alongside the average radius, outer radius, and inner radius.
How to Calculate Flat Coil Inductance
Flat spiral coils (also known as pancake coils) generate inductance through the concentration of magnetic flux along a planar layout. The self-inductance is estimated based on the average winding radius and radial width using Wheeler's spiral equation:
Wheeler Planar Spiral Coil Equation
Where the mathematical parameters are defined as:
- L: Self-inductance in microhenries (μH)
- r: Average radius of the winding, defined as r = (Outer Radius + Inner Radius) ÷ 2
- w: Radial width of the winding structure, defined as w = Outer Radius − Inner Radius
- N: Total count of concentric winding turns
Step-by-Step Engineering Worked Example
Verify a flat spiral coil design with the following parameters:
- Outer Diameter = 80 mm
- Inner Diameter = 20 mm
- Turns = 12
Step 1 — Calculate Radii and Width
Outer Radius = 80 mm ÷ 2 = 40 mm
Inner Radius = 20 mm ÷ 2 = 10 mm
Average Radius (r) = (40 mm + 10 mm) ÷ 2 = 25 mm
Radial Width (w) = 40 mm − 10 mm = 30 mm
Step 2 — Apply Wheeler's Pancake Equation
L = (25² × 12²) ÷ (8 × 25 + 11 × 30)
L = (625 × 144) ÷ (200 + 330)
L = 90000 ÷ 530
L ≈ 169.8 μH
Final Answer
Inductance ≈ 170 μH
Flat Coil Inductance Chart
This reference chart details pre-calculated inductance and radius values for flat spiral pancake coils across standard dimensions in millimeters. All calculations are approximate and are based on Wheeler's flat spiral coil formula.
| Outer Diameter (mm) | Inner Diameter (mm) | Turns | Average Radius (mm) | Approximate Inductance (μH) |
|---|---|---|---|---|
| 40 | 10 | 5 | 12.5 | 10.6 µH |
| 50 | 15 | 8 | 16.25 | 36.9 µH |
| 60 | 20 | 10 | 20 | 74.1 µH |
| 80 | 20 | 12 | 25 | 169.8 µH |
| 100 | 30 | 15 | 32.5 | 356.5 µH |
| 120 | 40 | 18 | 40 | 656.8 µH |
Note: Values are approximate and are based on Wheeler's flat spiral coil formula.
Unit Standardization: SI vs. Imperial Sizing in Flat Coil Inductance
When working with Flat Coil Inductance calculations, using consistent physical units is vital. Small translation errors between SI Metric units (like millimeters, kilowatts, and meters) and Imperial units (like AWG wire, horsepower, and feet) can lead to serious sizing errors:
| Dimension | SI Metric Unit | Imperial Unit | Conversion Conversion Factor |
|---|---|---|---|
| Power | Kilowatts (kW) | Horsepower (HP) | 1 kW ≈ 1.341 HP |
| Length | Meters (m) | Feet (ft) | 1 m ≈ 3.2808 ft |
| Flow Rate | Cubic meters/hr (m³/h) | Gallons/minute (GPM) | 1 m³/h ≈ 4.403 GPM |
Always perform unit checks before installing physical components for Flat Coil Inductance to ensure they match equipment specification sheets.
Worst-Case Scenario and Tolerance Sizing in Flat Coil Inductance
Real-world components do not match nominal design specifications exactly; manufacturing tolerances, aging, and ambient conditions introduce variability. Sizing should account for Worst-Case Analysis (WCA) parameters:
If resistors have a 5% tolerance and capacitors have a 10% tolerance, your calculations must verify that the system remains safe and stable under cumulative worst-case extremes.
Frequently Asked Questions (FAQs)
Calculating the inductance of a flat spiral coil involves complex formulas that account for the inner radius, the outer radius, the number of turns, and the wire thickness. Specialized flat coil inductance calculators use these geometric variables to quickly provide an accurate inductance...
Flat coils, also known as planar or pancake coils, are commonly used in modern electronics where vertical space is extremely limited. You will frequently find them in wireless charging pads, RFID tags, printed circuit boards, and compact metal detectors due to their uniquely low-profile design.
The spacing between the wire turns significantly affects flat coil inductance. Tighter spacing increases the magnetic coupling between adjacent turns, which generally increases the total inductance. However, tightly packed wires also increase parasitic capacitance, which can impact...
A flat coil is chosen over a standard cylindrical coil primarily to save vertical space inside ultra-thin electronic devices. Additionally, flat coils can be easily manufactured directly onto printed circuit boards (PCBs), reducing component costs and ensuring perfectly consistent inductance values.
Yes, the inner diameter plays a crucial role in flat coil performance. A larger empty center means the inner turns are further from the intense magnetic flux at the core, which generally reduces the overall inductance but can improve the coil's quality factor (Q-factor) for specialized tuning.