Circular Coil Inductance Calculator
Calculate the inductance of circular air-core coils quickly. Enter turns, coil radius, and length to get instant estimations based on Wheeler's empirical coil equations.
Circular Coil Inductance Calculator
How to Use Circular Coil Inductance Calculator
Determining the properties of a single-layer air-core circular coil is essential when designing tuning networks, filters, or antennas. Follow these practical steps to calculate the inductance of your coil:
- 1Enter the number of turns. Input the total count of wire turns (N) on the single-layer circular coil as a positive integer.
- 2Enter the coil radius. Input the physical radius (r), measuring from the coil's center axis to the middle of the winding wire.
- 3Select the appropriate units for the radius. Use the unit dropdown to choose mm, cm, or inches.
- 4Enter the coil length. Input the physical length of the coil (l) from the first turn to the last turn.
- 5Select the corresponding units for the length. Choose mm, cm, or inches from the dropdown menu.
- 6Click the Calculate button. Press Calculate to compute the inductance. The results will display in microhenries (µH) and millihenries (mH), alongside the radius and length values used in the calculation.
How to Calculate Circular Coil Inductance
Solenoids and circular air-core coils produce magnetic flux when current flows through them. The physical dimensions and the turn count define the total inductance. The standard Wheeler formula provides a highly accurate approximation for single-layer air-core circular coils:
Wheeler Single-Layer Circular Coil Equation
Where the mathematical parameters are defined as:
- L: Total inductance in microhenries (µH)
- r: Coil radius measured in inches (in)
- l: Physical coil length measured in inches (in)
- N: Total number of winding turns
Step-by-Step Engineering Worked Example
Verify a circular air-core coil with the following parameters:
- Number of turns (N): 20 turns
- Coil radius (r): 2 cm
- Coil length (l): 4 cm
Step 1 — Convert Dimensions to Inches
Convert metrics to imperial units using the conversion factor (1 inch = 2.54 cm):
r = 2 cm / 2.54 ≈ 0.7874 inches
l = 4 cm / 2.54 ≈ 1.5748 inches
Step 2 — Calculate Winding and Area Component
r² × N² = (0.7874)² × 20² = 0.6200 × 400 = 248.00
Step 3 — Calculate Denominator Constants
9r + 10l = (9 × 0.7874) + (10 × 1.5748) = 7.0866 + 15.7480 = 22.8346
Step 4 — Divide to Determine Inductance (L)
L = 248.00 / 22.8346 ≈ 10.86 µH
Step 5 — Convert to Millihenries
L = 10.86 / 1000 ≈ 0.01086 mH
Walkthrough Final Verified Results
- Turns (N): 20 turns
- Radius Used: 2.00 cm (0.787 in)
- Coil Length Used: 4.00 cm (1.575 in)
- Inductance in µH: 10.86 µH
- Inductance in mH: 0.01086 mH
Circular Coil Inductance Chart
This reference chart details pre-calculated inductance values for single-layer air-core circular coils across common turns, radii, and lengths. All metrics are converted to inches before applying Wheeler's formula.
| Turns (N) | Radius (cm) | Length (cm) | Inductance (µH) |
|---|---|---|---|
| 10 | 1 cm | 2 cm | 1.36 µH |
| 15 | 1.5 cm | 3 cm | 4.58 µH |
| 20 | 2 cm | 4 cm | 10.86 µH |
| 25 | 2.5 cm | 5 cm | 21.21 µH |
| 30 | 3 cm | 6 cm | 36.65 µH |
| 40 | 4 cm | 8 cm | 86.89 µH |
Note: Values are approximate for air-core single-layer circular coils.
Frequently Asked Questions (FAQs)
To calculate the inductance of a circular coil, you must consider the coil's physical dimensions, including its radius, length, and the total number of wire turns. Engineers use specialized formulas like Wheeler's formula to accurately estimate the inductance of these air-core circular coils.
The inductance of a coil is affected by four primary factors: the number of wire turns, the cross-sectional area of the coil, the physical length of the coil, and the permeability of the core material used.
An air core is often used in a circular coil because it does not suffer from magnetic saturation or core losses at very high frequencies. This makes air-core inductors ideal for radio frequency applications, transmitters, and receivers where high stability and precise inductance values are required.
Yes, the physical length of the coil strongly impacts the total inductance. If you stretch a coil to make it longer while keeping the number of turns the same, the inductance will actually decrease. A more tightly wound, compact coil concentrates the magnetic field and produces higher inductance.
Adding more wire turns to a circular coil increases its inductance dramatically. The inductance is actually proportional to the square of the number of turns. Therefore, if you double the number of turns while keeping the length constant, the coil's total inductance will increase by a factor...