Inductance calculation is essential in electronics and electrical engineering for designing circuits with coils, transformers, and inductors. This calculator uses Wheeler's formula to determine the inductance of single-layer air core coils, which are commonly used in radio frequency applications, filters, and oscillator circuits.
Applications and Importance:
RF circuit design and antenna tuning
Filter design for audio and radio applications
Oscillator circuit calculations
Impedance matching in transmission lines
Educational purposes in electronics courses
Formula and Variable Definitions
Wheeler's formula for single-layer air core inductors provides accurate results for coils where the length is greater than 0.8 times the diameter:
$$L = \frac{D^2 N^2}{18D + 40l}$$
Variable Definitions:
Variable
Description
Unit
Range
L
Inductance
microhenries (µH)
0.1 - 10,000 µH
D
Coil diameter
millimeters (mm)
1 - 1000 mm
N
Number of turns
dimensionless
1 - 10,000 turns
l
Coil length
millimeters (mm)
1 - 1000 mm
Formula Assumptions:
Single-layer winding
Air core (no ferromagnetic material)
Uniform turn spacing
Cylindrical coil geometry
Coil length > 0.8 × diameter
Wire diameter << coil diameter
Step-by-Step Calculation Process
Step 1: Formula Display and Theoretical Foundation
Wheeler's formula is derived from electromagnetic field theory and provides an empirical approximation for inductance calculation. The formula relates the physical dimensions of the coil to its electrical properties.
$$L = \frac{D^2 N^2}{18D + 40l} \text{ (in microhenries)}$$
Step 2: Example Problem
Let's calculate the inductance for a coil with the following specifications:
Coil diameter (D) = 20 mm
Coil length (l) = 50 mm
Number of turns (N) = 100
Step 3: Value Substitution Process
Substitute the given values into Wheeler's formula: