Inductor Coil Inductance Calculator | L = µ₀µᵣN²A/l
Calculate the inductance of a coil (solenoid). Enter the number of turns, cross-sectional area, core length, and relative permeability.
How to Use
- Enter the number of turns (N) — the total number of wire loops in the coil.
- Enter the cross-sectional area (A) of the core in mm².
- Enter the length (l) of the coil/core in mm.
- Enter the relative permeability (µᵣ) of the core material: air=1, ferrite=100–10000, iron=200–5000.
- Click 'Calculate' to get the inductance in µH (microhenries).
- For air-core coils, use µᵣ = 1. For wound ferrite cores, check the datasheet for the AL value and convert.
About Inductance
The Inductance Formula
The inductance of a solenoid is calculated as L = µ₀ × µᵣ × N² × A / l, where µ₀ = 4π × 10⁻⁷ H/m is the permeability of free space, µᵣ is the relative permeability of the core, N is the number of turns, A is the cross-sectional area in m², and l is the coil length in meters. This formula assumes a long, uniformly wound coil (solenoid approximation).
Effect of Core Material
The core material dramatically affects inductance through the relative permeability µᵣ. Air core (µᵣ=1) gives the lowest inductance but no saturation. Ferrite cores (µᵣ=100–10,000) multiply inductance by that factor but saturate at high currents. Iron powder cores offer intermediate values with good DC bias performance. Core saturation reduces inductance and causes distortion in switching power supplies.
Inductance and Energy Storage
An inductor stores energy in its magnetic field: E = ½ × L × I². This energy storage is exploited in switch-mode power supplies (boost converters, buck converters), where the inductor transfers energy between switching cycles. The inductance value determines the current ripple: higher L means less ripple but a larger physical component. Choosing the right inductance is a key step in power supply design.
Practical Coil Design Factors
In practice, inductors also have DC resistance (DCR) from the wire, self-resonant frequency (SRF) above which they behave capacitively, and current rating (saturation and thermal). Wire gauge affects DCR and maximum current. Winding technique (single layer vs. multi-layer) affects capacitance and SRF. For RF applications, air-core coils with high SRF are preferred; for power applications, ferrite cores with high saturation current are chosen.
Key Features
- Calculates inductance using the solenoid formula L = µ₀µᵣN²A/l
- Supports any core material via relative permeability input
- Results in µH, nH, and mH units for convenience
- Suitable for air-core, ferrite, and iron-powder coil design
Common Applications
- Designing RF coils for oscillators and filters
- Power inductor design for switching power supplies
- Calculating inductance of custom wound transformers
- Antenna loading coil design for amateur radio
- Educational demonstrations of magnetic field principles