Solenoid Inductance Calculator
Calculate the self-inductance of solenoid coils using physical parameters
Calculate Solenoid Inductance
Total number of wire turns in the coil
Radius of the circular cross-section
Length of the solenoid coil
Solenoid Inductance Results
Formula: L = μ₀ × N² × A / l
Calculation: L = 1.257e-6 × 0² × 0 / 0
Energy stored (at 1A): 0 J
Time constant (with 1Ω): 0 s
Solenoid Analysis
Example Calculation
Audio Inductor Design
Application: Audio crossover network inductor
Number of turns: 150 turns
Coil diameter: 8 cm (radius = 4 cm)
Coil length: 15 cm
Calculation
Cross-sectional area: A = π × (0.04 m)² = 5.027 × 10⁻³ m²
L = 1.257 × 10⁻⁶ × 150² × 5.027 × 10⁻³ / 0.15
L = 1.257 × 10⁻⁶ × 22,500 × 5.027 × 10⁻³ / 0.15
L ≈ 947 μH
Suitable for mid-frequency crossover applications
Solenoid Inductance Formula
L = μ₀ × N² × A / l
Solenoid inductance formula
Typical Inductance Values
Design Considerations
Turn Density
Higher turn density increases inductance
Core Material
Ferrite cores multiply inductance by μᵣ
Length/Diameter Ratio
Long solenoids (l/d > 10) for accuracy
Wire Resistance
Consider DC resistance and skin effect
Solenoid Tips
Inductance is proportional to N² (turns squared)
Larger cross-sectional area increases inductance
Shorter length increases inductance
Add ferrite core to multiply inductance by μᵣ
Consider parasitic capacitance at high frequencies
Understanding Solenoid Inductance
What is a Solenoid?
A solenoid is a tightly wound helical coil of wire that creates a magnetic field when current flows through it. It acts as an inductor in electrical circuits, storing energy in its magnetic field and resisting changes in current.
Key Physical Principles
- •Self-inductance from magnetic flux linkage
- •Energy storage in magnetic field
- •Lenz's law opposition to current changes
- •Electromagnetic induction effects
Inductance Formula Derivation
L = μ₀ × N² × A / l
For air-core solenoids
Energy and Time Relations
Note: This formula assumes an air-core solenoid. With ferrite cores, multiply by relative permeability μᵣ which can range from 10 to 10,000.
Applications & Use Cases
Power Electronics
Buck/boost converters, energy storage, power factor correction
RF Circuits
Antenna tuning, impedance matching, filter networks
Audio Systems
Crossover networks, speaker drivers, equalization filters
Design Guidelines
Maximizing Inductance
- • Increase number of turns (quadratic effect)
- • Use larger cross-sectional area
- • Reduce solenoid length
- • Add high-permeability core material
- • Minimize air gaps in magnetic circuit
Practical Considerations
- • Wire gauge affects resistance and current capacity
- • Core saturation limits maximum current
- • Parasitic capacitance affects high-frequency response
- • Thermal management for power applications
- • Mechanical stability and vibration resistance