Solenoid Inductance Calculator

Find the inductance of an air-core solenoid.

Inductance (H) 0.0003
Inductance (mH) 0.2513

Formula: L = μ₀·N²·A ÷ l

Step-by-step with your numbers:
1. Values used:
2. Number of turns = 200
3. Cross-section area = 5 cm²
4. Length = 10
5.
6. Inductance = 0.0003H
7. Inductance = 0.2513mH
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A solenoid's inductance grows with the square of its turns.

How the Math Works

The Solenoid Inductance Calculator uses the fundamental formula L = μ₀·N²·A ÷ l to determine inductance. Here, μ₀ (4π × 10⁷ H/m) is the permeability of free space, N represents the total number of wire turns, A is the cross-sectional area in square meters, and l is the solenoid's length in meters. The formula reveals that inductance grows with the square of the turn count and proportional to the coil's cross-sectional area, while inversely relating to its length. Squaring the number of turns means doubling the turns quadruples the inductance, making this relationship crucial for precise calculations.

Practical Applications

To use this calculator practically, first measure your solenoid's physical dimensions: count the total wire turns (N), measure the coil diameter to calculate cross-sectional area using A = πr², and determine the coil length (l). Input these values along with the standard μ₀ constant to find the inductance in henries. This calculation is essential when designing transformers, radio frequency chokes, or electromagnetic relays, where knowing the exact inductance helps select appropriate components and predict circuit behavior in applications ranging from power supplies to radio transmitters.

Day-to-Day Use

While you may not calculate solenoid inductance daily, this knowledge impacts many everyday technologies. The electromagnetic coils in your car's ignition system, the sensors in smartphones, and the wireless charging pads in your devices all rely on precisely calculated inductance values. Understanding these principles helps explain why certain electronic devices work and empowers you to troubleshoot problems, modify electronic projects, or simply appreciate the engineering behind common gadgets. When purchasing components like relays or solenoids for household projects, this knowledge ensures you select the right part for the job, preventing costly mistakes and ensuring your DIY electronics projects succeed.

Worked example

200 turns, 5 cm², 10 cm → about 0.25 mH.

FAQ

Why N squared?

More turns both create and link more flux, so inductance scales with N².