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Solenoid Inductance Calculator.

Calculate the long-solenoid inductance approximation.

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Inductance: 0.000314 H

Inductance

0.000000H

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Use Cases

Designing inductors for circuits

Quickly estimate the inductance of a solenoid coil for use in filters, transformers, or resonant circuits, helping you choose the right number of turns and core material.

Example: A 100-turn coil with 0.001 m² area, 0.1 m length, and air core gives about 0.126 mH.

Educational physics experiments

Verify theoretical inductance values in lab setups or homework problems, reinforcing the relationship between geometry, turns, and core permeability.

Example: Compare calculated inductance for different core materials by changing μᵣ.

Frequently Asked Questions

What is the long-solenoid inductance approximation?
The long-solenoid approximation assumes the solenoid is infinitely long, so the magnetic field inside is uniform and fringing at the ends is neglected. The inductance is calculated using L = μ₀μᵣN²A/l, where N is turns, A is cross-sectional area, l is length, and μᵣ is relative permeability.
How do I use the relative permeability field?
Relative permeability (μᵣ) is the ratio of the permeability of the core material to that of free space. For air or vacuum, μᵣ = 1. For ferromagnetic cores like iron, μᵣ can be thousands. Enter the value for your core material to get accurate inductance.
What units should I use for the inputs?
Enter the number of turns as a dimensionless number, cross-sectional area in square meters (m²), solenoid length in meters (m), and relative permeability as a dimensionless number. The calculator will output inductance in henries (H).

Tips & Common Mistakes

Tips

  • Ensure the solenoid length is much greater than its diameter for the long-solenoid approximation to be valid.
  • Use consistent units: convert area to m² and length to m before entering values.
  • For air-core solenoids, set relative permeability to 1.
  • Double-check your turn count; it is squared in the formula, so small errors have a large effect.

Common Mistakes to Avoid

  • Using centimeters or millimeters without converting to meters, leading to incorrect results.
  • Forgetting to square the number of turns in the calculation.
  • Assuming the approximation works for short, fat solenoids where fringing fields are significant.

Last updated: August 13, 2026