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Long Solenoid Inductance and Circular Cross Section

Calculate long solenoid inductance and circular cross section with compatible units, known-value inputs and clearly stated model assumptions.

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Calculator inputs

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

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Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.

Formula and method

For the worked inputs, Inductance of solenoid is approximately 3.9478418 microhenry.

L = μ₀N²A/ℓ; A = πr²

Worked example

Enter these known values and leave the other values blank.

Number of turns
100
Radius
0.01 m
Length
1 m
Cross-sectional area
0.00031416 m²
Inductance of solenoid
3.948 μH

Assumptions and limitations

  • The model assumes a long, closely wound solenoid with a circular cross section and vacuum or effectively nonmagnetic core.
  • Ignore end effects, winding thickness, parasitic capacitance and frequency-dependent core behavior.
  • Turn count is a positive effective value; fractional inverse estimates do not specify a complete-turn construction layout.
  • Numerical arithmetic uses 64 significant digits; displayed values are rounded separately. Captured particle-mass and astronomical unit conversions retain their stated approximations.

Common questions

Which inputs and assumptions does this result use?

The model assumes a long, closely wound solenoid with a circular cross section and vacuum or effectively nonmagnetic core.

References

Bookify retains the captured physical relationship and inverse controls, while replacing older or rounded constants with the 2022 CODATA values and full-precision π where applicable. Measured constants retain their physical uncertainty. The international acre is exactly 43560 square international feet; Bookify replaces the rounded captured area factor.

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