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Long Vacuum Solenoid Field from Current and Turns

Calculate long vacuum solenoid field from current and turns with compatible units, known-value inputs and clearly stated model assumptions.

Formula & worked example
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Calculator inputs

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How to use this calculator

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

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Formula and method

For the worked inputs, Magnetic field is approximately 0.0025132741 tesla.

B = μ₀NI/ℓ

Worked example

Enter these known values and leave the other values blank.

Current: 2 A
Number of turns: 1000
Length: 1 m

Magnetic field: 0.0025133 T

Assumptions and limitations

Approximate the central field of a long, closely wound solenoid in vacuum or an effectively nonmagnetic core. End effects and magnetic-core response are excluded.
Number of turns is an effective winding count. Inverse estimates may be fractional; an actual complete winding uses a whole-turn layout.
The model uses nonnegative current and field magnitudes. Length and effective turn count are positive.
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?

Approximate the central field of a long, closely wound solenoid in vacuum or an effectively nonmagnetic core. End effects and magnetic-core response are excluded.

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. Bookify requires physically valid mass or nonnegative field/speed magnitudes and principal scattering angles for this stated model.

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