Air core solenoid inductance calculator

It applies the standard long-solenoid equation with vacuum permeability and reports the result in henries, millihenries, and microhenries. Use SI units: metres for length and square metres for area. The calculation is deterministic and useful for early design work, classroom checks, and repeatable engineering pipelines, while remaining an ideal approximation rather than a substitute for measuring a finished coil.

Enter geometry in SI units

Provide the total number of complete winding turns, the axial length of the wound section in metres, and the internal cross-sectional area enclosed by a turn in square metres. For a round former, calculate area from its effective winding diameter using A = πd²/4. Use the diameter near the centre of the conductor rather than blindly using the bare former diameter when wire thickness is significant. The length is the occupied winding length, not the wire length unwound from the spool. All three inputs describe the same physical coil. Turns must be a whole, non-negative count, while length and area must be positive finite values. The calculator accepts zero turns and returns zero inductance, which is mathematically consistent and useful in automated validation. It rejects zero or negative geometry because division by zero and negative physical dimensions are outside the model. Convert millimetres to metres by dividing by 1,000, and convert square millimetres to square metres by dividing by 1,000,000 before submitting the values. Consistent units prevent the most common million-fold area error.

Understand the equation and result

The calculation uses L = μ₀N²A/l, where L is inductance in henries, μ₀ is the permeability of free space, N is the number of turns, A is cross-sectional area in square metres, and l is coil length in metres. The squared turn count is especially important: doubling the turns increases the ideal inductance by a factor of four when area and length remain unchanged. Doubling the enclosed area doubles inductance, while doubling coil length halves it. The response includes henries, millihenries, and microhenries so it can be used directly across common circuit scales without a separate unit conversion. It also returns the applied permeability, normalized inputs, formula, and model name for an auditable record. Precision controls displayed decimal rounding, not the underlying physical accuracy. A result with many decimal places is still only as reliable as the measurements and assumptions supplied. For automated use, the API price is $0.002 per request, and the same deterministic arithmetic can be run in the browser without sending the calculation to a remote model.

Know when the ideal model is appropriate

This equation describes a long, uniformly wound air-core solenoid whose magnetic field is concentrated inside the winding. It is a useful first estimate when coil length is comfortably greater than coil diameter, turns are distributed evenly, and no magnetic core or nearby ferromagnetic structure changes the field. A short or wide coil has stronger fringing fields, so a Wheeler-style geometry correction or electromagnetic simulation may better match reality. Closely packed wire also creates parasitic capacitance, and high-frequency skin and proximity effects make a real component depart from a simple lumped inductor. Lead length, turn spacing, insulation thickness, multilayer winding, conductive shields, mounting hardware, and measurement frequency can all affect the observed value. The calculator intentionally does not infer those corrections because its three requested inputs cannot describe them. Treat the output as a transparent baseline for design comparisons and sanity checks. When component tolerance matters, measure the completed coil with an LCR meter at the intended frequency and test it in its final mechanical environment. That final measurement captures construction details which an ideal analytical model cannot know.