HesapHanem

Solenoid Inductance Calculator

Find the inductance of a coil or solenoid.

How it is calculated

The inductance of a long, tightly wound solenoid is L = μ0 · μr · N² · A ÷ l. N is the number of turns, A the cross-section area of the core and l the winding length. The tool takes A in cm² and l in cm and converts them to m² and m, uses μ0 = 4π × 10⁻⁷ H/m, and treats μr (relative permeability of the core) as 1 if it is left empty or is not positive. Turns, area and length must be above zero. The result is shown in microhenries (µH) and millihenries (mH). Inductance grows with the square of the turns. The formula assumes the length is much larger than the diameter.

Worked example

A coil has 200 turns, a cross-section of 2 cm², a length of 10 cm and an air core (μr = 1). In SI units the area is 2×10⁻⁴ m² and the length is 0.1 m. Then L = 4π×10⁻⁷ × 200² × 2×10⁻⁴ ÷ 0.1, which is about 1.0053×10⁻⁴ H. That is 100.53 µH, or 0.1005 mH.

Try this example →

Common mistakes

  • Entering area in mm² or m² and length in mm or m. The tool expects cm² and cm.
  • Using the wire length instead of the winding length along the axis.
  • Entering the core diameter where the cross-section area is needed. Area is π × (d ÷ 2)².
  • Doubling the turns and expecting double the inductance. Doubling N multiplies L by four.
  • Putting a ferrite or iron μr on a short, fat coil. The result is an ideal estimate and assumes the field is mostly inside a long core.

About this calculator

This calculator finds the inductance of a solenoid (coil): L = μ0 · μr · N² · A / l, where μ0 is the permeability of free space, μr is the relative permeability of the core material, N is the number of turns, A is the cross-sectional area, and l is the coil's length. Inductance grows with the square of the turn count, so doubling the turns quadruples it, and a ferromagnetic core (high μr) can boost inductance dramatically over an air core.

Electronics engineers and hobbyists use it when winding custom coils or inductors for filters, transformers, chokes, and RF circuits, to predict how a design's turns, geometry, and core material will affect its inductance before building it.

Was this helpful?

You can pick up to 3 reactions.

Comments (1)

  • Editorial team

    Since inductance scales with the square of the turns, tuning a coil is quick. The 200-turn, 2 cm², 10 cm air-core coil gives about 100.5 µH, so 400 turns of the same geometry gives about four times that, near 402 µH. The formula assumes a long coil, so a short, fat one will read higher than it really is. What core and target inductance are you aiming for?

Popular calculators

Loan Calculator

Monthly payment, total interest and full amortization schedule.

Percentage Calculator

Percent change, percent of, and ratio calculations.

Discount Calculator

Calculate final price, savings, and discount amount.

BMI Calculator

Body mass index from height and weight (metric or imperial).

Age Calculator

Compute your exact age in years, months and days from a birth date.

Compound Interest Calculator

Calculate the final amount and interest earned with compounding.

All Calculators