Solenoid Inductance Calculator: L = mu0 N^2 A / l

The inductance of a long coil of wire.

Calculated from standard textbook formulas, with every step shown. The formulas are fixed, so the working does not need checking: what matters is the numbers you type in. Use these calculators only if you are competent to choose the inputs (loads, material strength, dimensions, supports) and check your units and assumptions. For learning and checking your own working: design and sign-off are for a qualified engineer. Drafting Central does not store the numbers you type.

How this calculator works

Choose which quantity you want to find.

Enter the other values in the units shown.

The calculator gives the answer with the formula, the substituted numbers, and the answer in other units.

Formulas used

  • L = \frac{\mu_0N^2A}{l}
  • N = \sqrt{\frac{Ll}{\mu_0A}}

Worked example

With the default numbers in the calculator above:

  1. The formula, arranged to find the inductance: inductance = (4 pi x 10^-7 x number of turns^2 x cross-section area of the coil) / (length of the coil)
  2. Put the values in (every value in its SI unit): inductance = (4 pi x 10^-7 x 500^2 x 0.0005) / (0.1)
  3. The answer: inductance: 0.0015708 H
  4. The same answer in other units: 1.5708 mH; 1570.8 uH

Change the numbers in the calculator to see the full working, every step, for your own case.

A second worked example

A different case, with these numbers: What do you want to find? Number of turns; Inductance (leave it as it is if this is what you are finding) 0.0015708 H; Cross-section area of the coil (leave it as it is if this is what you are finding) 0.0005 m2; Length of the coil (leave it as it is if this is what you are finding) 0.1 m.

  1. The formula, arranged to find the number of turns: number of turns = square root of ((inductance x length of the coil) / (4 pi x 10^-7 x cross-section area of the coil))
  2. Put the values in (every value in its SI unit): number of turns = square root of ((0.0015708 x 0.1) / (4 pi x 10^-7 x 0.0005))
  3. The answer: number of turns: 500.001

Common questions

What is the formula for the inductance of a solenoid?

The permeability of free space times the turns squared times the area, divided by the length.

How do I increase the inductance?

Add more turns (it rises with the square), increase the area, shorten the coil, or add an iron or ferrite core.

What is mu0?

The permeability of free space, 4 pi times 10 to the minus 7 henries per metre.

Related calculators

Got a question about this? Ask an engineering question and get a plain-language answer with references.

Further reading: Any physics or electrical text (inductance of a solenoid).

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