Quick answer
A long solenoid has L = μ₀ μᵣ N² A ÷ ℓ. With 500 turns, a 4 cm² core, 10 cm length and μᵣ = 1, the inductance is 1.2566 mH.
Enter turns, core cross-section, coil length and relative permeability. The calculator returns inductance.
Related tools: Capacitance Calculator: Capacitance from charge and voltage.
How to use the Inductance Calculator
- Enter number of turns (above 0).
- Enter core cross-section (cm²) (above 0).
- Enter coil length (cm) (above 0).
- Enter relative permeability μr (above 0). It starts at 1.
- Press Calculate to see the result, and use Reset to start again.
| Input | What to enter | Allowed values |
|---|---|---|
| Number of turns | A number | > 0 |
| Core cross-section | A number, in cm² | > 0 |
| Coil length | A number, in cm | > 0 |
| Relative permeability μr | A number | > 0, starts at 1 |
Formula and method
Formula
L = μ₀ μr N² A ÷ ℓ, μ₀ = 1.25663706212×10⁻⁶ N/A²
IEEE-754 double precision; shown to the decimals indicated.
Valid when the coil is much longer than its diameter.
Worked examples
These examples are verified: each one is an automated test case that the live calculator must reproduce exactly.
Example 1
Inputs: Number of turns = 500; Core cross-section = 4; Coil length = 10; Relative permeability μr = 1.
| Result | Value |
|---|---|
| Inductance | 1.256637 mH |
Example 2
Inputs: Number of turns = 200; Core cross-section = 1; Coil length = 5; Relative permeability μr = 1.
| Result | Value |
|---|---|
| Inductance | 0.100531 mH |
Example 3
Inputs: Number of turns = 1000; Core cross-section = 2; Coil length = 20; Relative permeability μr = 200.
| Result | Value |
|---|---|
| Inductance | 251.327412 mH |
The first line is the headline result (inductance). IEEE-754 double precision; shown to the decimals indicated.
Scaling
Inductance rises with the square of turns: doubling to 1,000 turns gives four times the inductance, 5.03 mH. A ferromagnetic core with μᵣ in the hundreds multiplies it further.
Assumptions
The formula is accurate for a coil much longer than its diameter. Short coils, winding spacing and core saturation reduce accuracy.
How the result changes with number of turns
Holding every other input at the first worked example, this table changes only number of turns. It shows how sensitive the answer is to that one value; each row was produced by running this calculator.
| Number of turns | Inductance |
|---|---|
| 250 | 0.314159 mH |
| 500 | 1.256637 mH |
| 1000 | 5.026548 mH |
| 2000 | 20.106193 mH |
What happens with invalid input
These messages are produced by the calculator itself, so you know what to fix.
- Number of turns: entering "0" shows "Number of turns must be greater than 0." beside that field and no result.
- Coil length: entering "0" shows "Coil length must be greater than 0." beside that field and no result.
Choosing between the Inductance Calculator and similar calculators
Each row shows what a related calculator on this site asks for and what it returns, so you can pick the one that matches your question.
| Calculator | You enter | It returns |
|---|---|---|
| [Capacitance Calculator](/science/capacitance-calculator/) | charge and voltage | Capacitance |
| [Voltage Divider Calculator](/engineering/voltage-divider-calculator/) | input voltage, r1 and r2 | Output voltage |
| [RLC Impedance Calculator](/engineering/rlc-impedance-calculator/) | resistance, inductance and capacitance | Impedance |
| [RMS Voltage Calculator](/engineering/rms-voltage-calculator/) | i know the and voltage | RMS voltage |
| [Parallel Plate Capacitor Calculator](/engineering/parallel-plate-capacitance-calculator/) | plate area, plate separation and relative permittivity εr | Capacitance |
Assumptions and limitations
- Short coils have lower inductance
If a required value is empty, not a number, or outside its allowed range, the form marks that field with a message and shows no result instead of a misleading number. The automated checks deliberately try invalid entries for number of turns and coil length to confirm this.
Frequently asked questions
What is the unit?
The henry (H); this coil is shown in millihenries (mH) for convenience.
Does wire thickness matter?
Only through the number of turns that fit.
Why is μ₀ constant?
It is the permeability of free space.
What does the Inductance Calculator calculate?
Inductance of a long air- or core-filled solenoid. It returns Inductance.
What formula does the Inductance Calculator use?
L = μ₀ μr N² A ÷ ℓ, μ₀ = 1.25663706212×10⁻⁶ N/A². Valid when the coil is much longer than its diameter.
What do I need to enter in the inductance Calculator?
You enter Number of turns, Core cross-section (cm²), Coil length (cm) and Relative permeability μr.
How is the result rounded or limited?
IEEE-754 double precision; shown to the decimals indicated. Short coils have lower inductance.
What is an example of a inductance result?
With number of turns 500, core cross-section 4, coil length 10 and relative permeability μr 1, the inductance is 1.256637 mH.
Where does the method come from?
The method follows: CODATA 2018 / SI exact constants.
Related calculators
- Capacitance Calculator — Capacitance from charge and voltage.
Sources
- CODATA 2018 / SI exact constants
Content last reviewed 2026-11-04. Formulas and worked examples are checked by automated tests against independently computed values.