Coiling wire concentrates magnetic field and creates inductance, which grows with the square of the number of turns. An iron or ferrite core multiplies it further.
How to use the Solenoid Inductance Calculator
- Number of turns N
- Cross-section given by
- Coil radius
- Cross-section area
- Coil length ℓ
- Core relative permeability μ_r
Results update as you type, every field has its own unit menu, and everything is calculated in your browser.
How it works
Enter the number of turns, coil radius (or area), length and the core’s relative permeability (1 for air).
Inputs explained
| Field | What to enter |
|---|---|
| Number of turns N | A number |
| Cross-section given by | Choose one: Radius, Area |
| Coil radius | Units: cm, mm, m, in, ft |
| Cross-section area | Units: cm², mm², m² |
| Coil length ℓ | Units: cm, mm, m, in, ft |
| Core relative permeability μ_r | A number |
Example values
How the main result changes when Number of turns N changes and everything else stays at the example values above:
| Number of turns N | Inductance L (mH) |
|---|---|
| 100 | 0.0395 |
| 150 | 0.0888 |
| 200 | 0.1579 |
| 250 | 0.2467 |
| 300 | 0.3553 |
| 400 | 0.6317 |
Formula
L = μ₀·μ_r·N²·A / ℓ
Worked example
Inputs — Number of turns N: 200; Cross-section given by: Radius; Coil radius: 1 cm; Coil length ℓ: 10 cm; Core relative permeability μ_r: 1.
Results — Inductance L = 0.15791 mH.
Key terms
- Solenoid
- Long, tightly wound helical coil.
Frequently asked questions
Why does inductance depend on N²?
More turns produce more flux, which links more turns.
How accurate is the formula?
Good for coils much longer than their diameter.
What does a ferrite core do?
Multiplies the inductance by its permeability (until saturation).
How do I get more inductance in less space?
Use a high-permeability core.