Inductance from Flux Linkage
L = N · Φ / I
Quick answer
This calculator solves L = N × Φ / I for Inductance. With Number of Turns 0.5, Flux per Turn 10 µWb, Current 2 A, the result is 2.5 µH. It solves in 4 directions, so you can enter the values you have and get the one you need.
Calculator
Formula
Description
Inductance is defined as the total flux linkage (turns times flux per turn) produced per ampere of current. This is the fundamental definition from which all inductor geometry formulas derive: pack more turns or guide more flux per turn (with a high-permeability core) and the inductance rises. It links the magnetic-circuit view of a coil to its circuit-level inductance.
Variables
- L — Inductance (H)
- N — Number of turns
- Φ — Magnetic flux per turn (Wb)
- I — Current producing the flux (A)
Practical Notes
Because Φ = F/S = NI/S, this reduces to L = N²/S—inductance grows with the square of turns and inversely with core reluctance. Saturation makes Φ sublinear in I, lowering effective L at high current.
Symbols and units
| Symbol | Meaning | Default unit | Accepted units |
|---|---|---|---|
| L | Inductance | µH | nH, µH, mH, H |
| N | Number of Turns | — | — |
| phi | Flux per Turn | µWb | µWb, mWb, Wb |
| I | Current | A | pA, nA, µA, mA, A, kA |
Step by step
- 1. What you know: Number of Turns 0.5, Flux per Turn 10 µWb, Current 2 A
- 2. The relation: L = N × Φ / I
- 3. Substitute: N = 0.5, phi = 10 µWb, I = 2 A
- 4. Result: Inductance = 2.5 µH
Nearest standard component values
| Series | Nearest value | Error |
|---|---|---|
| E12 | 2.7 µH | 8% |
| E24 | 2.4 µH | 4% |
Worked examples
Minimum range
Given: Number of Turns 0.025, Flux per Turn 0.1 µWb, Current 2 mA
Result: Inductance = 1.25 µH
Low range
Given: Number of Turns 0.25, Flux per Turn 1 µWb, Current 20 mA
Result: Inductance = 12.5 µH
Typical
Given: Number of Turns 0.5, Flux per Turn 10 µWb, Current 2 A
Result: Inductance = 2.5 µH
High range
Given: Number of Turns 0.8, Flux per Turn 100 µWb, Current 100 A
Result: Inductance = 0.8 µH
Maximum range
Given: Number of Turns 8, Flux per Turn 1 mWb, Current 1 kA
Result: Inductance = 8 µH
Solving for each variable
Solve for Inductance
Number of Turns 0.025, Flux per Turn 0.1 µWb, Current 2 mA → 1.25 µH
Solve for Number of Turns
Inductance 100 nH, Flux per Turn 0.1 µWb, Current 2 mA → 0.002
Solve for Flux per Turn
Inductance 100 nH, Number of Turns 0.025, Current 2 mA → 0.008 µWb
Solve for Current
Inductance 100 nH, Number of Turns 0.025, Flux per Turn 0.1 µWb → 25 mA
How Inductance changes with Number of Turns
| Number of Turns (input) | Inductance (result) |
|---|---|
| 0.05 | 0.25 µH |
| 0.125 | 0.625 µH |
| 0.25 | 1.25 µH |
| 0.375 | 1.875 µH |
| 0.5 | 2.5 µH |
| 0.75 | 3.75 µH |
| 1 | 5 µH |
| 2 | 10 µH |
| 3.5 | 17.5 µH |
| 5 | 25 µH |
The same result in other units
| Unit | Value |
|---|---|
| nH | 2500 |
| µH | 2.5 |
| mH | 0.0025 |
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<p><a href="https://vbatpower.com/formulas/inductance-flux-linkage/">Inductance from Flux Linkage</a> Calculator by vbatpower.com</p>Frequently asked questions
How do you calculate Inductance from Flux Linkage?
Use L = N × Φ / I. With Number of Turns 0.5, Flux per Turn 10 µWb, Current 2 A, Inductance works out to 2.5 µH.
How do you calculate inductance from flux?
Rearrange for Inductance: with Number of Turns 0.25, Flux per Turn 1 µWb, Current 20 mA, Inductance is 12.5 µH.
How do you calculate inductor flux linkage?
Rearrange for Inductance: with Number of Turns 0.5, Flux per Turn 10 µWb, Current 2 A, Inductance is 2.5 µH.
What is the formula for Inductance from Flux Linkage?
The formula is L = N × Φ / I. Inductance is defined as the total flux linkage (turns times flux per turn) produced per ampere of current.
How do you find Number of Turns when you know the other values?
Rearrange for Number of Turns: with Inductance 100 nH, Flux per Turn 0.1 µWb, Current 2 mA, Number of Turns is 0.002.
How do you find Flux per Turn when you know the other values?
Rearrange for Flux per Turn: with Inductance 100 nH, Number of Turns 0.025, Current 2 mA, Flux per Turn is 0.008 µWb.
Related Concepts
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