Magnetic Coupling Coefficient
k = M / √(L1 · L2)
Quick answer
This calculator solves k = M / √(L1 × L2) for Coupling Coefficient. With Mutual Inductance 100 µH, Inductance L1 0.22 mH, Inductance L2 0.47 mH, the result is 0.311. It solves in 4 directions, so you can enter the values you have and get the one you need.
Calculator
Formula
Description
The coupling coefficient quantifies how much of one coil’s magnetic flux links a second coil, ranging from 0 (no coupling) to 1 (perfect coupling). It relates the mutual inductance M to the two self-inductances. Tightly wound transformers on a shared core approach k = 1, while loosely coupled air-core coils may have k far below 0.5.
Variables
- k — Coupling coefficient (0–1)
- M — Mutual inductance (H)
- L1, L2 — Self-inductances of the two coils (H)
Practical Notes
Power transformers aim for k > 0.98; loosely coupled resonant wireless-power and tuned-RF coils deliberately use lower k. Leakage inductance is (1 − k)·L and directly sets a transformer’s voltage regulation.
Symbols and units
| Symbol | Meaning | Default unit | Accepted units |
|---|---|---|---|
| k | Coupling Coefficient | — | — |
| M | Mutual Inductance | µH | nH, µH, mH, H |
| L1 | Inductance L1 | µH | nH, µH, mH, H |
| L2 | Inductance L2 | µH | nH, µH, mH, H |
Step by step
- 1. What you know: Mutual Inductance 100 µH, Inductance L1 0.22 mH, Inductance L2 0.47 mH
- 2. The relation: k = M / √(L1 × L2)
- 3. Substitute: M = 100 µH, L1 = 0.22 mH, L2 = 0.47 mH
- 4. Result: Coupling Coefficient = 0.311
Worked examples
Minimum range
Given: Mutual Inductance 100 nH, Inductance L1 0.22 µH, Inductance L2 0.47 µH
Result: Coupling Coefficient = 0.311
Low range
Given: Mutual Inductance 1 µH, Inductance L1 2.2 µH, Inductance L2 4.7 µH
Result: Coupling Coefficient = 0.311
Typical
Given: Mutual Inductance 100 µH, Inductance L1 0.22 mH, Inductance L2 0.47 mH
Result: Coupling Coefficient = 0.311
High range
Given: Mutual Inductance 0.47 mH, Inductance L1 1.03 mH, Inductance L2 2.21 mH
Result: Coupling Coefficient = 0.3115
Maximum range
Given: Mutual Inductance 4.7 mH, Inductance L1 10.3 mH, Inductance L2 22.1 mH
Result: Coupling Coefficient = 0.3115
Solving for each variable
Solve for Coupling Coefficient
Mutual Inductance 100 nH, Inductance L1 0.22 µH, Inductance L2 0.47 µH → 0.311
Solve for Mutual Inductance
Coupling Coefficient 0.025, Inductance L1 0.22 µH, Inductance L2 0.47 µH → 8.039 nH
Solve for Inductance L1
Coupling Coefficient 0.025, Mutual Inductance 100 nH, Inductance L2 0.47 µH → 34.04 µH
Solve for Inductance L2
Coupling Coefficient 0.025, Mutual Inductance 100 nH, Inductance L1 0.22 µH → 72.73 µH
How Coupling Coefficient changes with Mutual Inductance
| Mutual Inductance (input) | Coupling Coefficient (result) |
|---|---|
| 10 µH | 0.0311 |
| 25 µH | 0.07775 |
| 50 µH | 0.1555 |
| 75 µH | 0.2332 |
| 100 µH | 0.311 |
| 150 µH | 0.4665 |
| 0.2 mH | 0.622 |
| 0.4 mH | 1.244 |
| 0.7 mH | 2.177 |
| 1 mH | 3.11 |
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<p><a href="https://vbatpower.com/formulas/coupling-coefficient/">Magnetic Coupling Coefficient</a> Calculator by vbatpower.com</p>Frequently asked questions
How do you calculate Magnetic Coupling Coefficient?
Use k = M / √(L1 × L2). With Mutual Inductance 100 µH, Inductance L1 0.22 mH, Inductance L2 0.47 mH, Coupling Coefficient works out to 0.311.
How do you calculate coefficient of coupling?
Rearrange for Coupling Coefficient: with Mutual Inductance 1 µH, Inductance L1 2.2 µH, Inductance L2 4.7 µH, Coupling Coefficient is 0.311.
What is the formula for Magnetic Coupling Coefficient?
The formula is k = M / √(L1 × L2). The coupling coefficient quantifies how much of one coil’s magnetic flux links a second coil, ranging from 0 (no coupling) to 1 (perfect coupling).
How do you find Mutual Inductance when you know the other values?
Rearrange for Mutual Inductance: with Coupling Coefficient 0.025, Inductance L1 0.22 µH, Inductance L2 0.47 µH, Mutual Inductance is 8.039 nH.
How do you find Inductance L1 when you know the other values?
Rearrange for Inductance L1: with Coupling Coefficient 0.025, Mutual Inductance 100 nH, Inductance L2 0.47 µH, Inductance L1 is 34.04 µH.
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