Mutual Inductance

Q: How do you calculate Mutual Inductance?

Use the formula M = k × √(L₁ × L₂). Mutual inductance M quantifies the magnetic coupling between two inductors. Enter the values you know in the calculator above and it solves for the remaining variable.

Q: What is the formula for Mutual Inductance?

The Mutual Inductance formula is M = k × √(L₁ × L₂), where M—Mutual inductance (H); k—Coupling coefficient (0 to 1, dimensionless); L₁—Self-inductance of coil 1 (H); L₂—Self-inductance of coil 2 (H).

M = k × √(L1 × L2)

Quick answer

This calculator solves M = k × √(L₁ × L₂) for Mutual Inductance. With Coupling Coefficient 50 %, Inductance 1 0.22 mH, Inductance 2 0.47 mH, the result is 0.1608 mH. It solves in 4 directions, so you can enter the values you have and get the one you need.

Calculator

Coupling Coefficient

Inductance 1

Inductance 2

Mutual Inductance (µH)

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Formula

M = k × √(L₁ × L₂)

Description

Mutual inductance M quantifies the magnetic coupling between two inductors. When current changes in one inductor, the changing magnetic flux links to the second inductor and induces a voltage: V₂ = M × dI₁/dt. The coupling coefficient k ranges from 0 (no coupling) to 1 (perfect coupling). Power transformers on ferrite cores achieve k = 0.95-0.99. Air-core coils used for wireless power transfer typically have k = 0.1-0.5 depending on distance and alignment. RFID and NFC systems rely on mutual inductance for energy and data transfer.

Variables

M — Mutual inductance (H)
k — Coupling coefficient (0 to 1, dimensionless)
L₁ — Self-inductance of coil 1 (H)
L₂ — Self-inductance of coil 2 (H)

Practical Notes

The total inductance of two coupled inductors in series is L_total = L1 + L2 ± 2M, where + applies when fluxes aid and − when they oppose. For transformers, the leakage inductance is L_leak = L × (1 − k²). Tight coupling (high k) is desired for power transformers to minimize leakage inductance and improve regulation.

Symbols and units

Symbol	Meaning	Default unit	Accepted units
M	Mutual Inductance	µH	nH, µH, mH, H
k	Coupling Coefficient	—	—, %
L1	Inductance 1	µH	nH, µH, mH, H
L2	Inductance 2	µH	nH, µH, mH, H

Step by step

1. What you know: Coupling Coefficient 50 %, Inductance 1 0.22 mH, Inductance 2 0.47 mH
2. The relation: M = k × √(L₁ × L₂)
3. Substitute: k = 50 %, L1 = 0.22 mH, L2 = 0.47 mH
4. Result: Mutual Inductance = 0.1608 mH

Nearest standard component values

Series	Nearest value	Error
E12	150 µH	6.7%
E24	0.16 mH	0.48%

Worked examples

Minimum range

Given: Coupling Coefficient 2.5 %, Inductance 1 0.22 µH, Inductance 2 0.47 µH

Result: Mutual Inductance = 8.039 nH

Low range

Given: Coupling Coefficient 25 %, Inductance 1 2.2 µH, Inductance 2 4.7 µH

Result: Mutual Inductance = 0.8039 µH

Typical

Given: Coupling Coefficient 50 %, Inductance 1 0.22 mH, Inductance 2 0.47 mH

Result: Mutual Inductance = 0.1608 mH

High range

Given: Coupling Coefficient 0.8, Inductance 1 1.03 mH, Inductance 2 2.21 mH

Result: Mutual Inductance = 1.207 mH

Maximum range

Given: Coupling Coefficient 8, Inductance 1 10.3 mH, Inductance 2 22.1 mH

Result: Mutual Inductance = 120.7 mH

Solving for each variable

Solve for Mutual Inductance

Coupling Coefficient 2.5 %, Inductance 1 0.22 µH, Inductance 2 0.47 µH → 8.039 nH

Solve for Coupling Coefficient

Mutual Inductance 100 nH, Inductance 1 0.22 µH, Inductance 2 0.47 µH → 31.1 %

Solve for Inductance 1

Mutual Inductance 100 nH, Coupling Coefficient 2.5 %, Inductance 2 0.47 µH → 34.04 µH

Solve for Inductance 2

Mutual Inductance 100 nH, Coupling Coefficient 2.5 %, Inductance 1 0.22 µH → 72.73 µH

How Mutual Inductance changes with Coupling Coefficient

Coupling Coefficient (input)	Mutual Inductance (result)
5 %	16.08 µH
12.5 %	40.19 µH
25 %	80.39 µH
37.5 %	120.6 µH
50 %	0.1608 mH
0.75	0.2412 mH
1	0.3216 mH
2	0.6431 mH
3.5	1.125 mH
5	1.608 mH

The same result in other units

Unit	Value
nH	160800
µH	160.8
mH	0.1608
H	0.0001608

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Frequently asked questions

How do you calculate Mutual Inductance?

Use M = k × √(L₁ × L₂). With Coupling Coefficient 50 %, Inductance 1 0.22 mH, Inductance 2 0.47 mH, Mutual Inductance works out to 0.1608 mH.

What is the formula for Mutual Inductance?

The formula is M = k × √(L₁ × L₂). Mutual inductance M quantifies the magnetic coupling between two inductors.

How do you find Coupling Coefficient when you know the other values?

Rearrange for Coupling Coefficient: with Mutual Inductance 100 nH, Inductance 1 0.22 µH, Inductance 2 0.47 µH, Coupling Coefficient is 31.1 %.

How do you find Inductance 1 when you know the other values?

Rearrange for Inductance 1: with Mutual Inductance 100 nH, Coupling Coefficient 2.5 %, Inductance 2 0.47 µH, Inductance 1 is 34.04 µH.

What units does Mutual Inductance use?

Mutual Inductance is shown in nH, µH, mH, H. Values are held in SI base units internally, so you can mix prefixes without converting by hand.

Related Concepts

All Inductors formulas →

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