Mutual Inductance Calculator

Find the mutual inductance between two coupled coils, or solve for their coupling coefficient, from their individual inductances.

🔌 Mutual Inductance Calculator
µH
µH
Coupling coefficient (k)0.50
01
A/ms
µH
µH
µH
Mutual inductance (M)
—
Induced voltage (V2)
—
Step-by-step working
Coupling coefficient (k)
—
Step-by-step working

🔌 What is the Mutual Inductance Calculator?

The Mutual Inductance Calculator finds the mutual inductance M between two magnetically coupled coils from their individual inductances and coupling coefficient, or solves the reverse problem, finding the coupling coefficient k from a known mutual inductance and both coil inductances.

Transformer, wireless power, and RF circuit designers use mutual inductance to predict how much voltage one coil induces in a nearby coil for a given rate of current change, characterize measured coupling between real coils, and understand the coupling strength that drives efficiency in transformers and wireless charging systems.

A common point of confusion is treating coupling coefficient as an inductance value. k is a dimensionless number between 0 and 1 describing how completely one coil's magnetic flux links the other, it is not itself an inductance, mutual inductance M combines k with the geometric mean of the two coil inductances.

This calculator computes mutual inductance directly from k, optionally estimates the induced voltage for a given current ramp rate, and, in its second mode, solves for k from a measured or otherwise known mutual inductance, flagging the physically impossible case where a solved k would exceed 1.

📐 Formula

M = k√(L1L2)      k = M / √(L1L2)      V2 = M(dI1/dt)
M = mutual inductance (H), k = coupling coefficient (0 to 1)
L1, L2 = individual coil inductances (H)
Example: L1=100µH, L2=100µH, k=0.5 → M = 50µH.

📖 How to Use This Calculator

Steps

1
Choose a mode. Select Find Mutual Inductance to compute M from k, or Find Coupling Coefficient to solve for k from a known M.
2
Enter the coil inductances. Type L1 and L2, the self-inductances of the two coupled coils.
3
Enter the remaining value. Type the coupling coefficient k (Find M mode) or the mutual inductance M (Find k mode).

💡 Example Calculations

Example 1 — Equal Coils with Moderate Coupling

Find Mutual Inductance mode: L1=100µH, L2=100µH, k=0.5, dI1/dt=10 A/ms

1
M = 0.5 × √(100 × 100) = 50 µH
2
V2 = 50µH × 10 A/ms = 0.5 V
M = 50 µH, V2 = 0.5 V
Try this example →

Example 2 — Unequal Coils with Strong Coupling

Find Mutual Inductance mode: L1=50µH, L2=200µH, k=0.8, dI1/dt=5 A/ms

1
M = 0.8 × √(50 × 200) = 80 µH
2
V2 = 80µH × 5 A/ms = 0.4 V
M = 80 µH, V2 = 0.4 V
Try this example →

Example 3 — Solving for the Coupling Coefficient

Find Coupling Coefficient mode: L1=10µH, L2=40µH, M=20µH

1
k = 20 / √(10 × 40) = 1.0000
k = 1.0000 (perfect coupling)
Try this example →

❓ Frequently Asked Questions

What is mutual inductance?+
Mutual inductance M is a measure of how strongly two coils are magnetically coupled, describing the voltage induced in one coil per unit rate of change of current in the other. It is the fundamental parameter that makes transformers, wireless charging, and coupled resonant circuits work.
What is the formula for mutual inductance?+
M = k x sqrt(L1 x L2), where L1 and L2 are the self-inductances of the two coils and k is their coupling coefficient (a dimensionless number between 0 and 1 describing what fraction of the maximum possible coupling is actually achieved).
What is the coupling coefficient k?+
Coupling coefficient k describes how much of one coil's magnetic flux actually links with the other coil, ranging from k = 0 (no coupling) to k = 1 (perfect coupling, where all flux from one coil passes through the other). It depends on coil geometry, spacing, orientation, and any shared magnetic core.
How do I find the coupling coefficient from a measured mutual inductance?+
k = M / sqrt(L1 x L2). If you have measured or otherwise know the mutual inductance M along with both individual coil inductances, this rearranged formula solves directly for the coupling coefficient.
What is a typical coupling coefficient value?+
Tightly wound transformers sharing an iron or ferrite core commonly achieve k of 0.95 to 0.99. Loosely coupled coils, such as those used in wireless charging or RFID, often have k in the range of 0.1 to 0.5 or lower, depending heavily on the physical spacing and alignment between the coils.
How do I calculate the voltage induced by mutual inductance?+
The voltage induced in coil 2 by a changing current in coil 1 is V2 = M x dI1/dt, the mutual-inductance equivalent of the familiar self-inductance formula V = L x dI/dt. This calculator's Find Mutual Inductance mode includes an optional field to estimate this induced voltage.
Why can't the coupling coefficient exceed 1?+
Coupling coefficient k represents the fraction of maximum possible magnetic linkage between two coils, and by definition cannot exceed the theoretical maximum of perfect coupling (k = 1). If a calculation produces k greater than 1, it indicates measurement error or inconsistent input values, not a real physical result.
Is mutual inductance the same in both directions?+
Yes, mutual inductance is reciprocal, the same value M describes both how current changes in coil 1 induce voltage in coil 2, and how current changes in coil 2 induce voltage in coil 1. This symmetry is a fundamental property of magnetically coupled circuits.
How is mutual inductance used in transformer design?+
Transformer designers use mutual inductance (via the coupling coefficient and turns ratio) to predict voltage transformation, leakage inductance, and coupling efficiency, tightly coupled windings (high k) are essential for efficient power transfer with minimal leakage losses.
What units does this calculator use?+
Coil inductances L1 and L2 are entered in microhenries, coupling coefficient k is dimensionless (0 to 1), and mutual inductance M is reported in microhenries. The optional current rate of change dI1/dt is entered in amps per millisecond, giving induced voltage V2 in volts.
Tags: Mutual Inductance Calculator Coupling Coefficient Calculator Transformer Coupling Calculator Coupled Inductor Calculator Induced Voltage Calculator Calculator Formula Free Online

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What is mutual inductance?

Mutual inductance M is a measure of how strongly two coils are magnetically coupled, describing the voltage induced in one coil per unit rate of change of current in the other. It is the fundamental parameter that makes transformers, wireless charging, and coupled resonant circuits work.

What is the formula for mutual inductance?

M = k x sqrt(L1 x L2), where L1 and L2 are the self-inductances of the two coils and k is their coupling coefficient (a dimensionless number between 0 and 1 describing what fraction of the maximum possible coupling is actually achieved).

What is the coupling coefficient k?

Coupling coefficient k describes how much of one coil's magnetic flux actually links with the other coil, ranging from k = 0 (no coupling) to k = 1 (perfect coupling, where all flux from one coil passes through the other). It depends on coil geometry, spacing, orientation, and any shared magnetic core.

How do I find the coupling coefficient from a measured mutual inductance?

k = M / sqrt(L1 x L2). If you have measured or otherwise know the mutual inductance M along with both individual coil inductances, this rearranged formula solves directly for the coupling coefficient.

What is a typical coupling coefficient value?

Tightly wound transformers sharing an iron or ferrite core commonly achieve k of 0.95 to 0.99. Loosely coupled coils, such as those used in wireless charging or RFID, often have k in the range of 0.1 to 0.5 or lower, depending heavily on the physical spacing and alignment between the coils.

How do I calculate the voltage induced by mutual inductance?

The voltage induced in coil 2 by a changing current in coil 1 is V2 = M x dI1/dt, the mutual-inductance equivalent of the familiar self-inductance formula V = L x dI/dt. This calculator's Find Mutual Inductance mode includes an optional field to estimate this induced voltage.

Why can't the coupling coefficient exceed 1?

Coupling coefficient k represents the fraction of maximum possible magnetic linkage between two coils, and by definition cannot exceed the theoretical maximum of perfect coupling (k = 1). If a calculation produces k greater than 1, it indicates measurement error or inconsistent input values, not a real physical result.

Is mutual inductance the same in both directions?

Yes, mutual inductance is reciprocal, the same value M describes both how current changes in coil 1 induce voltage in coil 2, and how current changes in coil 2 induce voltage in coil 1. This symmetry is a fundamental property of magnetically coupled circuits.

How is mutual inductance used in transformer design?

Transformer designers use mutual inductance (via the coupling coefficient and turns ratio) to predict voltage transformation, leakage inductance, and coupling efficiency, tightly coupled windings (high k) are essential for efficient power transfer with minimal leakage losses.

What units does this calculator use?

Coil inductances L1 and L2 are entered in microhenries, coupling coefficient k is dimensionless (0 to 1), and mutual inductance M is reported in microhenries. The optional current rate of change dI1/dt is entered in amps per millisecond, giving induced voltage V2 in volts.

📌 Quick Tips

💡Coupling coefficient k ranges from 0 (no magnetic coupling at all) to 1 (perfect coupling, all of one coil's flux links the other), real air-core coils typically have k well below 1 unless tightly wound together or sharing a common core.
💡Tightly wound transformers with a shared ferrite or iron core commonly achieve k values of 0.95 to 0.99, while loosely coupled air-core coils (like RFID or wireless charging coils) often have k in the 0.1 to 0.5 range or lower depending on spacing.
💡Mutual inductance is symmetric, the same M describes how much voltage coil 1 induces in coil 2 for a given current change in coil 1, and how much coil 2 induces in coil 1 for the same current change in coil 2.
💡If solving for k gives a value greater than 1, that is physically impossible, it means the entered M, L1, or L2 values are inconsistent (measurement error or a mismatched unit somewhere), always double check inputs in that case.
💡The induced voltage formula V2 = M x dI1/dt is the direct mutual-inductance analog of the single-coil self-inductance relationship V = L x dI/dt, and is the basis for how transformers and wireless power transfer actually work.