0.001
H
1
mH
1,000
μH
1,000,000
nH
0.001
H
0.001
H
1
mH
1,000
μH
1,000,000
nH
0.001
H
The Inductance Conversion Calculator converts inductance values between henrys (H), millihenrys (mH), microhenrys (μH), and nanohenrys (nH). Inductance quantifies a conductor's tendency to oppose changes in electric current by generating a back-EMF proportional to the rate of current change: $$V = L\frac{dI}{dt}$$ where L is inductance and dI/dt is the rate of current change. One henry produces one volt of back-EMF when current changes at one ampere per second.
The metric prefixes cover the practical range: $$1\ \text{H} = 10^{3}\ \text{mH} = 10^{6}\ \mu\text{H} = 10^{9}\ \text{nH}$$
Henry-level inductances appear in power line reactors, large transformer windings, and audio crossover networks (1–50 H for low-frequency woofer filters). Millihenry inductors are used in switching power supply output filters (10–1000 mH), motor drive circuits, EMI chokes, and sensor coils. Microhenry inductances dominate RF and switching converter design: DC-DC converter inductors (1–100 μH), RFID antennas, and LC filters. Nanohenry inductances are critical in high-frequency circuits: PCB trace inductance (1–10 nH/cm), wire bond inductance in ICs (1–3 nH), chip inductors for GHz-range filtering, and parasitic inductance of capacitor leads.
The inductance of a solenoid is given by $$L = \frac{\mu_0 \mu_r N^2 A}{l}$$ where N is the number of turns, A is the cross-sectional area, l is the length, and μ is the permeability. This explains why power inductors (many turns, ferrite cores with high μ_r) achieve millihenry values while a short PCB trace (essentially one turn, air core) has only nanohenrys.
In resonant circuits, the resonant frequency depends on both inductance and capacitance: $$f_0 = \frac{1}{2\pi\sqrt{LC}}$$ Accurate inductance conversion ensures correct frequency calculations when L and C values come from different sources using different units. The RL time constant τ = L/R similarly requires inductance in henrys for results in seconds.
This calculator instantly converts any inductance value to all four common units, supporting design work from power electronics through RF engineering.
The calculator normalizes the input to henrys (the SI unit), then converts to all target units:
Step 1 — Convert to Henrys:
$$L_{\text{H}} = L_{\text{input}} \times 10^{n}$$
where n is the prefix exponent: H (n = 0), mH (n = −3), μH (n = −6), nH (n = −9).
Step 2 — Convert from Henrys to all units:
$$L_{\text{mH}} = L_{\text{H}} \times 10^{3}, \quad L_{\mu\text{H}} = L_{\text{H}} \times 10^{6}$$
$$L_{\text{nH}} = L_{\text{H}} \times 10^{9}$$
All conversions are exact powers of 10 with no rounding error.
All outputs represent the same physical inductance at different scales. Use henrys for large power-frequency inductors, transformer analysis, and audio crossover design. Use millihenrys for switching power supply filters, motor drive chokes, and EMI suppression. Use microhenrys for DC-DC converter inductors, RF matching networks, and LC oscillator design. Use nanohenrys for high-frequency PCB design, IC package modeling, and parasitic analysis above 100 MHz. When computing resonant frequencies or time constants, always convert to henrys first: f₀ = 1/(2π√(LC)) with L in henrys and C in farads gives frequency in hertz.
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A 47 μH inductor — common in buck converter designs — equals 0.047 mH or 47,000 nH. At a switching frequency of 500 kHz with 12 V input, the peak-to-peak ripple current is ΔI = V × D(1−D)/(fL) which depends critically on the correct L value in henrys.
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A 3.3 nH chip inductor used in a 2.4 GHz Bluetooth matching network equals 0.0033 μH. At 2.4 GHz, its impedance is Z = 2πfL = 2π × 2.4 × 10⁹ × 3.3 × 10⁻⁹ ≈ 49.8 Ω — close to the 50 Ω standard impedance.
Inductance is a conductor's property that opposes changes in current by storing energy in a magnetic field. When current increases, the expanding magnetic field induces a voltage (back-EMF) that opposes the increase. When current decreases, the collapsing field induces a voltage that sustains the current. The energy stored is E = ½LI². Inductance depends on the conductor geometry and surrounding magnetic material — more turns, larger area, and higher permeability all increase inductance.
One henry means one volt of back-EMF when current changes at one ampere per second. Achieving this in a single-layer air-core coil would require enormous dimensions. Most practical inductors are in the μH to mH range because typical circuits use moderate currents changing at kHz–MHz rates. Henry-level inductances require many turns of wire wound on high-permeability cores (iron or ferrite), which is why they are physically large and heavy — a 10 H audio choke might weigh several kilograms.
Every conductor has inductance — roughly 1 nH per mm of wire or PCB trace. At low frequencies this is negligible, but at GHz frequencies, even 1 nH has significant impedance: Z = 2πfL = 6.28 × 10⁹ × 10⁻⁹ = 6.28 Ω at 1 GHz. This parasitic inductance causes capacitor leads to become inductive above their self-resonant frequency, creates ground bounce in IC packages, and limits the effectiveness of decoupling. Minimizing trace lengths and using ground planes are key countermeasures.
Mutual inductance M quantifies the magnetic coupling between two inductors. When current in inductor 1 changes, it induces a voltage in inductor 2: V₂ = M × dI₁/dt. The coupling coefficient k = M/√(L₁L₂) ranges from 0 (no coupling) to 1 (perfect coupling). Transformers rely on high mutual inductance (k > 0.95). In contrast, circuit designers minimize unwanted mutual inductance between adjacent inductors by using shielded packages or orthogonal orientation.
The choice depends on operating frequency and current. Millihenry inductors suit low-frequency applications (50/60 Hz power filtering, audio circuits, low-frequency switching converters below 100 kHz). Microhenry inductors suit higher frequencies (100 kHz–10 MHz switching converters, RF matching, EMI filters). The relationship is inverse: higher frequency needs less inductance for the same impedance (Z = 2πfL). Also, mH inductors typically handle higher energy storage (E = ½LI²) but are physically larger.
Every real inductor has parasitic capacitance between its turns, forming an LC circuit. The self-resonant frequency (SRF) is f_SRF = 1/(2π√(LC_parasitic)), above which the inductor behaves as a capacitor. A 47 μH inductor might have SRF of 5 MHz, while a 3.3 nH chip inductor might have SRF above 10 GHz. Always select inductors with SRF well above the operating frequency — typically 10× higher. Datasheets specify SRF; this calculator helps convert the inductance value to verify LC calculations.
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